A bicycle odometer (which measures distance traveledi-5- h )1yuxf 3llueou) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use ityhflu- i l3eox uu-15) on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the :: 2*wfolyqdw1ooy) e1vrn9trim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitudeywdrwlvyno:2 q)1t*o9e f o1: of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the kn1bl2zv0jkrvaaj m+ hxzk61/2 ,j*iangular velocity $\omega$ Explain.

Can a small force ever exert a greater torquk 24nz /+0mbojo5ff wde than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your head thanrvibslvh( b-bx7 d,8a 6uk /*y when your arms are stretched out in front of you? A diagram may help you to answer thish b(-rkvi8 xb ay/bud*7vsl, 6.

A 21-speed bicycle has seven sprockets at the repuvef+ o.:zlzmf;7 k4tc7 l6f62xncxar wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a lap27:nctk e4fol;ffxv7 .ulm6z6xc +z rge rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being abley:p tm e5arg7o6wr7+ w to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mag7 orwawe7m+pt r5: 6yss is advantageous.

Why do tightrope walkers (Fig. 8–35) ae y: .:gv:fgpcarry a long, narrow beam?

If the net force on a system is zero,qrss 5nvrkh -4gbp4 ): is the net torque also zero? If the net torque n )pvrss gkb4-qr4: 5hon a system is zero, is the net force zero?

Two inclines have the same wi . g-04tdosiheight but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be gr-d iog i4ts.0weater? Explain.

Two solid spheres simultaneously start rollingc1 o*g02y5rptpe1 kaz (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at theppkrce o 015*a1g2tzy bottom?

A sphere and a cylinder have the same radius and the same mass. They pzlr4 v/ 10wx qt7;l --jjgyrv4rzzk79 l (sugstart from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Wh/1qt97(j ;g4jg7pvzr-vl4zx u rzy s0rlwlk- ich has the greater rotational KE?

We claim that momentum and angular momentum are co+ ihc3ei,s;) gdow1uswlh.z ,nserved. Yet most moving or rotating objects eventually slow down and stop. Explaihszw3i.l +w)uoe;d, is gc1h,n.

If there were a great migration of people toward the Earth’s equator, hoqn7bfzh)e2svjf4i*gg1 ef , - w would this affe4vfe zn ,h-gb7qi)fs1g2f *ject the length of the day?

Can the diver of Fig. 8–29 do a somersejvw a g0 /rot)h9v5g1;5 na ike5;wsoault without having any initial rotation when she leaves o;1h iwewvrna9oves5t jg;/0 5g)ka5 the board?

The moment of inertia of a rotating solin/; *jsngh;,nkpehzha 8:p r .d disk about an axis through its center op,kz* ;nh:enh /.r j;npahs8 gf mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a bvjc//-shtu6-y, ) )elv lusu 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angula)el/ -vy cs-lbs)6 vhj/utuu,r velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is holl4hx bv7b hkdekb4k20xxzj3zi ;u ; :1iow and the other is solid. Describe an experi1 xxvb ujh4;:kx e;hk4i32z7idk bb0z ment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. I3pk. ;mnh fs/qn what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the ang/k.hm n ;qspf3ular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating zg t054o dq1opu90gvlturntable. What happensq 450o d gv1uz9o0lptg if you walk toward the center?

A shortstop may leap intmn b.y(2 sp: niyjv77mymuixxiu 504)o the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips amb s2 pj4un7yix)7i.:i(5y n0yv umx mnd legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of ay/ n2 4turklvqub:cn w:43h0angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can op:4 32 /v4: n0qcukhrwlny uatberate to keep the helicopter stable.

  Express the following angle f,u0;zdb78qnynl f b+s in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, usingw -i/2fp8u zn v)bwym(ji *k0v the information inside the Front Cover, the a 2/kbw)m zi(0j*fwnv8 pu-ivyngular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beamaix aco .2r /bgx92fe0 diverges at an cr.ixebo02fx/a2 9gaangle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the mot oyc n+dzfi9llqw8k6i; )d0j- or is turned off during operation, the bladey 8fi9jo+lwqn 0d;)l6kz-i cd s slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a n-uj:. rdhd :t 6lv38k5kidiz level floor 3.5 m to another child. If the ball makes 15.0 revol l8: 63kvij. d:dnzkirdht-5uutions, what is its diameter?    m

  A bicycle with tires 6y+7;/3gd y2lmnf+ lg: rd eezl8 cm in diameter travels 8.0 km. How many revolutions do the wheels madfeyg+z/+2g7y; m d 3lnr:el lke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate*y +xyb2rg g-n its angular velo* -xy+gr2gb yncity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-3 6b4p9wzowxj round makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of awo 4x693 pbwzj child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbic(xppq+h/ in/ i6s.*qnfr8pj t around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of ad.yxp4z 8c*5rlk z.0(ktbukd point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle2,02ar veixm:q/guk2xttv(d 7.0 cm from the axis of rotation is to experience an ae x: k2at,rt gxqim(du20vv2 /cceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from z,g-tp*,a4 lg(7c no lpl8alu130 rpm to 280 rpm in 4.0 s. Del apc*,p7 olzg-8a4gnl, u(t ltermine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu2 xzrd+f 83roas $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put t9-r-wmdeeq;)su7 ,g+3zbue 0el wrsf hemselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft,r3+ - beuz qewdug9w 0sfl7e-res;)m can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates unv. rzx x7* r0qmgei0)biformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this timex0rmz0* r) exqi b7.vg?    $rev$

  An automobile engine slows down from 4500 rpm to 1+hknhn ak,+*n200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested ( j;91(mzh)uz)oinvk.2lo j/n/trg iuah u:afor the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions beforev lrk1)ij/juz(. :uh2m)n(nt/hao i g ;o9uza reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 2+h2hb 1s /xkzx40 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel zbs+k x2h1/xhhave traveled in this time?    m

  A cooling fan is turned off when it is runn.detgj .0-vki:nyg 0-si ( ndsing at 850rev/min It turns 1500 revolutions iev -s:y0nidd ggts(j 0.-n.kbefore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolution sy7ut v88(gv ;vo6bf c)voxc,s as the car reduces its speed uniformly from 9,vbfocx87 gvv6 8) yu(stoc; v5km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutionsxbqrh8ei 762 v as the car reduces its speed uniformly from 95km/h tbh vieq2r768x o 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puth e6r(7iqm; rds all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17dr i( 6herqm7; cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N.tag f3p5;xa n on the end of a door 74 cm wide. What is the magnitude of the torque if thxa .g35;n fatpe force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assuy 90o ul 6fk(;h1mibakme that a frl ifmyo691u kh;(k a0biction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to th+5h yhmj +5ympv-pqv7 e ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque 5 +yqmv+j57 phm-pvyhon this system.

  The bolts on the cylinder hea :2td++g,ausyf au ka 8i)eg:od of an engine require tightening to a torque of 38a 8ggak+:s odu: f2eyu+, t)ai $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when tj * d89+n)lxe*.yb(t/snahhtf*) 9m cryf yr hhe axis of rotation is through its ts8.9nfd+ rxbhhemy l 9)cnyty*/r h)(faj**center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diametew5fdgy 5 ;lwkh.7lq ,vr. The rim and tire have afl hwqv5.glwk7y; 5 d, combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on titdwh,p tk d/-: i9k) x).fmjahe end of a thin, light rod is rotated in a horizontal )i, i/kd mah.:fwd-txj )t9pk circle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’m( rvs7o2 nma :bvuv/r5al 04xs wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands anda nab05m:ls4x2vmrv(u/ v 7r o the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point z p24p8: ptuqc0q xlv4objects shown in Fig. 8–43 40 uq qp:4zlpv2tx8cpabout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms wh:5w1gaxn)mpaof ik7 2 ose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical sateg:j 7x bsz3t lgii*:*fuuggu9/ds/w ;llite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite i9:siul fggt/gs d:; 7jbuuzix/gw* * 3s to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uni3 qenquh1 schv q7t(8:form cylinder with a radius of 8.50 cm and a mass of 0.580 kgv( qqnhsqe71hu38t: c. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating itmvap fp(3u::hzo-6w;rin ) bn from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentia n0.fmbe pe8mub0k+f nh3n w5l9n.wt4lly on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on thkmp3ee +80b0h n5nm4w.9ufnwt flb .ne edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off aek k-ip 8- wmp2,+3hm.u czkfynd is eventually brought uniformly to rest by a frictional torque of 1.2hy 8fpc-kw ke+mz3.k 2-,p uim $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at 7 8y7-81j*zpyc u hq s )l4q c;.qcqeskf$m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which,d2 -m37itp n/ct0uj w a8vwgh rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifoimc /w,vhdju0w a-tt 2 3gpn78rmly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as showuqq h;x a6:bd(n in Fig. 8–46d(qbq u6;: xah.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine bh enze8 ejnhp5u8) *mofxzl16 f+/m,consists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer fro8soo oi6a0fd q6 y*k:t7sb a5zm rest within four full turns (revolutions) and releases it atoktsd*oi6 f 86sz ab7 05qoa:y a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor hy/.o3dz59 (sal hrcyg as a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine devel6pt)su(xarm mq0o 8y8ops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm.0( s,qj n7 yhyx0d hoo2tso)t rolls without slipping down a lane ath7o 0tj o,nyth s)2q .xsy(0do 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic e k7lbtcs i5m.*nergy of the Earth with respect to the Sun as the sum of two terk7s it*5bl c.mms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 mqkqsl;0frb,-4pez 5 b. How much net work is requireef;s z5p,q0 kbq4 br-ld to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolf 3ozptxtn g-b 8h:/p(ls without s/h x:pp- otf(bt8ng3zlipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and s-ef1;mc aamr1t ex-x. .ygb9 its lower end does not slip. What will be the speed of the upper end of the pole just t9x b.a1-1y ax;grmeems.-f cbefore it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum p1ju +fp 0zbrzw,ai6 2of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular spee,1z6 uzppi0jw r bf2+ad of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical /sbvg xv54xrxgba -4) grinding wheel of radius 18 cm when rotating at 1500 rpm? vbsgxg5xxr/4)a-b 4v    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at hc b7a qz tkc36+cnb:)tis side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a h bz aq7)cbctt6n3:kc+orizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment yg7vu o8cd3 el9,le8-gzk yo)of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck positigz-yel9c8 8d 3vyuk eoog7l) ,on, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can ir1ki.- )ibdcxqng )v;bx4ay6 ncrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a finaln1;6 -gxxa ) .kv dy)iqr4bibc rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a +)acnz;oab 52hb* 7mdqu,lx cfrequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, ap2ad+lu;cxamb q )hzcb *75o, nproximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skatpkmihv.y-aoyxg .3 5-mi: k3ler spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum :ul z e,i-fa7rof the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of6 l tnp (0de8cr:k;zn4a;a xyn inertia I is dropped onto an identical disk rotating at angular6dcn8 ; rtk;pleaan4x(y:n0z speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.9sa.u148r, 7tjydsv gurv5zivhb60 p 4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round pla e2gmo.7 qh2v/ 6woynhah(8 /bzub6g ltform of2y/ h.8hm/lwq ozg ob uve(bh726gan6 radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating free6 j6dsqc1r1 shk p2pa-ly with an angular velocity of 0.6 6ra2ks1pchps-qj d 18 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half itsgi(*7qk txld+80htwk mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away ixg q*8(wtkh+7t0 ldkno angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excesf )/vhir3vyg n .6qyu7 :m9nmos of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass eu n6 ++2v fv.eyr:bmk$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on an x:x didcpbe,3t: u9j9(i+xs m7go1 y platform, initially at rest, that can rotate freely without frictionyit dup:xg9,:7o( ji9b3exsx 1 mcn +d. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at9*sxy6ocjkx cax2 48j the edge of a 6.5-m diameter merry-go-round turntable th96 *x4 jk2acy8oc xsxjat is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rozfwn 7 ,tfs1 vhuz)0g)lls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass mo0 )nff st1,)ugz 7wzvhve?

  The Moon orbits the Earth such tv6 8)znw7kj- wvlt 8fkhat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case,)zk-j n l7v8w6f8vtkw treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ramhrn+ 0.)se2 yw3lkv tte of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cyliwtg e1/dnu)ldv bjlvwq c0t;(9 o0p //nder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular accelo d wv(dw0)pjl1;t9c0q/l ugebn v//teration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical6h 0:x*cd2;x+ az;hqlgeql u h disks, each of mass 0.050 kg and diameter 0.075 m, jog z;lqaxlcx* u6;+0dh:h heq2ined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the an5m v70gop0qbkbbjr 2,gular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our 6vs yp12g5o8q ,apeaz Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the loste,8oagqys16pv 5z2p a mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollu9 4kcszwa28jlv+(o/vp ga :r ntion automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindriwpjk+aov:8 4 rg2/9azv(sln c cal flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates vjzbg (h/9 b 3uzty67san $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed d6 t*/,tgh fh2 ed0l*nhw-e u7 hesb.wv=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length 60)hjy3l s0ir kn*ts66yhjbu L can pivot freely (i.e., we ignore friction) about a hinge attj63ss*0lh)rk hi n6 6tu0yby jached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standi cshjf)u3t gl,,q ju5yy3.l(/fr xsc,zopu+:ng vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has herz5qtyf,s(y l:. ,fp3g )hclc 3 /u+ous,uxjjight h, where h

  A bicyclist traveling wv/fhon)mlv p;m(r6upbg- 2a/ ith speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are th pfbn2u) /m(6/ ;v- vmalrhgpoe normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m alao 4 rmah.(9pnd begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.ah r.a( poml940 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylizy1r95qa8u 6 c+hmfp jnder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with ar uzh5rqm a1yf8+j6c9p ms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindvfbfes:a4g+ rm d(,b9 0mtyh*rical plates, of mass rh:9a t4seymg,mv*dfbf0b+ ($M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fi7(* lp u;i,()yy rtvzkos/9lehl h;cxg. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving thr(;e*,l;/iyylv7 ohthlk z p( u)sx9ce track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but doohk*bxp+f 3l0 85wezy not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car 6z+f+ci5 as jxreduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tixa z+56+c fjsire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s