A bicycle odometer (which measures di:7d dy3mc jn-istance traveled) is attached near the wheel hub and is designed for 273cddi7- n jm:y-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angulqq l:bhpa:l90i+gr:w- qo8hjorj o2 :ar velocity. 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 acceleration? For which cases would the magnitude of either component of linear acceleration chanawjolj:b- pr 9i0:rq h :q 28:lgooh+qge?

Could a nonrigid body be described by a single value of the an--70k(bob j p*i7guaimn:cizgular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain.ez8 4a(6rw2u-g 5ww8 uze cjaip 8m-wz

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 behi6 acu:mnf p9eco(.u 7mnd your head than when your arms are stretched out in front of you? A diagram9e6n m7au:u m(po c.cf may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thre zpkehr2 -.he)e 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 sprocket or a large fronkz)rehe. 2-p ht sprocket? Why?

Mammals that depend on being able to run fast have slended+p4 7tfg-bwm r 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 -4 wtmp+fd7bg mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narroemlm knm9(aln/49 im9ezx8mj9d3t a (w beam?

If the net force on a system is zero, is the net torque also zero? If the net p 0v)w1fatw/ ,ygw,cj torque on a system is zero, is the n,g y,jww/wt1acf ) 0vpet force zero?

Two inclines have the same height but make different mclqzc e;)) xu;c.1syangles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball ) su;;c.qcyzl x1)mce at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down tif zqw x.y-z,d2v6gmm7ols m8:(3s can incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bott zt2l wc v6 ,o-7:8fsmys i(xmdqz3mg.om 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. Thhfpkg) k4: zdbsv09lc-0b hzwh 22 r0gey start from rest at9 sk c h 0h)r:kwzfh002 lbgdp4gbv-2z 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? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most m ;k j1 ei2gpj8)r tyt/bm-7vwjoving or rotating objects epb2 /)jtj1wyv8rjmk ; -7egi tventually slow down and stop. Explain.

If there were a great migration jd,+c (e.vjorof people toward the Earth’s equator, how would this affect the (+d,vcoerjj . length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial r376h2og x +kuvpx.zkp otation when she leaves 3.z 7hupgv+po2x6k xkthe board?

The moment of inertia of a rotating solid disk about an axis through itjn hfzs28n0d*s center of massnj*nfd z0 8hs2 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 rotat0fde 3kv(jvu m0. rkl8ing stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay th8. ldfv3 k e(mv0ku0rje same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and tyjlu+ zg)mqx n8:s1xvkw6. p( he other is solid. Describe an experiment to det v .j g(wmkxpy n68s:1qz+x)luermine which is which.

The angular velocity of a wheel rb, pcxz7n+gu 8otating on a horizontal axle points west. In what direction is the linear velocity of a point on b,n cg8p+zu x7the 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 free vbkq,p /hfl9;ly rotating turntable. What happens if you wap q/9khb; l,fvlk toward the center?

A shortstop may leap into the air to catch a a t3a-w1p,kty ball and throw it quickly. As he throws the ball, the uppatp 3w-k 1t,ayer part of 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 angubl 0,.pq yj;ajlar momentum, discuss why a helicopter must have more than one rotor (ol , .0pyja;qbjr propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radij,pd0lx3oo s 3cqx/fn s-m 9s8ans: (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 0q6o0py1wyx6 rml p;d amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) o6wm ; py 1rpd0yq6l0oxf the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directey z:x6fgt*n2 id at the Moon, 380,000 km from Earth. The beam diverges at anxngt:*fyi2 6 z 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 motor is turned ozu1j+uiih8yyx : m.)r ff during :j u.1mh uz8+)yiyxiroperation, 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 lemu2bu4/j m*vdx.hne;9; ouj hvel floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is it;24 d.mejbxuuh *nmjho9; u /vs diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Hoyp 9rdh4bvzr ,b , (yax3n5gj,w many revolutions do t4an d,v(pb5ybh jx, 9 rr,y3zghe wheels make?    $rev$

  (a) A grinding wheel 0. qvzqug /0(o2g35 m in diameter rotates at 2500 rpm. Calculate its angular velocity in/vg(0 uq gq2oz $rad/s$ $\omega$ =    $rad/sec$
(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 revol djje3t ye5m+zhth ocs j3,7vs09;tr.ution in 4.0 s (Fig. 8–38). (a) What,es hjj.9yocszhvr0jt+m 3t75 t;ed 3 is the 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 velocity of q- cvct*2uks6 0yslx8the 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 poinpt(3rs y0i9yc t
(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 ch,6s)qo r8aoaoz yzkyx+52w * i8wu45x1nhvoentrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an xqyoy8w5+r*xunaah o5),1o o 2vk48zwi z sh6acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uus.,rulovkuu 5b 6lo3 hf- f+uo;.-mt niformly about its center from 130 rpm to 280 rpm in 4.0 s. Deter 6 o ubo. .-m;r5 ofulk-uf,suuth+vl3mine
(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 radiu9r/bv 9-qcs yp)-oys os $R_1$ 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 sp p42 l1dymm,rzacecraft put themselves into a slow drz14ylm, 2mprotation 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 from rest to 15,000 rpm in 220 s. Through how/u*6j fyihlr5 1gv dg8 many revolutions dv 6*l5judfg h/iy 81grid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. nv x:75t2ria epqt0c: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 for the stresses of flying v q/okde*+r2p;7yc ni highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn to eknp+i7 yv ;rqd*2/chrough 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.k -x :njknm50kx/m (wa5 s. How far will a point on the edge of the wheel have traveam:k50- m jwnx(n/kk xled in this time?    m

  A cooling fan is turned off when it is running at- k/ 01fnhk (pukzx j(;t8cg g,b1pbpj 850rev/min It turns 1500 revolutions before it comes to a stogk b jh 0x- zcp8t1g(/,f1pkknpb;ju(p.
(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 reduces its speed uniformlfui 1r/.kpa5fvm18ngy from 95km/h to 45km/h The tires have a diamet naf11k umf58vrp.gi/er 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 fmcveyg:u ;9*tmdfyl0t *f )bz;fg.34hm)ho speed uniformly from 95km/h to 45km/h The tires have a diameter of 4 c)u0y e mfydmfhz. h:f*t9 3lgf*tog);b;mv0.80 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 puts all her weight on each pedal when clim8nr1gmj) ;qrt bing a hill. The pedals rotate )1mrjqrt8ng;in a 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 doz gjx pk0u0b,,qcm.z59fk. lz or 74 cm wide. What is the magnitude of thelmb zu5 fg,cjp.zx0 90.kz,qk 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 wh ew0r c9*okbo u9 fgctch* jx.r)04hd/eel shown in Fig. 8–39. Assume that a friction t hb/x)hce ogj4*o*u0r9 f9d ckw.0ctrorque 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 the ends of a 8b5:d5wb n 8mpo k8uqgmassless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then rel upo5gk bb8d5m8qw:n 8eased. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torquev0vvycjy:+sj:d j :o2 *yq ow; of 38j0cydw:vyvvso: jo: 2*;+ qj y $m \cdot N$ 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 n6:i3cb fl n:vsphere of radius 0.648 m when the axis of rvflc b6:n3:ni otation is through its center.    $kg \cdot m^2$

  Calculate the moment of in/k5ucfni ego4,p e4d4tf4+mofdy6 t6yq f -l4ertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass 4gkn pqf4tdy5 6fcdul+4fetoe/fy- 446i ,moof 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 d,g1d bchwa 7 :txhp7y-/ka57 4fwtcyin a horizontal circle o/b g5 c7:-a tydw7y7 1 t4x,kawcdhhpff 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’s wheel rotating at constant angula6j c wzu4la:.vr speed (Fig. 8–42). T c al:vzwu4.6jhe friction force between her hands 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 ofc ms*r5e9,lab inertia of the array of point objects shown in Fig. 8–43 abo9*,e5ar l sbmcut
(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 ookfc;: c wf9x *e2;wgff two oxygen 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 cylindrical satellite spinnb7ahmu 6a;)zq* p :vhwing 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 i* ) u6zvqwb7;map:h has to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm y8ewb1zp9 vk7rn ;q6vw uvg )(and a mass of 0.580 kpvq u9bv6;g)ywk(v71r8ze nw g. 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, accelerat+m-dm d73mwyn71 jidv ing 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 on a small hand-driven me k:h21jpzuw2yrry-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 the torque required to produce the acceleration, neglectz ywjhk2: u2p1ing frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating * rt3uf6hp2qo i1tskw 6k,wt:at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torquefqk sitw6k 6r* ,:3tw 2op1uth 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 a6i cut 8v h nryngm5lgrk; n;).1u4h2r 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 byc8e fr-y*iz)y 6our)l the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. T u cryfery6) izl-8o)*he 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,(u(a7+2di ahem u/t2 e*qcpdm as shown in Fig. 8–46em cdih(m * (7+pte2q2dau/ua.
(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 masshgh3w ( /iaih1cc)rm)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 the hammer from rest within7 0ki4ya)igcn,p nw*ke5p 6kr four full turns (revolutions) and releases it at a speed o5wyr n 6apiec70 npgik k4k)*,f 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 momenty -rhg/hfz))yqus 3, r fq;y0a 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 develops a torque tlvs v-55kiz1of 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 without slip 9kkb/n;rl,5y a yaa2hping down a lanel 92 ah/kyyk5ran a;,b at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth a:p0i sz ;969uxraqxlq: ;ck vwith respect to the Sun as the sum of two terms;kviuq90q :ap6az:csxxr 9 l ;,
(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 1640v9uizxnb e -a/z.7j ,b kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation .bbn7i,v/xe z - uzj9arate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and masyr neycqymb, g(058,cs 1.80 kg starts from rest and rolls without slippingbrgn ycc,y, 08(5 ymqe 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 balanc 2.ghuqqf0g5yw98r rned vertically on its tip. It starts to fall and its lower end does not 5wh.fruq9q0gy rn8g 2 slip. What will be the 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 moment1jvh6ug o6 c)ccv/goym/ f7v0um of a 0.210-kg ball rotating on the end of a thin string in a circle o6v/fov7o c / v)c10umg6hj ygcf radius 1.10 m 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 cydebj6 py8yg :,lindrical grinding wheel of rad86d g :yj,epbyius 18 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, on a platform that is rotating at a y)xd4l 4kas 4v vpjiw-r 02n6drate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of v ik4n0ldp) dyj-ra2x 6 4s4wvrotation 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 of inertia byv70dok 8eo*qy(*f 7y emybjqa3 3k :pq 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 position, wq y7p(m:bavq8j*yo7f ke edo q3*yk30 hat is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rateh7 fh 7na:fhubt+;hw6 from an initial rate of 1.0 rev every 2.0 s to a ahhbfnf;uwt6h7:+ h 7final 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 -i 9tm kpiiv0/h l1gjxk6e7z/f)s3p na 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 then throws a 3.1-kg chunk of clay, approximately sxgikve9ijplp - /3mt in)k0shf 176/ zhaped 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 mom(/1oii;lmch cu ed: z2entum 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 jw 3p.mr56fzxcpjc*5 y h67fi momentum 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 of moment f j;r7az ppy1q0a29. a aq5yihof inertia I is dropped onto an identical disk rotating at anp2a 5rp9 0 7a1;qhy.yfaqajzigular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.45 te0rpe/g4kge+ v/ht $rev/s$ 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-1h k: gc(x,zou9 mrdw*yh )w-wround platform of radius 3.0 m and mom-wg,r) 91dkm: xzh*yo( uhc wwent 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 angul8k ut*sdznvwu;-b4k01 oq3uz(fdbq 4ar velocity of 0.qfd4*zd b n-4k 1t0suq u3( o8uwkz;bv8 $rad/s$ 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 x.8.tvjtqbe .white dwarf, losing about half its mass in the process, and wi xe.j t8b..qtvnding 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?(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 windstv; 8nvpp :l/r qx2ez -k5kl4l in excess 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 lns77ycgu yej1w+ 4c46r/em1u0o;mudjar m ,$ 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 platformo ))8zspgg5u pjd+ x ehd8i6t1, initially at rest, that can rotate freely without friction. The moment of inertia of the zx1d8t6 jpug5) h)gsd po8+eiperson 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 651xv qc7qgh o5wues-( .5-m diameter merry-go-round turntable that is mounted on frictionsq 5wh1 ou5-7vq(xegcless 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 rolls on the qmu r gh( f1x)rv8bp0(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 )pr8rgbmh uqf v1(0x(center of mass move?

  The Moon orbits the Earth such that the same 6z3nzhez20*)z nuubo side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular mn)hzn6zz0uob 2 3z*eu omentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rae7aq(r3b8h4i mfcjr9 : ,/7p lnzmc oyte 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 cylinder of radius 0.2f+m )k e)cs7qw0 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivere w7ce+s ))kqfmd by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass+g 5-x;sjv xruzs;c q) 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 calculate the linear speed of the yo-yo when it reaches the -5; sqx jcxgrzus;)v+ 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, ho ;4 bdlf;v piefmr68h(w is the angular 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 Sun, but with mass 8.0 times as g0 +zg(uakp, dxy,w+y0 (/jmpt f4yzbereat, 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 woulddpy + /wzy0y(ap+ kbj4fzg,0te x(m,u 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-pollution automobile is for it to use ener2 +uu +9nyuif5kn1hgd gy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg,u f 5ui2+ndhn+k 1y9ug 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 illustratesm4iv3mx*dna ,h( j0b g 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 sr6q;8j -ch lkeurface 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 piv ure fffdj)o3rj057/ zot 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, determine (a) the adfuf z0 ej7jr)/3f or5ngular 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 vertically v nv./xajgf0v ,)*syb on the floor, and we want to exert a horizontal force F at its axle so that it will cla.),vv*0fygvbx/ nj simb 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 on a flat road is makingn.(ljr5oe p3igm - -eij7 2y rfmre/;l a turn with a radiu7l; fjirg-e. erper3(l/ojm2y i 5 -mns The 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 in8qe ozg+wh30mfvbl3 y:3kvf3to a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle abovev m0+3q3eo k:flgw8 fh3z bv3y his head, 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 as a solid cylinder atle9g2yode y6u1. ah +nd 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 arms held tightly against heu h29yl 6d 1e.+goaetyr body.   

  You are designing a clutch assembly0)p fwqnwbdi6e/60)l b use +; t:qnrq which consists of two cylindrical plates, of mass +rdwtqfb ln0:i)0u b6nw/;)qeq6esp $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fig. 8–58.iv) +dl r 6xhx8 6s03qdxu9 t/ytsz)tj What is the minimum value of the vertical height h that the marble tqvt)z6t93 u+s8 idh)lrx0 d ys 6/xxjmust 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 not :ly+eri4qj5yss er )) assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly u3ubf, p p; l45ljys/xfrom 90km/h to 60km/h The tires have a diameter of 0.90 m. (a)3xfp,ujy/;4lbl5 p us What was the 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