A bicycle odometer (which measures distance traveleslfo2gtg:u0jk m8b /(hjg1+ww h3b g6-nz/sxd) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you usl830hs gt fo2z+ 6w-ks bj(gwjbnh/mg1u /gx:e it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Doesnm-tyj,u)l7kwr6 - c;idlm3s a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the pojy muln;ls7t-rwc- 3) i6md,kint have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velocity qek ;*adu gx z;;m*xb($\omega$ Explain.

Can a small force ever exert a greater torq*.pp3,:vs xs( lfhv8g qc08fanmcq h 9ue 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 hbf2ph74( sdf with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer tdfhh fsb 47(2phis.

A 21-speed bicycle has seven sprockets at the rear wheel and t3 g13ujp7-+0 k/ecxm q bjfgarhree at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sbc mxq-/k j+3ja 7f0gug3p r1eprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slenduz,2gnj6 s 3v+ja4pkler lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distributio,4njzvs3+2p 6kj au gln of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, nar bjaf/,-,xj xy0a 5pdxrow beam?

If the net force on a system is zero, is the net torque also zero? I 9xztjy:k) l)9oi t9yaf the net torque on a syst:aolxy 9 y)kt99jz)i tem is zero, is the net force zero?

Two inclines have thea4;o6cyx en4ej 4)6)ywnn neg same height 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 greater? Explain)oejnync e w g6)en4n ;64yx4a.

Two solid spheres simultaneously start rolling (f7 ca7v; kpow0 bt *mrub:y)o;wrom rest) down an incline. One sphere ;yw7o )ma : *7wpvouktc 0bb;rhas 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 the bottom?

A sphere and a cylinder have the same radius and the same mass. They sju6555a3c dkwle 2rk6ev3 ildtart 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 enekj5353kv waed6 cle6ld52r i urgy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most mn*trsa/jciaual -8 :2oving or rotating objects eventually slow down and2/a js*aa -:cir8ulnt stop. Explain.

If there were a great migration of people toward the Earth’s equator, how l m4fw0ja n):dwould this d0a)lnw 4 m:jfaffect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any inijy5x8j3 scp 6rtial rotation wh86c3jx p5jysr en she leaves the board?

The moment of inertia of a rotating solid disk about an axis thgw:svi9 w.fewq+7) tlrough its center of masv7 fe)+wtw9l:sgwq i .s 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 2-kg mass i2p7eh,enj3;h0ubhv z*gx vo: ,v,r gan each outstretched hand. If you suddenly drop the masses, will your angular velocity in;ahn:z,2uoe* 3gg,rhv0,vpvb h ex7j crease, decrease, or stay the same? Explain.

Two spheres look identicao q2j- b;0lmw.izhdl,jb 7 4 t1mjk:djl and have the same mass. However, one is hollow and the othej t b4m7., ;21jl diwod-mh:qlkjzbj0r is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axm ,y./ 8hsekrg0nr9q0w bi* hqle points west. In 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 r yg erq0i89n,hqs* .hb/ kmw0of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotktlq;j03: )o,yz er 2gpqsm)pating turntable. What happe2j; zlom,epstyk)30 p rq qg:)ns if you walk toward the center?

A shortstop may leap into the air to ca /fxg1;f0 )hxjz +ksfotch 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 and legs rotate in thexsgfjh0z+k);1 / ffxo opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momex mfo(q8.b/:8 xpk 2pbtet;pfm9p-f. thr sq;ntum, discuss why a helicopter must have more than one rotor bm rf/pppex mtx-q9fh;b .8p8.s(t;kf : o2 qt(or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in ragn0eza)4t cy-k v uu: er)(7hzdians: (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. Ca27m(qkaem mv+z 1kn9 alculate, using the information inside the Front Cover, the angular diameakk(mn+m qm 7a21v 9zeters (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 bed+83req* ryo8tn5xk dps t 4n-am diverges at nnxk5p-y38+e 84rod st qrt*dan angle $\theta$ (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 motort1/qi rv1pbq8vwcr ,s7 u5/oia1o 9dm is turned off dut/ a1o 9 7i85i dwqv1mqso1 rv/pbcr,uring operation, the blades 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 level floor 3.5 m to another child. If the b+g rmc;rh z2*gall makes 15.0 revolurcr h* g;2+zmgtions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels pa)l ;jrek5lzx * /,qt8.0 km. How many revolutions do the wheels me; x)p/k5rql*zal, t jake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angu 3 (me )xue)z,ihrtw ;q3(ijejlar velocity i3ijmrx,e)) et(wz3e(q ;ihju n $rad/s$ $\omega$ =    $rad/sec$
(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-round makes one complete revolution in 4.eq3dnxvi+) ga x ((:in0 s (Fig. 8–38). (a) What is the linear ((i v aqxi)3x:+ denngspeed of a 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 orby c/9 s ru(tsyt7lh57bit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pn0pv rtnz* cig.:pq-i+ ue +)joint
(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 6y,9ntuvk; mk centrifuge rotate if a particle 7.0 cm from the axis of rotatio,mkk6 v9; tunyn is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centebmx *g5bm97 bdr from 130 rpm to 280 rpm in 4.0 s. Dete9m* m bx7db5bgrmine
(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 radiuse+dp z0m)v3lh $R_1$ 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 pu0gem fm:s e 4ay,7ik5zt themselves 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 revolution5f a kis7m:y0ee,m z4g every minute during a 12-min time interval. The spacecraft 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 uniformly from rest to 15,000 rpm in 220 s. Throzo 8 8 ynxsx*+f 1rphu9 t(9cm6i;bwe i.3ylscugh how many revoluthi .+8 8iocufmns e9rlwb19y; y pczs3xx*t6( ions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm t f /nlh5 4v.d/mskrxs-o 1200 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 fdy2n08 b.emdj)bojy ja+r)b 6w2nez1or the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching itsz n.2+jwjdy6de 20 b o1r yj)ebmab8)n 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 240 rpm to 360 rpm in 6.5thu85hww 3 ep/ s. p8hwt h5w u/3eHow far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turk4s97f uem y+u8 ug-hgizu r-7ns 1500 revolutizk g7h8uu u r- +u-sig4fy7me9ons before 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 revolutions as the car reduce 47gjv;, jxhsmvk7)mjs its speed uniformly from 95km/h k)4jj7 smg,jxhv;7v m 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 revolutions as the car reduces its speed unifo m01p;wuyv ,by6akc, armly from 95km/h to 45km/h They wc0,6p ,;bkuvmay1a 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 biknm2zhk2). j; 6divuj:d:4 lqage ia(de puts all her weight on each pedal when climbing a hill. The pedals rotate in a emdhquj4 kd2va: ( ia;.dzing6lj 2:) circle of radius 17 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 on the end of a doo uve23n d(ym6;8c arvbr 74 cm wide. What is the magnitude of theuryv86; mb(a2dvcen3 torque if the 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. as-q*f*9d,t tahrf *a8i0ymj 8–39. Assume that a fricti,-f*9ti raq *jtams8hyd* 0f aon 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 tv zec p-(3nf4qf 5;rllir7 8iche ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horiz (58pe v nqlz3ici;lff-c r74rontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylg6sl s;p-y5 lcz58puww)jg (j v 2dzq8inder head of an engine require tightening to a torque of 38lw(8p vgs;zw6- 2z pgqj55)8lusjy dc $m \cdot N$ 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 omu.k9qe fh q0u -ol(8uf inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through itq 9qume( ul -k8.of0uhs center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in ,b9 ;zvgrx /xydiameter. The rim and tire have a combined mass of 1.25 zy, /9;vbrxgxkg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in ahdcom pw7 lc uouo) 3,f 8;hum8./e2ol horizontal circle of radius 1.2 om2 8cfw.cmu3u8uho/ d7ll;op)he o,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’s wheel rote4und84xym e6lg ne/ (8gr xz3ating at constant angular speed (Fig. 8–42). The friction force between her 6 d4 gex /ue(3zxelg88n rn4ymhands and 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 objects shown in Fikv9sx(bf j g c +lqwa)n1mu6a)7ee/8wb,x-aag. 8–43 aboutx9ac,1q bvk/j 7)mgf swwb-+xu a6n(l a )8aee
(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 oxygeg+w- p;ikge* p) jw+cp -kgggp;8/x kin atoms whose 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 cylinjbb8:f)dan df nw72(bdrical satellite 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 is to reach 32 rpm i jfbfnd2b(8dw:a)bn 7 n 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a rxrsd 4ff-q u6*-fyh, uadius of 8.50 cm and a mass of 0.580 kg. Calc yff*4 -xrd fq6hsu,-uulate
(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 i5bpwq(0:, bq;a 5uqgjtoy um+ t 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 tangentially on a small hand-dr,gv w 25nfc-feiven 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 the edge. Calculate thev-fnf cew ,5g2 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,oq mkmth.zhzj, 0z; /x-y1qr 8300 rpm is shut off and is eventually brought uniformly to rest byk z,hzhqrq- m. 1o0zyj/8;x mt a frictional torque of 1.2 $m \cdot N$ 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 i dtq3(uf5 pg.sq6mj s6,b9 zhaccelerates a 3.6-kg ball at 7 $m/s^2$ 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*+so6jhtd9xxldo n /zx0h k:6, which rotates axh06o9*k dszjlo+:hn xd6x / tbout the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly 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 shown in Fig. 8–3:q)wi* djwp 0h )fdnv46w0 d3:dj)*hn fpvwiq) .
(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 consists of two masses,r1b77d;zj4eyr0dpxu6h 7cvvu,w: ym $m_1$ 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 from rest within four fullq18bz3vmx 1q v turns (revolutions) and releases it at a speed of 28 1q b38xqmvvz1 $m/s$ 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 has a moment of inertiayg4s;pbxqi q)*a) 6h i glm01v 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 develops plkk84gh.no9a 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 rolls withat:gnxi)a m1 *1j03whcf uuq *out slipping down a lane ata ja xg*h*iqnw) f1u1u:c03mt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sut ga5+yr 5x 7u*uwczc(;kkli)g) ly6gn as the sum of two termsacx (5k rl76gktgl)+ wuy*ugi)cz;5y ,
(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 ma *7,vsds m:i /oar6cyrss of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.006 vy*7sicd:, ao/rrsm s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls6 z dg;9(zwfuv without slipping(9w6d zvf z;gu 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 iz7+lfv(( - ter hq+oyrs balanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the grounr zotf+-he+yvq7((r l d? [Hint: Use conservation of energy.]    $m/s$

  What is the angular mf8 cjc5dga2/y/m6/qcdm oq th7k1* iromentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an anguld6cc1ojm y g7fr/hqt/ iqdc/8mk5* 2aar speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular dff7.ci +pw-ywego8r:how3e7u k .c6momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rp ig7-8yw6w .3 o+okffpe :u.rd7ccwehm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is cxoj,,s p;lug0yc (: lrotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rot,g cs,xc;jpl oy( u0l:ation 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. 8–2(q* vq-mm.ryio6-b nq9) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuymq -6q* -moriq.n(v bck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can slbg./ mbl8z+n 17ze6lntz2lincrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate nzse8+b.mtnlzgz/b l 16ll 2 7of 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 y9nel0b ff0 r7around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter ln0 r bef0y79fthen throws a 3.1-kg chunk of clay, approximately 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 skater spinning at 3.m7ha j;vvmc rs1 )n-+n5 $rev/s$ 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 of the Eart9wb y.8 qri9tuh
(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 of inertia I is dropped ont)o5 o ;jz1viyho an identical dis)oj1 ;zioyv5hk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at lj) 0 lro+l/py1xv *ab8a afi03qa:pgr6 v-ts2.4 $rev/s$ 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 a8 5+ n8su whh,y,isigj ;enq7i6q 4bmat the center of a rotating merry-go-round platform of radius 3.0 m iq5n4 i ean,ms w7+b8gu8yh6i;hj,sqand 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 freely o7 o0ss2px.v rwith an angular velocity of 0.o0rxpso7v s2.8 $rad/s$ 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 whbg sd8gyp;v3; ite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of itsvgdy; p8s3 b;g existing radius. Assuming the lost mass carries away no 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 excessuxplbht+q g qv9),2jjt4:ci 9 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 1lr mm/i13wytq7fv;cbynk.)$ 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 a platform, initialhhl44bj)fho . ly at rest, that can rotate freely without friction. Thhb. 4l)jo4fhhe 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 at the edge of a 6.5-m diameter merry- vw us1:-gkuiye1ay:( go-round turntable that is mounted on frictionless(iv:-sk 1 ye:ugwu1ay 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 ropl3ma-:)/mamlq qs +n te rolls on the ground with the end of the rope lying on the top edge of t/nt m a qsall:-+3qm)mhe 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 move?

  The Moon orbits the Earth such that the same side always faces the E7ni c(; +0m wj(efib,xprsr6b; tb ;tnarth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital ;,7(t6nmi ;jtb+xpr; 0(e rc bsbfinwangular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from re g2eqn1cg )p8q6q b uqw;,0ahgst at a rate 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 shaukghr1:;z4 ynq3y, g kpe of a uniform cylinder of radius 0.20 m acquires a rotational rate of from r3 znhy;g :yq1kk4u,rgest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.0509adg7:; psiqfks-std e+r 7 x1 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrik1res7tq f9pd+x gsis:; 7-adcal 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 angular speed of the rear w ga6 j0hw3rli8heel ($\omega_R$) 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 Sun, but with mass 8./aytbgr o;4ebn3*fuzv, )e)s0 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 th,onb)at)4eu3v /y f;gs* erzb ree-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 lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutio(hob5aami 1m(dux l )/n automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1405/am mo )ih1xd(b(lau 0 kg, uses a uniform cylindrical 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 illustra.s)b6dv x2ti qtes an $H_2O$ 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 surface5 /3thwcdxngcm,h03 zsu30g 6l wvq,s at speed v=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 le )ovszl -fol2zp4 tw75ngth L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine5fv7 z-w24)tzsplol o (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 standing vz ) cg2tej omf7.+a szw3ngg20ertically 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 heig)n7 o.2csfg m ejwz0agzg+t32 ht h, where h

  A bicyclist traveling withz8a -dk3 k)al+jqt e1k 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 the norj3 de z-18ktkaal kq)+mal 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 1.5igx6cf33gpx / m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rp ggf3x6/cxi 3ate of 120 rpm after 5.0 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 wr4t 2 ,nrvlq24 ke9jzsolid cylinder and her arms as thin rods, making q494ln2v2,j retrzw kreasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates,gs(p3:ebo * af of ma (sgp* ab:o3efss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ra54pok)pwvs a abl9n36dius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highestb osapl9nk3 45a6 w)vp point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, buqv: q9 hv3zcq71oas 6r6px)oft do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car r wuj2b7l vh.vd y80e1ceduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was thuv18y 0.dlej 7wvhcb 2e angular acceleration of each tire? $\approx$    $rad/s^2$(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