A bicycle odometer (which measur8cdxmh 6enzdm.z*(9 .s1gbu -bo mb3ovre, q1 es distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch whebr1nm, ogez.*.91h b6(8 sdm3mvozb u-xceqdels?

Suppose a disk rotates at constant angular velocity. Does a point onlzthwf p,+xz ;vvg- ,+ the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or taz h+ fz l,t+,gpv-xwv;ngential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the and )xbp6o+ gzl/78k wgtgular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a largr9fw g 49fj1+ic-rlgger 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 t,:fbo ip;g7iu8ba( rwo do a sit-up with your hands behind your head than when your arms are s;7u:(,r8 i obpbg aifwtretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at:d2g c/e:za sm the rear wheel and three at the pedal cranks. In which ac d::2/mgsez 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 front sprocket? Why?

Mammals that depend on being able to run fast hagjucg; s r /n4 vw:wr:wxyp45t 0woq50ve slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of ro55wu:4jr x r/gyq ;nw4s:t0g0 vpwcowtational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkersl01kn x:fib -h/vmc6r (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque ali25;d wlppeub p:/p4lso zero? If the net torque on a systeup;d wlpi: l5 p2pb/4em is zero, is the net force zero?

Two inclines have the same height but4bg m+pqt*c9p.w;eo5 iq c xi0 make different angles with the horizontal. The same steel ball is rolled down each incline. On which *q e ib pgc+;p4xc5twoi.q0m 9incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (s2 d snd7osfv46::eznfrom rest) down an incline. One sp67sd2nv4o:n :fs s edzhere 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 bottom?

A sphere and a cylinder have the same radius 8 7w pelmbubq 4b.ol,1and the same mass. They start from rest at the top of 8e obb p.1lm qlbw47,uan 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 u :;2ovw5y6uipg;xg b1xk /ty momentum are conserved. Yet most moving or rotating objects eventually slowupvg x1;x/wyy6 t ;:bgu2 5iok down and stop. Explain.

If there were a great migration oc6e .jww0wv3rf people toward the Earth’s equator, how would this affect the lengthrj6wve .c3w0w of the day?

Can the diver of Fig. 8–29 do a somersault without having any initid3fk 28mox2dia;c .k ks:,, j+f tbpi3t/ evxbal rotation when she leaves kb3tm3,dtc + savek;28 2 b/jp.i kd: ofx,fixthe board?

The moment of inertia of a rotating solid disk about an axis thr ker:mf) r60tiough its center of mass kem) ft0:6i rris $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass um;s3ae. e55 8hipbvwin each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the sahauebp 5is3em 8w.5v ;me? Explain.

Two spheres look identical and have the same mass. However, one is hollqe83hkk6rn; n r( -g6yhb7 vc ycyai/:ow and the other is solid. Describe an experiment to determine which is;ycke6vhcr (6 3b-ny8i :qgky / ah7rn which.

The angular velocity of a wheel rotating on a horizosjpkrldm /hn 5x/5 /b+qqzy7 8ntal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed iyxh 8q/lb/ q+zsnprd5j/7 5km ncreasing or decreasing?

Suppose you are standing on the edge of a large freely rotatt/t p5*hqc,g* -mp;popoa8s*ep0 krjing turntable. What happens if you walk toward the cpp; p- mp e,jkqc8tt prgo*h*0/o5 s*aenter?

A shortstop may leap into the air to catch a ball and throw it quickly. As he i* b/qek; i,oethrows the ball, the*kb ;,i/ qeoie upper 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 angular momentum,gs52j7 icdgvy 22u o; 7:a69lfjujtfy discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the:igj o26cuftu;vd2y75ys 2j9f laj g7 helicopter stable.

  Express the following angles in radiow3 rxy6o;+o s ds0c.xans: (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 ofk4bj*5a b. ocwq9aoo; an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as cwobja5o bqa49. o;k* seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at th k)zb q)cbv(fh+(f* pva6r;gxe Moon, 380,000 km from Earth. The beam diverges at afc;gvp x+)b frk (*a6zhvq(b)n 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 rpma8eb7oc rbo5(m7x )nn. When the motor is turned off during operation, the blades sb cnno()8mr7o75 abxelow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball mak*t ;tek6uaq y8u.hl*mes 15.0 revolutions, what is its h e6t;kta*8ly.*qum u diameter?    m

  A bicycle with tires 68 cm in diameter travels 6 i4p;juz,p* nohl0tt 8.0 km. How many revolutions do thh0t pp6o 4i jnzt;ul*,e wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcu(f3z e 6xijcz5late its angular velocitzzij x( fc356ey 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. 8–3s u8jf-73rkuk8). (a) What is the linear speed of a child seated 1.2 m frou7j kk ur-3s8fm 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 ;y3cap hk -96o/airliEarth (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 ;0qycintk05 x a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from i+)xqe) .e9mzy gyc/(vz.u es,j:w ka n8brn6 the axis of rotation is zmw,ye /8k.9en)i)j zcvqx(n:6ysb. egu a+r to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel , vujmc :alhjg/,qgj 7/1djg- accelerates uniformly about its center from 130 rpm to 280 rpm j/,jmg 1g/q,-lgvdu7 h:jcaj in 4.0 s. 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 radius vzg0-bxem.5c 8e 1zfhl4 *oee$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft punb ;z-xohv* w.t themselves into a slow -.zx own*h b;vrotation 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 )5xj;6bl1jg4 f;mebzhobp 1 buniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it ;z6 bbfe)1mh;b5gboxl14j p j turn in this time?    $rev$

  An automobile engine slows down r3 dfl/k, 3z:ma;nn :asm-fewfrom 4500 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 for the 0kb(my9 sw ga1u*8wu+t .kwn lstresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn thn+mwgbys8w *wl .0k(91uukta rough 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 rj :oqdolbv.mh f(m1 )6pm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? v j d mqo1:.ho6b(mf)l    m

  A cooling fan is turned o * qgs7am1sajb*n 0lb;ff when it is running at 850rev/min It turns 1500 revolutions befo jq bs0a*gl*sb ma1;7nre it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its spe9qin /pyw9bg7ed uniformly from 95km/h to 45km/h The tires have a diameter w9iy bqn7pg/9 of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly io4e1x(evd; xm+1jb l from 95km/o+11xeev; xjbdm4( l ih 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 puts all her weight on each pedal when climbi 9k m3j8fylr,(*bawav mv w-.kng a hill. The pedals rota3 .w akl9,rkjwv8(m*vb -yfm ate 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 *zlfrp *u9saj8adeu *51zz v9of a door 74 cm wide. What is the magnitude of th 9pzd 5uf1zual9z*jvsear* 8*e torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel stp g(t/ph;0e1 ce0i6qdwbi*nhown in Fig. 8–39. Assume that a friction torque p(d1tiqw*e6 0/ph; iebn0 gtcof 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 m-n gfj8+xzdk+ assless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitudx8++ f jk-gzdne and direction of the net torque on this system.

  The bolts on the cylinder head of an engine ru+. 0o xkaxy((- pxlwyo-c,pq5ovg9x equire tightening to a torque of 38yxx5- qc(u0 vglx.k,o (w9 ox+o-papy $m \cdot N$ 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 ineb3ytqa 9,6o ayye46dfrtia of a 10.8-kg sphere of radius 0.648 m when the axia,4t aey6qf 3dby69yos of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.10 a*zk7o*q 3jxwfzrn:bhss92m7 tzo7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hubo 3wzj mznh0 s :2b7xfat*srzk7 *o91q can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the en99lhsb;; eo+ra 3m l:fitwt9bd of a thin, light rod is rotated in a horizontal cirwi eb slf ;;aml9bt:93oh t+9rcle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a pokd;6l8, 1qad4muhhyn tter’s wheel rotating at constant angular speed (Fig. 8–42). The friction forceyq ,dm4nldh6ua;k1 8h 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 of inw ,g 44jywd2az66tsdrertia of the array of point objects shown in Fig. 8–43 abou42,6sr 4jady wdzg6tw t
(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 brkke y g/0g57qt;r;datoms 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 cylindri118ay88d2 c; n7besxsgigeyi t7tx d1cal satellite spinning at the correct rate, engineers ti11sctg;8 x8a ed xd8 sy77 yn12iebgfire 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 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform c) q bp4nbog9bxb9 8z/oylinder with a radius of 8.50 cm and a mass of 0.580 kg. Cal4 bx98pn 9/bq)ogobb zculate
(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, acceleratic.lav*;- gbv4vd- ccyi( u oy0ng 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 hfb0kjyr g8 - bf6(s, bbji394g9 jvbcfand-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-g , 9gb skjg -ib9jcf 4frb(jybb3f60v8o-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, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rota)d h*cgeucw tfz 7)x7-ting at 10,300 rpm is shut off and is eventually brought uniformly-f)dtzce77xg* cwu h ) 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 7dm:nlxgxq ) b*7vr.; s $m/s^2$ 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 ballm(0ra6jft o; l is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of;amrjo6(0 f tl the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rg.e;1z ihemc- z4 e:bsx k+kp/od, as shown in Fig. 8–46.kexzc .4:e;-bsm+keg z1ih /p
(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 confe/ edwm1p/y9r7 dxd( z )azf3sists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer frk 4 7z +dsdz*u1 r;do3rhrji,udm .9taom rest within four full turns (revolutions) and rele7m4 ;h.j9,+1kdrd *r zoda udizrst3u ases 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 inertia i d/b2say*bbpmz/ h9;hz mm*2of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a tot b 6my.2hwvr+rque 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 7( wvfcdu; emz;z7n u9and radius 9.0 cm rolls without slipping down a lame(v;zu z7uwfdn9;c 7ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth whs37)np79t,ppl7dnqzi a yk0 :8r dwbith respect to the Sun as the sum of tyarh p8 pq7 szpw :nb70tdkndl9 7i),3wo 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 dgdryvr mdc f44x3 m4755id q-and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is7d- dyq 4drmm5g4cxd53ir4fv a solid cylinder.    J

  A sphere of radius 20.0 bq3u 6bka:0uw cm and mass 1.80 kg starts from rest and rolls without slipping down:qbbu6w a0u3k 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 as.qbq-sk8+90kgmhv starts to fall and its lower end does no8h.s 0+aqk9kb smq-vgt 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 mome8i)*gtaf(jvl u :hqx3 kzx5f -ntum of a 0.210-kg ball rotating on the end of a thin string in hauzk( lv-f:3xf )g5*xit jq8a circle 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 te6p6p1o 2zj icylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? o 6p12i etz6pj   $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his sikl:hudjf ;*9 ide, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–4ju*k; ifd9h:l 8, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inertia byba:; lpfva; f u7r;/ux a factor of about 3.5 when changing frxula ;7;v;:u p frab/fom the straight 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 rate from an initial 6d+qs:gi dw* akp*o )qrate of 1.0 rev every 2.0 s to a a o* qd*ws:pd+)iqk6gfinal rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis ty*zxkn 4 3:2oqokbxoof /zc) 7hrough 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 flatxzxo *:ckfo4k/ onyz2q7b3 )o disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinnin4d *8cuu,pysmg 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 anguladgr0kyque5zk,b7+0v8gb d1 x r 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 onto an zgtb1 q vd0c/,identical disk rotz0 ,tqbv /g1dcating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.rtah) m/rt f(4vgz//r.mb.ev4 $rev/s$ 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-d d-e 5l91vhlf;ck *nuround platform of radi- hln9c5ekf;dd 1uv *lus 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 angular ve:zb q4wh2m7uav8p 9 eolocity of 0.8mqz82ewu7bohv:a4p 9 $rad/s$ 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 eventu6c n9d ic u;ypm/jst74ally collapses into a white dwarf, losing about 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 the4/6dny cc7 jms9itup; 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 ecnou./, vo +:nbtnt/txcess 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 ejr95;sjcx3t(b x-kh ; iu8ua$ 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 at reskqv)lm069juex1r g8it, that can rotate freely without friction. The moment of inertia of0l86)jueq9gm x ri1vk 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 bm z i4cv95bn zyt:y+ j;5gnb3stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inern5y9 iyjt3:b5bbm z +ng4 zc;vtia 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 grou(v )w tz6vux5 r3kdwo p2y+r3pnd 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 lexvz3dpu(2rw+y53 p r6 w)okt vngth of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Dot.jg(fj;7- nhhys;fi 5-sr netermine the ratio of the Moon’s spin angular fs-;(tojf g;n-j hy.n5ihrs7momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a )ep)9 w3z sg9n2nsyvvrate 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.q8 wjx+8 +zqrn20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque deln+jz8q+xqrw8 ivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0./ot21xp; do1wyk9u (wjdx,bt 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 end of iu1 tykd1 x;j(2px,bdt o/ww9ots 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 th**)33njg+vy.t t wt bgstkp .ze 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, burgylr9oz+75 h 0yxetmp :/)zr t with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mg y r):r7ehz0 r9+m5 ply/xtozass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pe)pr/uvh 9tos6a/p*k 9b: nn-r7s xaeollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 *-p)s6/rt spru x:ek/ ab99o v7nenhakg, 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 illustrates an32nhdpd * f0or $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at sz)g 2t jd2c 5+zmunz.gpeed 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 (imc a5p a,jh8: oo/1as+,pm ggq.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 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. 8–21gpo a/ghjs 1,gq8 a5p :mmac,+o.]

A wheel of mass M has raq+l rqu(rrp :w7a6sc* dius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb aarp csr(6 *q7:+urq lw 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. vo6 ra*mkhe*a3tr9k n0 pqv6 making a turn with a radius The forces acting on the cyclist and cycletanvr. m*0 6oh 36kprq k9va*e 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 slp,ad.aqpz. 6 1ouaf9 king of length 1.5 m and begins whirling the rock in a nearly horizontalzdfu ,o9qaka6.1.ap p circle 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 szhb1z;s2 s k x(1g5rabolid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spsgk5b1r2zs 1az ( x;hbinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cy ufc57:.babd/ 0+v:7e b 1/yrp (tjmiixytmsalindrical plates, of ma /ta0y /emts 7bvdai5b.:m1p( 7ixjf+ycrub:ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 trackgxmhe:*f;t *yzvq+ 3h s21asu of Fig. 8–58. What is the minimum value of the vertical height h that s hg+fhevxy;3 :2z*mus*1qt athe 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 notc/4f-aroilo- w0 23 qcjbj7 ka assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed m5(fp25p tyu 8macqo- c +l.mbuniformly from 90km/h to 60km/h The tires have a diameter m o q(ctpapm5bf8-luym2+c5. of 0.90 m. (a) 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