A bicycle odometer ( sl)vmx ;6zu5owhich measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a b5xv; mu) 6solzicycle with 24-inch wheels?

Suppose a disk rotates at constant ang.2f8nm(zj te9mmc.j uc:yf:qular 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 ny8mjet9zm.ucq.: cjf2(:f m radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be dzhwly(3 o.cdqf)k kuvzsvgn,546f-; escribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque th( /h4vzcw5 dkhan 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 wit.8(nkez 6qa1ty 8nm gth your hands behind your head than when your arms are stretche6t nnm81 y(z.g8qetak d out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thv ljg+k, 86m*ee4jsfrx)af e/ ree 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/ eexf j,er8v 4s gjk+lam*6f) front sprocket? Why?

Mammals that depend on being able toc ; kiq3u9.an1o,ypwl run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics9n;.kowui31lyap,c q , explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lro z9 1g) jqy5owe,)fbong, narrow beam?

If the net force on a system is zero, is the net torque ali1oaqpl2wm65 so zero? If the net torque owa5 12oliq6pmn a system is zero, is the net force zero?

Two inclines have the same heedpb34a0xh +( 8llqhd.h1kc o4mz4jvight but make different angles with the horizontal. The same steel ball is rolled down each incline. On which 4jcopeha l.kb +1hq4dz4 l0 x3vh(d8mincline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. Oyjglj0uy,d wgvc93 6qy:au09ne sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the wu 90jdjuqgyy9 y,avl3:g06cbottom?

A sphere and a cylinder have ta 6de 5kv ,sp;prsdw(6he same radius and the same mass. They start from rest at the top of an incline. Which reaches ksa66pd; dw, vp(5esr 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 momezc+-;jcq,enfsyycxz t. -05vntum are conserved. Yet most moving or rotating objects eventuallvc0q-y5c-xz yfs + ;n ,tzce.jy slow down and stop. Explain.

If there were a great migration of people towar..u ge7j)f jevd the Earth’s equator, how would t.ujeejg.v f7 )his affect the length of the day?

Can the diver of Fig. 8–29 do a somernw:b s4ewzv 8*sault without having any initial rotation whw8*se 4wznv b:en she leaves the board?

The moment of inertia of a rotating solid disk about an axis through its center *+luj9q1d dcar18z 91ho xhejof mj*z1 qh+u x ja hl9ddoc1e8r91ass 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 a26qn 8fn/qmq l 2-kg mass in each outstretched hand. If you suddenly drop the masses, wi8q2 q/n nmfql6ll your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is ht4orr8p5y6jmf9 foe)c h d*l7ollow and the other is solid. Describe an experiment to determine which ism6e54cl p* frro) 79johfdty8 which.

The angular velocity of a wheel rotating on a horizontal axle points wmf. 3z ywzugd ,f;9k;iest. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleratfzm ;dkg9.; w u,zyif3ion 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 thegv nv)-95nisr .7gdng edge of a large freely rotating turntable. What happens if you walk towardg7-)dgvr95. isgnnv n the center?

A shortstop may leap into the air to catw (2pr2i 7 iicj5b9kksch a ball and throw it quickly. As he throws the ball, the upper part of his body( 75 wrjpbsi29ikcik 2 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, discuss why a helimg/qz :n2 rs2.17yeoe 8kwlyncopter must have more than one rotor (or propeller). Discuss one or more ways tn2qoel18mskr2y :w /.z 7yenghe second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30vfrveq6-- nsu99 ; 3tg h.gxdqmwp.j 8 $^{\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 an9uiur50 e2 n vhlex.s. amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the M.e5lxu.9e h nu2r0 sivoon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directz1(ry v abv/-eed at the Moon, 380,000 km from Earth. The beam diverges at an an(-vazy 1/vbre gle $\theta$ (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 mo u*ijv ;o,pkoa 19zk*jtor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blajjoku*,va 91k;o *zpides slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makaw+zk -2wiq;nu vo,8 des 15.0 revolutions, what is its diamete;-8vnwauo +2qkidz,w r?    m

  A bicycle with tires 68 cm in diameter trave a8 hll hk+/;kw -*h-ipze1zzmls 8.0 km. How many revolutions do the wheels makem/h*8z zw-al ;ikl1h-p zh e+k?    $rev$

  (a) A grinding wheel 5,z qdd:o imah m-di,;0.35 m in diameter rotates at 2500 rpm. Calculate its angulamm-5;d,d: hoiiq z,dar 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 in 4.0 s (Fig. 8–38). (aj2d-ovev (ohb 2. ebt9) What is the linear speed of a child seated 1.2 mh bj.vvb9o( eetd 2o-2 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 orbit around the 6au +nogs8ht- Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a skh cpkx9k.8/j0 ge1vpoint
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particlegokx*-w; m1w5d27 ynlq g: dug 7.0 cm from the axis of rotation is to experience an acceleration of 100,00 *m wlgoq5dw1unx 2g k:g7yd-;0 $g’s$?    $rpm$

  A 70-cm-diameter wheel acc5 wb.cr6t1o8ubs es5w elerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determi8s.1c5e5bsw6o tubrwne
(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 radius bs/scj10da/ q $R_1$ 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,hghge7 g7 6nq)h0l; cb astronauts aboard the Apollo spacecraft put 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 revolution every minute during a 12-min time interval. The spacecraft can be thought ofg67;)hh lbc7ne 0 gghq 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.via2)e( 62 8ge a4hjst qej/ag Through how many revolaq(2g2/ee ij s6ha)g v48t ejautions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 :5bha .l jv*sp0fb- dcoy6nv1 rpm to 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 fwxts w jptks1(d).9y (or the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its finax.w ty9ktjdwp)s s(1(l 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 frous ,jy2, 9i hy j*v/xyfuea ckv.t*),,aw tit+m 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge ofw k,y sxt a ,uj,+ut, te2c.avy9 j*y)ihifv/* the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runninoowzku 5y+bqy() uh8rgvdoz6 + .7:x zg at 850rev/min It turns 1500 revoluth ud ozokgzv yq8x+5+):w6zru (.7oby ions 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 revolution3 zp ae86.ebuqs as the car reduces its speed uniformly from 95km/h toeq aub6e 8.zp3 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 csv49 yem(y t3ucjih)wve;i :1hzq.gs7m, x9far reduces its speed uniformly from 95km/h to 45km/hh7sme3)tg:. qm;uwxshy4j f eci yv9 iz 9,(v1 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 ridin bu6x() j3sosildu .d+g a bike puts all her weight on each pedal when climbing a hill. The pedalso xs)dd l(s63ij+. uub rotate 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 obcvr:7tmv 5 y*fbd /1mn the end of a door 74 cm wide. What is the magnitude of the torque if m7:bymv1b5cdtr fv/* 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 tor,uv8z l6)lakqque about the axle of the wheel shown in Fig. 8–39. Assume that a fri, vul 6)lqak8zction 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 ai :5 wiu+o/i4av xz5dto the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal pv+ ixa5 /4i5iduzw: aoosition and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require n5 scgxnc bh:88rd+4 wtightening to a torque of 38 ncg5wnrb8 c4:sd8x +h $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when tmdl3o,oy;h ( hhe axis of rotation is through its center. l ,hhyo(mdo;3    $kg \cdot m^2$

  Calculate the moment of inertia of a bi7wmycdcvb ajk ,(y40;dop; g:cycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (whpcydmo0;kvj yw: 7bc(; dag,4y?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated; p(jfrq.gu1 h y*v/3qtvb 4fl in a horizontal circle of radius 1.2 m. Calculat fb(4uqvr1plv*yfg. tjq;/h3e
(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 x ,dfubq1q9y; bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hand fquyd;q1,x9bs 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 gbcharp,4ku 7 ak 4ob)6q0mf.the array of point objects shown in Fig. 8–43 about 7ha k4 q prfu46o0bacm),gbk.
(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 at .0q py 7a2wwc2otlsn7:i yzgwge150 yoms 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 spinning at the correct rate, engi / 3uszi8+ceconeers 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 reeczc8/ +s3ui oquired steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radiu, bunbimgvky9hv;vk9/v6 a7 6s of 8.50 cm and a mass of 0.580 kg. Cauikmbv h7vvb9/ ,9yg6 vn;k 6alculate
(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, accelz:n)-o 3iv4t/wicn xuerating 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-drive8dz3 zj5z u3bdn 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 zd5dzbu3 3j8z 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 eventually brought j((zg gc6b 8bg3bopy0unif3 yb0ob( j6 gzpg8(gcbormly 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 f q4 qpbq(6kwy:,z,r ijm/a4r 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 bady0( klmbffpz28+06u g 8nspy the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifo20 p806aml usyfb p8+kdzngf(rmly 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 ta3owjgmq vvl 7k+;3yvp8o jf 730 kw(nhin rod, as shown in Fig. 8–46. 3jaww7koyk p0vvg v3j+ ;7mf83qlo(n
(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 consistsfr 1jzzf 3q w2y:.sfyo;8cv0-a ced)h of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the 4 ftlejxvx. 8i5pai: o72gmt; hammer from rest within four full turns (revolutions) and rex.ttv7fag54;j mi: o2li8p ex leases 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 hahf12ct*rid s0/6huwda e5 b3js a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develop45+d;*g qj0rxpi c yrts 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 rolls with:g w :id5+n1kc ts.poeout slipping down a lane5gepwi .+c on:ts:dk1 at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with res0z)d l 6a(p t+ jzh/,l(nndodmpect to the Sun as the sum of t,(+ hdmzl/njd0tn6loa( dpz ) wo terms,
(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. How much net wm 3l)p5w3;awz hf vn3xork is required to accelerate it flzx;m33n3hw wf)vp5 a rom rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and lmnk0t 0bss8s o ;:izlg sjw/ re48+n5mass 1.80 kg starts from rest and rolls without s gjs+ b/s4kl ss08o8;e0nzmi5lrtw: nlipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts tol/,3 8+jfq;o/qh+amcaeiky ic)mdj. fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hitok+3y /a . il8j;mc/af)qj heic,q+mds the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotatiwm x 2bjf zgxxfad o388.gh4v)r8s8-;txi y*sng on the end of a thin string in a ci .dmg;hxi 3x* x-xg4o y ff8wa8rsjz t2svb8)8rcle of 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 cyli iqfq2qtjw*d 6 )mz:s1ndrical grinding wheel of radius 18 cm when rotating at2iw:*)f1q6d qmqt sjz 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 9wt9r/e,-ykm k8hdeotxx+ 9ihis side, on a platform that is rotating at a rate of 1.3rev/s If he raises his awidko9 +h et8 xky-9rxme,9t/ rms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in7g7zp(md eql5h-pu1 g Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she 17gd5(e lzhm- pqgpu7makes 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 ie1,6ueynm5)j ag mnz1ncrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3mm)g151 yenj na, zue6 $rev/s$ 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 verthnyd (7*1ukzs ical axis through its center at a frequency of 1.5rev/s The wheel can be considered a unifu1*ny ( ks7hdzorm 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 after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum h8u4ljj1r1k 0x sght5of 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 angulaxks:mjf7* z *4f3fl pvr 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 of inertia I is dropped onto2y pvuw/ p,j9n an identical disk rotating at angular spjun, p29py/wv eed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 9;tsv qei x6xy0op,5q hje8* twr)l(z2.4 $rev/s$ 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-couwy u4*ek/ 79+k5 l y 4clx/i0ssitwgo-round platform of radius 3.0 m l7/+kltxs4wy u*cii/eo 0ku4wysc59and 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 hpd::q h7-* yegel 3bewith an angular velocity of 0.8 7-hg3yebe:ql p *e:dh $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about) a+sbqe vi.rcg b4a/cg::y6y half its mass in the process, and windinisyv:a :g+/. rb6qce c4abg)yg 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 winds in ;j6c dpz-4swv 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 y(+kt )jfjrh +ml.1 jm$ 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, initially atux 8i8u*)sk sj+dfhvh1 vc /s) rest, that can rotate freely without frictio/udsuj)ch* 8vxv) k1 fh s8si+n. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6id-c k-zjjf1 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has df6jkjzc1i--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 roll0+h.uhfxsdfx yi (5 k0v jk27qs on the ground with the end of the rope lying on the top edge of the spool. A person grabs t2 hyk5s+0 fx(iv7fjdh .0qxkuhe 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 tl jq2ba;n22v9 a,prk 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, 9,b2alp nk;tj 2q av2rtreat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates f) q0s cq9tm8ukrom rest 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 shape of a uq+kf-l p.ct7av;*rzuniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular accpfz;l-7 .c*rk +utqaveleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid c 7qms+fr ,4ugfylindrical disks, each of mass 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 q+s7f,urg4mf 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 sgsh8)ix * lfoy-jh 6(kpeed 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 4xvp;) z o+cxdmass 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 woc+vz4o ;)xxp duld 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 automob-k d q3hl ) 5ow0mtlq5rinwkdu*i16 o,ile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kq0- dm)1wir6kl uo*iwdnq o ,hk 5lt35g, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates a3kpu, 7t5+) jv ul 9(fgjbvtypn $H_2O$ 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 ah4jn,/fj pbj - horizontal 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 fricr 3b df+ks+1y98kysbgc5c)khtion) about a hinge attached to a wall, as in Fig. 8–5gkd ybc)8k9yhscb ++5 3 1kfsr4. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and weo yy +cic1-ly5 want to exert a horizontal force F at its axle so that it will climb a step against which i+y1lic yyoc -5t rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/sjbzpn/l7e *r. :eq 1esv 0iyv- on a flat road is making a turn with a radius The forces acting on the cyclist and cycle aienv7e01e -z*r/j:. vspqyblre 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 7t7kgxyd1 zq3 sling of length 1.5 m and begins whirling the rock in a nearly horizontal cxtz 37yq1gk d7ircle above 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 soli8 fg9qycs-fyby7m7pqk) d) v+ d cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of t+ 7byysd pc8m-7 q gfk)vqyf)9he 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 t: 4x3tg-y8cqi oa9sp*ama t*0/mva ldwo cylindrical plates, of masm i**y aa 9vt80d-/3socmaaxq: 4 tlgps $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 gqox p1om;/3lradius 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 h;mpqoo x1/3glighest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu:p,+z4eank06spk wu vme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions asdi3-6d4przdlrr 0pi,yb/:q )3 ktz dw the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eab zr3-4l: dtdiw/6,zrdk dip)yrq p30 ch 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