A bicycle odometer (which measures distance ykp a0t(p.nedlu e(94st iu7+traveled) is attached near the wheel hub and is designeltn(.(4 etd yup7episua0k9+d for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the o6r. oi: /vphvh)nya*rim have radial and/or tangential acceleration? If the disk’s angular velocityia :hopyvv *r6.ohn/) increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular veloci 3*tl2nn fxf7mty $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forceb0x.vnhr) e f/? 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 sitg.:ivio b.q,t-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you ,q.vii: og.btto answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the t s3ueq: v1pr(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 large1 u3:eqsv(tpr front sprocket? Why?

Mammals that depend on being able to run fast have slender lr 1aq*fl9*pjg ower legs with flesh and muscle conq19*ajg* r flpcentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carruo y*he p;:zj4/m6+ vyvv5 xury a long, narrow beam?

If the net force on a system is zero, is the net nqy ik:k0si; )torque also zero? If the net torque on a system is zero, is the niy)i 0 ;k:nksqet force zero?

Two inclines have the same height but make different angbmn8yknv5x 8 7i x*pc8les with the horizontal. The same steel ball is rolled down each incline. On which incline will the 8n vm *7inxk58ybc 8pxspeed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down6oy25t aq 5) 5+uqqwwhlvf7o j an incline. One 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 thewa+ )h526 j5foqvt5 q ywou7qlre? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass,,;regk xw* m7infwc:,x. oxp . They start from rest at the top of an inf ,:x g; xop *x,n.m7ceirwk,wcline. 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 momows7;44sw yp9i.iwxog ,.rcc entum are conserved. Yet most moving or rotating objects eventually slow down9i ,oiw44;c y.gswxc7rw.spo and stop. Explain.

If there were a great migration of people toward the Earth’s equator5 /n 9ewhhmc4 zecr0o7, how would this affect the leng5cch94eeor 0mzh7/ nwth of the day?

Can the diver of Fig. 8–29 do a somersault witkbu*6lmh;u-xlqn- 1s hout having any initial rotation when she lean-llhb ukx-*u6s; 1 qmves the board?

The moment of inertia or bn k(r. 1;plp t+wdmr7cl.j(f a rotating solid disk about an axis through its center of m(;jrnm .cbpldrtp(k lw+1. 7rass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstreltrj444*9z+qom ebo h tched hand. If you suddenly drop the b oz+4*qh4ml9je4o rt masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same massxats6h*3 zes* . However, one is hollow and the other is solid. Describe an experiment to det*zs63sh ex*a termine which is which.

The angular velocity of a wheel rotatiox3s3 oo b3i5ionl21rng on a horizontal axle points west. In what direction is the linear velocity of a point on ob13xi25ilono3 3rsothe 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 ed1boc:;gmc6e/hv w ow 7ge of a large freely rotating turntable. What happens if you walk toward the centerbhwoge 7w/cvm1c;:6 o?

A shortstop may leap inditcm who zh1d;0 bi, ;drr9;6to the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If yt,d6 dob1;izh;d9mwrr ich0;ou 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 c jl xe*k.se44xonservation of angular momentum, discuss why a helicopter must have more than onjlxesex* k4 .4e rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radiank3* wps tr,1ues: (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 amazin/wmq;p y01wyh -if cuu xh5i7y(q do07g coincidence. Calculate, using the information inside the Front Covp/ 7fx0 wu myyc- h1hqqui0w75(iy;do er, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed atnhp71. 4i bqka irhy /ft*hbt zr;.e/7 the Moon, 380,000 km from Earth. The beam diverges a/e i ;b7. 1fyhqzrnrt7t.b *khiah/4pt an 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. Wmw:yxfmx /g jd eyb. *2t;myo 6yks5/8hen the motor is turned off during operation, 8o.;5fkb/x mem2/* yyty6 x jg:smwyd the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chila;wmmd 4us:s7utaw03e zj a02d. If the ball makes 15.0 revolutiozs;u742e0 uaj: mdsaa t0wwm3ns, what is its diameter?    m

  A bicycle with tires 68 cm ink:vbfzqf8w9 - diameter travels 8.0 km. How many revolutions do the wheel89wqv :ff kz-bs make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its an icr* )uk88acv8lv) rbgular viu8c rvk l8) r8b*avc)elocity 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).7hi3bsq ;jac 8 (a) What is the linear speed of a child seatedijqacb 7s ;h38 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 vel3b *cd(,hc)tvi a,(olwxe8vu b3mf9x ocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of - d- kn. xbxds8ek47rra 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 par2ely y0b83 nogticle 7.0 cm from the axis of o 02 y38lbeyngrotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 13,-(qg9 v nky9; kbbzxpul3o7tv-s/ql0 rpm to 280 rpm in 4.0 s. Detervgvk ys,9quxt--kl;(bz39boql 7 /np mine
(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 dm1ll rpd,s5j7m3 tqj78j w0e$R_1$ 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 ab yh ba dt.-5qv3 m4yj.mrm1ux+oard 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 rotr+1m jhmt.ay.34-x bq5 yduvmation 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 re h;jq;u994 nb jmlqy3wo:ilt. st to 15,000 rpm in 220 s. Through howh;jjtwq4l3;9mlni.9 o:y b q u many revolutions did it turn in this time?    $rev$

  An automobile engine sz;i:gjkxzrc /: )-kqylows down from 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 stresses of flying highspeedy 7 -mg*htlelj6;r.e v jets in a whirling “humagly*vhme j-;el6.t r7n centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates u1 8 yw6qcx+d1 zr*dpzhniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travel6phd* yrz8dq1wc zx1+ed in this time?    m

  A cooling fan is turned off when it is running at 850rev/mq7-f- *l/ f,o fvqlhpxin It turns 1500 revolutionso-p-fql /h lv7* fxfq, 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 yzrwjgga77 l002t..vl ns ti+ 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of +jsagy lv0t7l0n w27 .ztrg.i0.80 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 u 8508rczi*ciayf1i hw niformly from 95km/h to 45km/h The 50y8cizi*hf8a w 1ric 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 peda01mf(k( v hnugl when climbing a hill fkg1(un(v 0mh. The pedals 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 on the end of a door 74 cm wi9 8jdz ; +le+jd(dpw-zf hdstdcq5+o1de. What is the magnitude of the torque if the force 5 +t+9dpd(h8j f+d-d1zczdwlq oe j; sis exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assum q)v8:mo* - /)hwmbs ru4mhtjte that a friction torque ofmhv s:t8/hom t4r-)* m)bqujw 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 )f 2qk.2bxluyez id(2 ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the )xe2kf q dbi2(2uzl.y net torque on this system.

  The bolts on the cylinder head wc qxj4ht (9l4e ,hhi1of an engine require tightening to a torque of 38 4 (tc he4jihwq l,x19h$m \cdot N$ 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 radiusw xx9yy)z no/( 5ryi)ckp6a6e 0.648 m when the axis of rotation isynry) cipy6wxoz x5e 6 9(/ak) through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. T.tik *21if5 rtoqex7h he rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?). qh it*7k1eitf2o r5.x    $kg \cdot m^2$

  A small 650-gram ball bwn,mwnkq 63ccn,24 kf v8y :yon the end of a thin, light rod is rotated in a horizontal circle of radius 1.kkc 3 2v4bnywwyncqfn68m ,, :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 c4fnj5no)n (nm8fb p6qg jo o9(onstant angular speed (Fig. 8–42). The friction force between her hands and the cln4jgm(f6fjoopn n 5)(noqb9 8ay 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 momentyxw t qbl2rp*u br98:/ of inertia of the array of point objects shown in Fig. 8–43 abou2rl9q 8tyu xb b:wr*p/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 atoms whose t3ta(,nt0hp (:sgiqbp otal 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 cylitcwe6x(z9.t)i)gq 0i -smb k vndrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in .b6zq -))i s(kxtvcewitmg905.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius oeb4(.-yxb d; m(fn rrpf 8.50 cm and a mass of 0.580 kxne4 (mbrprf.y b;(-dg. 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,17k c*p pt6 -mx+tdoh;q) vo*(eozirq2 ,o mqs accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is u 5e6xkih 4oegq08:fo 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 ote ofoh8:kx6qe 5u4i0 gher 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 10,300lb vt);zrqv6 6 rpm is shut off and is eventually brought uniformly to rest by a fri; )qv6rv6lt bzctional 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 7kuvs w.6 nzq97 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the ajg.6s jovr.:.dao nf4u9 tr* action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accel* r:fojjtu.9a.odvrg . n as64erated 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 lo9to6h7 qtg ;ygng thin rod, as shown in Fig. 8–47og;g9t6 t yqh6.
(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 cl: cnf6 5+pkmlonsists 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 from rest within four full8ah7msu13l a h turns (revolutions)8hs1 3laah m7u and releases 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 mop s+ fsj0kpw4 cb6-qeeu 1r22oment 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 of 280 e;8 m jntd-b+r$m \cdot N$ 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 w0dq3cf4+*p 5.wit:rs hyp-kiqwf;r b ithout slipping down a lane at 3.3 w .ydskhf+i*-3rfwp05b4cqt:i;rq p$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of tyt6 6u)2ko(vigtqvt ,wo tetvo)u 2tt 6g6qv(k,yirms,
(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 3zl ta.5k )d7 fvcp7vfand a radius of 7.50 m. How much net work )fp7lz.k v5f3d7 vatcis required to accelerate it from 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 mass 1.80 kg stajpkm3 1i:-rj 5(txbmh rts from rest and rolls without slippingpr k5jbm:m1it 3(- xhj 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 ocpxlpxsms/d7 *a; 97*xl) wucn its tip. It starts to fall and its lower end does not slip. What will be the speed of t**ca xc/ u)x7d wpsls;pmx l79he upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating one z79ajcazjtnc8u e1tu 5(7k( the end of a thin string in a circle of radius 1.10 m aak 8 tzt ce5c797(an uej1(jzut an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentumh 1b0cy )2pbcw of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rocb1b2hp cy)0w tating 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 atvd 7bp1u3ht u1 his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal positibhp1d3 1t7 vuuon, 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 in Fig. 8–29) can reduce her momu/4vh 1y gppa/ /gehl+ent of inertia by a factor of ab /ep /gh4hg/ya1+p luvout 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, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can incx-tk / /xdmc4gqw+z (ts(z(gurease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate o(d gx/ (gkcwxsm (qzz- ttu/4+f 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 througuijy tw,e 1z *:vw(9anh its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg yavunte ,wijz*(w1: 9and 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 of a figure ska+q;g9vy i fmrt(xo-g(ter 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 momentum of thpkgaod5f.,ps :p s8 a*q.b)kt e 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 onts(i0;,slq6d(dw u f tv5e0irx k9c2nvo an identical dis 6euv(d x09iws;0 t d (vif5snq2c,lkrk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ah501,u3fhigyd)2 ew m7 clhfvt 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round ps1x6 vr2rn95we e-sh 683pp bpd6kcv elatform of radius 3.0 m and moment of p59p c vk r6x-6s1 3ewb 2esne8rhp6vdinertia 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 angul vasg/ht0 g/3b2 lr3haar velocity of 0.8bgs0lhratv2 a3 g/3/h $rad/s$ 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 eventu7*7 kqs z8qcwfally 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 the Sun’s new rotation rate be?(round to the neare7sq c7zk*fq8wst 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 ixw c:7.vebsw*e k x3n)n 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 :013wtpi x :iujg 6umu$ 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 rest, tharcg)xc( c*x-ueeiq( ;t can rotate freely without-xx;u *cecerq(gci)( friction. 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 j0g3-l.h3duh1tm5 tvf0 w+bov v p /rgstands at the edge of a 6.5-m diameter merry-go-round turntable3g5hw0b udt+lrv j-hmvv1g/opt f3 . 0 that is mounted on frictionless 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 ground w8ynkw;br g6b:,o(1cl7 ; etd7 sgcdyluz 93s jith 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 8eclolk7b s1; g37,wbn:sdyy(;j 9dzgrtc6u 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 4h68tl a* 5s y1u,n hhf9sxntmre2tf;Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (Intl6hm ;tf8xahh9nnf51ys u2t sr, e4* the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 dou. 8axs p(cp16slg :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 rad:no) f;q 3i;/y3)aooxbcjok1 ec sup *ius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque del/ o*;;ckfep1u)3scnioj: ba oo xyq 3)ivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of t ,y/6sc ie2jwcwo solid cylindrical 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.j,ec 6y2iw/sc 010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheel (maeigfuc2 ;+($\omega_R$) 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 ourqw e-/8nie:rf. qjm5 6 ab;pwd Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the a wq :.b5wrd mf6n/-ji;eeqp 8star 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 us5w;2qya uw ;uke energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 35yq k;2aw5uu;w 0 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an d m5t em6bl.:,zq;va s$H_2O$ 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 h xc sje ydl5nq,db .zak9*,67q ,mxq+ )xpch3korizontal 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.vx vban3z8k9,yp+t zw f 6h(kb8kyj/ 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 acceleration6zb pkb y3 vj8 kzvkh8yf,n+(9tawx./ 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 verticalljlm y*j9 q)( vgzmio(9y on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step i9m yqzvjglm jo)((*9 has height h, where h

  A bicyclist traveling withmlbt +/cszqy,l4x4;v.zxek* speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are tx,yxbsz4.* eqklv+c z /t ml4;he normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling oqogcj7abk8y y3, e4 :bf length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque rjobe kyqb 3y:ag84,c7equired to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as aovn mbk1;y6v :q;v7 x* qd,lrmc w;z8z solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater witvqlq*;6 n;dz 1yzr;m,:vv8xkmw7bo c h outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which4w r,ehr2 8ecmwa p55u consists of two cylindrical plates, of5cpae,wruer 4wh5 82m mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fikm; 0if30rs5.akes*o: p qdxsg. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to rsk3 ak;*:px5q00 sse.o rid fmeach 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 not6dxsnvih:1i8 4 ;yhj b assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduc 8c hy5ftg vkjs/8/i8u8 c;dates its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 5k88s a;8fj tc/v8 igthy cu/dm. (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