A bicycle odometer (which me(/ rk w9vkcx,zasures distance traveled) is attached near the wheel hub and is designed for 27-inch wheel ,kx9 kcvz(w/rs. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular e:bgnz7)kx1a: a;4 hzgmol x 3velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential a; ha1k: lxg oa gx4:em73bnzz)cceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single voqa( 0+-fh(grprl f ;oalue of the angular velocity $\omega$ Explain.

Can a small force ever exert a gre rhx w-fx2kc7)ater torque 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-u new/;nnh ;un,p with your hands behind your head than when your arms are stretched out in front of you? A d;ehnnun; ,/ wniagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and p vx;utfbire 2;) ,nx/three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front/bvi;)nxue t 2f xp,;r sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with ft8n;d1*m/gcek ;pnen lesh and muscle concentrated high, close to the b;g/kpt*n e emc18n ;ndody (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carrx,s7 4smip82 glss*dpy a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net jp 2 wn2usj96n:q7vyk torque on a system is zero, is the net forc7q9 n2ns pju:26kj wyve zero?

Two inclines have the sameldmnp;dr(x.t; pizqte, +2+ v height but make different angles with the horizontal. The s(xqp +zdn2+.dl;trevi ; ,pmt ame steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclinqo 3t+0cb e.lqe. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incliel+oqqt.0bc3 ne 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 radilikpw8 8v.-n q(fxwt0us and the same mass. They start 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 -.w(pxn8 iwql8tk0 vfbottom? Which has the greater rotational KE?

We claim that momentum and angular momentum a/7v- kobv kdl +1ygi5gre conserved. Yet most moving or rotating objects eventually slow down and v/kglk 15vg+i 7 bdyo-stop. Explain.

If there were a great migration of people toward the Earth’s equator, how s81r7e1f gou)v3zjn ip; vp;mwould this affect the pf1 or ens)u31 v7vz;mgij8p; length of the day?

Can the diver of Fig. 8–29 do a somerscvzt5sg - ifdgz-,8 (fault without having any initial rotation when shet-c8d 5z( vgifsgz,-f leaves the board?

The moment of inertia of a rotating solid disk about an axis through its centers) :b85aazj n(yp/alki/ g 4rv of mass il )//ia ay r48v (bnzgk5a:pjss $\frac{1}{2}WR^2$ (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 hol+* gsom dbk )60mvur g5o;uyi,ding a 2-kg mass in each outstretched hand. If you suddenly drop yuob+m)0 uk mrs; *ig ,d5o6gvthe masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hoon-5jrxy 2uh *l6;,raxbbof4llow and the other is solid. Describe an experiment to determine whichhx46o -b fo,n*;xra yrl5b2uj is which.

The angular velocity of a wheel rotating on a host1e-tf - e/ex9 k2l hdk(udr+rizontal axle points west. In what direction is the linear velolt-( fdk/1de9ke r+sx2-htu ecity 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 angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntably/wil jmuz;dk6s, e+8jp7fj 6e. What happens if you s7;lpj+jy f68eum6iz w dj/,kwalk toward the center?

A shortstop may leap into the air to catch a balljs47jjmsybl +wfj02 u3,2. knl 2 ndto and throw it quickly. As he throws the ball, the upper part ouontl,m+nfjjl34s 0s2.dk2 j 2wjb7yf his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, di*m-wfoi8n.ne gf+6kpt0 *f yq mr-;evscuss why a helicopter must have more than one rotor (or propeller). Discuss oq+;fnm-yt80invm goe .f wk**fpr6e -ne or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles injcsk.m32e 4u9 )v fxgb 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. Cuztwfx,0e 1i*alculate, using the information inside the Front Cover, te,u 0t1wizxf*he angular 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 beam ditq) c1tcprx1:verges at an anglexp1tc q :crt1) $\theta$ (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 motor issts80 iy red)q.q2 +ss turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down? 8 sesqdir).y 0s2 +qts    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makes vj;c9pk,a wnoh(2 hnew0;lh*w(vl9hoh;p ;ak,hc 2 n*ejwn0 15.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travt mrzw2b )-qy9y3 otykxu/7;d els 8.0 km. How many revolutions do the w2-9y owu zt )x;t/kyyqmr3d7bheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculateb0 / mkk9nijs+dg(wj0 its angular+idw9k(s0 j/mkg0b j n velocity 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-round makes one complete revolution //:krn mnb7)k 9xkjsy:to2j c in 4.0 s (Fig. 8–38). (a) What is thk o/ s 7:cyk/nxtj)2rn j9m:bke linear speed 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 velocit)f kzkw2fynw xrq, jq 8p-f+,2; zplb0y of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poin5-4t1r0 2 prbytyvtpx3+)zs sl /jnt ct
(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 centriohc)tn j hbdym03 6i10fuge rotate if a particle 7.0 cm from the axis of rotation is to e36jhcmh01 nodt0i y)bxperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center aegthic3dazg p4c *254 xvn*,1 ( serqfrom 130 rpm to 280 rpm in 4.0 s. nza3hr*pex44g c5ti1s e*vc gq(,da2 Determine
(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 radiuaf (g/qa3 sw/ds $R_1$ 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 Apollq v ,dsy(z 2fcifehd--hm))8qo spacecraft put themselves into a slow rota,dyhcz fv)d- fe )-msiqh2q8(tion 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 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 gey. 57mfdszkp +a24k* e3qt efrom rest to 15,000 rpm in 220 s. Through how manyfq 5g 2kepde.et*7 sky +4mz3a revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Ca8lon*)j .ux.iwxko ; re yoo:2lculate
(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 for the stresses of flying highspeed jets in a- 9) 5xlk;pt7hx detcb whirling “human centr9xhc tpb5;xde-kl t 7)ifuge,” which takes 1.0 min to turn through 20 complete revolutions before 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 240 rpm to 360 rpm in 6.5z3 6eeatby6tve3dy* ;izm (9h s. How far will a point on the edge of the wheel have traveleh d6 zi9zvy(mate63 yetb3 e;*d in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It tnmx-zc* 1/mnnw x6le1 urns 1500 revolutions before it comes to anm11*mz6 -n/wel cxxn 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 revolu qqv :2fhqm0cju/t(q.tions as the car reduces its speed uniformly from 95km/h to 45k2t qj:/cquvh(0qf.q mm/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 redjdw.n hdi 18hh37)d .e t6h:kn1ocycduces its speed uniformly from w oc3h.hjdd7hehct1k d1in:n.dy68) 95km/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

  A 55-kg person riding a bike putdi bgq,voc/z.au.e- eo(++ iis all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 c/e au-vb dozo+i( c. g+ei,iq.m.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force pth*datp/76x::e r-uujmv)ar ):dx f of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force ir vtmp7t: aa/h*dr))x:p -fu:e uj6xds 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 t iqm/sr7z3mec eg8(s*(ou :uche axle of the wheel shown in Fig. 8–39. Assume th 8*/7 qusmurzie c(gm(c3o:se at a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attach +(y .pbopw7gzed to the 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 a(ozb 7wygp+.pnd direction of the net torque on this system.

  The bolts on the cylinder head of an engine require ti.aca izjy.wn rc*1p -(8ox7cqghtening to a torque of 38qr1(-8aa7j .cz.o w* i yccpnx $m \cdot N$ 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 uec- l43- hkmcwhen the axis of rotation is through its center. cu4kmh- 3ec- l   $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel rt8 gwyj52 ym-66.7 cm in diameter. The rim and tire have rg2mywyt8 5j- a 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 the end of a thin, light 3j gptqs3y.2toc4 l-in f0ev04jwg g;rod is rotated in a horizontal circle of radius 1ipfvgo0jq0 c.ey3ggl4ts;32j-wn4 t.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 ,gl/i3fj4e.mav0c mu potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her handscm4f0 a v jlig,e3u./m 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 s5v a:peb 4e)zchown in Fig. 8–43 aboutpc a vee5b4:)z
(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 whose total*gs z+m2y7vo ih39gvr 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, uniformlq 9 i0 yab xv01du5o1mp-8imk cylindrical 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 in 5.0 m v0b85pu ay1xo d1iqi0km l9-min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unif j2s2xxu -.5vjwl i7diorm cylinder with a radius of 8.50 cm and a mass of 0.580 2i 5 s-dx.uji7v2xjwlkg. 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 swingb xga sl*6po9g. m/s)is a bat, accelerating it 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 h7/eb*uqa v x27 a.tvqon 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 massbua7*v aqv2.h7q / etx of 25 kg) sit opposite each other on the 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 and is n/i ubqketln9(5 - l8t;)25ltd bkeit eventually brought -)(kqtlb dlui n9 8 ;ei25tt5ntelbk/uniformly to rest by 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 accelerates a 3.6-kg ball at -ykzd ajit+0bd )b1y9 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-kbozg *cwlpe+r w;/sj 8 rum 7xgke10.,g ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of w,u+jp wszgx b1le.87k eogrcr*;m/0the 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.: pd jh;hrnfp8djm5t/ 0.f1pu 8–46.0: hjuhfdjp;p1tm5dr.n8 pf /
(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 mass0 cwf5r:xn.b eb-v.iv es, $m_1$ 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 thgttd;3h*os* :p q8dfh-anm :ie hammer from rest within four full turns (revolutions) and relea:pn:ogqf8- sdhh;d 3tm ta*i* ses it at 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 has a moment of inertiarpwkfxtx60o3 a;+gfy hej-l66ei ,p0 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 engineel/e+ 2ghupp ; ip0qh- develops 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 ro3ujaa x ;+qfryu6)u)nkvgo f3+x42qplls without slipping down a lane at 3.ffar n3vg j)upukx)yoq+63xq2 au +;4 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy ocz-1kttw : h y6rs;g9ck/5 n9bjgn2)jpas1hs f the Earth with respect to the Sun as the sum of two te :;6k1s-hzgypgbkah w2cn9) 5tcnj sts/1j 9rrms,
(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 m. (jvjyi s: n7b3How much net work is required to accelerate it from rest to a rotation rate n 3(ys :jib7vjof 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 kgx6*c3g qwvfnd /qrk:zzcl: ++ starts from rest and rolls without slipping dcz::q c n *g+lxd3rwfqv kz+/6own 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 sjb:lt95j7o c89r zy6wzym+v fall and its lower end does not slip. What will be tmzo:t z+yw 8cjyvlbr59679 j she speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on thqvbs .pej3 i*)e end of a thin string in a circle of radius 1.10 3qbpsie v*.) jm at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel boyt yps/ 9:/yof radius 18 ybsyy:/9/ otp cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, fyreqn99v (-a ja5j.x on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig-9x9j.a( yfn rqajve5. 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–ya + z*7z7 5+vcctta +/iagfoi29) can reduce her moment of inertia by a factor of about 3.5 when changing from the stra+vyc a ++attci zg7o7* f5/ziaight position to the tuck 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 increase her spin rotation rateko+ mthodv2p ,u0cl79 from an initial rate of 1.0 rev everloc7 om 2h dtv0p9,+kuy 2.0 s to a final 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 ved3 0r86za ve.mxl thlg2*x6 pvrtical 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 then 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 afterel6z0 a*g6v8ltx. m2dvr3phx the clay sticks to it?    $rev/s$

  (a) What is the anguldpn; epvq6 v59((w trkar momentum of a figure skater 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 mome5zbk4qt p1rj7 sl-k1r ntum of 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 o0b1yzjz7xt zz+y/cga 5uca u 0vw+65 gf moment of inertia I is dropped onto an identical disk rotating at angul5a7 gjuza+w 51 zuyb xt/+z06cvy0zgc ar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns lf:-a )lptj,e at 2.4 $rev/s$ 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-gohe40yl 2h-ckxl/, ivf-round platform of radiusyilf-v0k2hhe4/ c,x l 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 freely with an angua.+pzbd./x q1w n kv+nlar velocity of 0.8 w/kzdq b 1.na.+nvx p+$rad/s$ 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 abouwnz (.ah66hq1 8ayteqt half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(rqh ay6nw he z(at.186qound 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 ex; 7ugwosn0n h-/hwck(7 gum l1cess 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 v;y 1qfdct,e 8+ 6vfvg$ 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, initi0tf5olw vms85 k,w/twq 32)nm:zibavally at rest, that can rotate freely without friction. The moment of inebf ok2, w3:5i 5al8wt0nv/qz smmwvt)rtia 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-go-round )o0 2:zv*fm 7yua7xogrqo /h dturntable that is mounted on frictionless bearings and has a moment of inertizr/27:a )dv fmogq7* hoy0 uxoa 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 rolls : l e*-5ldrdqkon the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the r5rd*q l-klde :ope 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 suc95,uzjnyq8j y h that 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, treat the Moon as a particle orbiting the Earth.qn8y5j 9y ujz,)    $\times10^{ -6}$

  A cyclist accelerates from rep.r z82 1 i0 ,njube3tvfbpbv3st 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 4 xwdxcr-(/bk the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the w-k4cb(rx/ xdtorque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of masfgakcpj c(9o jef:l9*b9v*b3s 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to caf9(lfo:b vpeg9jj 3c*bc ka* 9lculate 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 rc ,.lgpoe qfp2,0j1uthe 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 siz s*7wzq 3;zu+m5s epxl.f;w sic1l7efd u5zg 1e of our 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 thee 7ieff *3l sm5w;zzssgzc;wxp11.7+dulqu 5 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-pollution automobile is37xnj6az1/dkq 2o lkvnwyq*bk9a7s 2 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 cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be ablj 7*6zavkkawyd232l s/ 1n obk97qnxqe 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 an ))cl+kti+ ijo $H_2O$ 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 horizo) 9eq:jare5d rntal surface 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 length L can pivot freely (i.e., we ignore frictiol/pqgyq0q 8+gj, 9mvwn) 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, determine (a) the angular acceleration of the rod, and (b) the linear acw,8 pv+/q j0qmg9gql yceleration 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 vertically on the floor, and we zz17dholo;3g want tzog1 ;ozl7h3d o 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 height h, where h

  A bicyclist traveling with speed v=4.2m/s od9,e sk1nmlv;6z ovoa*8q r5xn a flat road is making a turn with a radius v v86*qros,91 eo5xnk laz m;dThe forces acting on the cyclist and cycle are the 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 a2.c cyopx*q64l q w*uxnd begins whirling the rock in a nearly horizontal circle above his hea*wu. colxcp6q2*xqy 4d, accelerating it from rest to a rate 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 ;7q;sxfhq6 jdg z8f5h as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speq8dg h js 75zqf6f;;xheds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which co:)wb:l ztl8xg nsists of two cylindrical plates, of mbll:g z8:wx)t ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rolls21swk*rlld xbvv ,3fubrda)5, 2y ) dwqj:jn5 along the looped rough track of Fig. 8–58. What is the minimum value ,wxr 5lf byds 1*qjbr2lv)vau2n:5jd 3kwd, )of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do no ;jfo7q 7gr jlqev+::ca9skd:t assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly ohh- /,nzo:1sz xq bg4loq,z9from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of ea,/qx,9h:zn zo4zsq -oo l1g bhch 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