A bicycle odometer (which measures distance *3:m h.ubla vu i2n;yutraveled) 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 w.ub;vu: a*n23liuy mhheels?

Suppose a disk rotates at constant angulag sr- fc*bh. :b2ossjv8x ai. oi.x9+yr velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either compo-v8oia9.cjs bxoxbisr 2 s+h: . .*yfgnent of linear acceleration change?

Could a nonrigid body be described by a single value of the angulco,c+fr .cvpodu o186zu 7mq)f,y (poar velocity $\omega$ Explain.

Can a small force ever exert a greateh p4/t-wv5loccrk. wsr ()u9fr torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a v i.k- ;f:xub73 /ea(zmgmesksit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer tmzi-3gua /f:xk v7. kbem;( eshis.

A 21-speed bicycle has seven sprockets ci --62kuw*tjcn vluc+ihk2,2s 3ger at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? ej2*ci-wch gk lv-6t k3icusn,u+22r Why?

Mammals that depend on being able to run fast have slender lower legs with pjt;;bq .hu;y87bycl cs6k/ rflesh and muscle concentrated high, close to the body (Fig. 8–34). On the basi7r;by;sc .kt u6 ;qybhjl/ 8pcs of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fb gmj th6*bap4;m6u)x/3fr xv)0m.u g nivkt 8ig. 8–35) carry a long, narrow beam?

If the net force on a system is :**u*y 3ejgca , zhfwazero, is the net torque also zero? If the net torque on a sys:c e*g*ay z ajhu*w,f3tem is zero, is the net force zero?

Two inclines have the sam ,hi8dcttw o-9e height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Exdt-c,w9iht8o plain.

Two solid spheres simultaneously start rolling (f:*sx:w3nptr qrom rest) down 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 there? Which has the greater total kineti n:qrw 3tps*x:c energy at the bottom?

A sphere and a cylinder have the same radius and theol93 qot1 x9fp mjki.4*ukko; same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bm 3o94;ok oqik jlft9p.x* u1kottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conservedw ,1am9/x*f -fcugeh r. Yet most moving or rotating objects eventualhf-m *1rguac 9xf,/ewly slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, w6+yqv3 f:w(seybm+a z w/w8 khow would thwyq63ws+f8e(k/v:wa+ w zb ym is affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any inw3bs) vk. 6tqrqlf*vq;dcoz p/-i7 1nitial rotation when she leaves the board?no ; ds) 1q6i v3-wt*rf.q7cl/ qzpkbv

The moment of inertia of a rotatih4rl4 4ukjp;* 4wrsflng solid disk about an axis through its center of ma;4shf4 u 4p*4 lklwrrjss 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 ac.3cqxo,,.jc ox ajoqraqk4 k +7a8w1 rotating stool holding a 2-kg mass in each outstret q.cjoqkq4xcca,7 x 13oo ,a8wa.r+kjched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the swoctutrmh73zina(w e )8;+ 0 zame mass. However, one is hollow and the other is solid. Describe an experiment to determine whi0zm ( nratzuw3w+7 c e)o;h8itch is which.

The angular velocity of a wheel rotating on a horizontal gyu1tbx8y2;h )*u b0vlafr q)o, 0 msiaxle 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 ofb;g1lsuh *vo)fy qa8),m0u ti 20xbyr this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge oxlcw4(1+p mmnf a large freely rotating turntable. What happens if you walk toward the cen1xpmw m(n4 +lcter?

A shortstop may leap into the aiynd1)oael6 yo ps 0,d7r to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that hi y)l dody6ea,1osnp 07s hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angulay:s s gf 8ublt;(w45ecr momentum, discuss why a helicopter must have more thg5wb:y4( ;ufl8ct s esan one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the followinglyt( - *kiy im6gvi.dvo44j8p angles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazingtim -m**a rd3)j7km rq coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.ka*)tm* 3qdr jm i7-mr
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The bk1(sp+ cbm gk7g3x( xmeam diverges at anx(kg17mk(+bg ps xm3 c 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 rota5o e)bw9gr7ebpj/1 mcte at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blade/ 7bjebgropc15) 9mwes slow down?    $rad/s^2$

  A child rolls a ball ondm(l q:zhtu *67ah i-l a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is :lh -du(6imhz*tq7al its diameter?    m

  A bicycle with tires 68 cm in diameo 5ua1 n. jth7egybgev(p3w b:+i i46dter travels 8.0 km. How many revolutions do the wheels make? gbw:ij7t e6 ahn+5u(.i14ogy3vdbep    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its ang5b1hm 9a :ifoaular velocityiaao5:hm f 9b1 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 (Figda;kge28; rpg6 z3j rs. 8–38). (a) What is the linear speed of a child seated 1.2 m from td;2; srje3p8 6grzkg ahe 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 itsz2sh e ho2g*qex6*7gfzmw2+p orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed 9 d0citm;h1 juof 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.kan7a0 l 7+aws0 cm from the axis of rotation is to experience an acceleration of 100,0000lsk+a aa77wn $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its a))csy gxzxk00* i huqg))j4fcenter from 130 rpm to 280 rpm in 4.0 s. x4 )0y)a0z )c)*suqgjkgf hixDetermine
(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 radiusjipn (3y4),s gdod z+l $R_1$ 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 theqn d7uy/x0ik1a b 2sr4 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 of as a cylinder with a diameter of 8.5 m. Determin i2 /dbkqx041anyusr 7e
(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. m ju75ryk znmtnf4. t0fckt1m,3uv)4Through how many revolutions did it turn in this mzf fn, u.yc43r) 5ntmtju4 1kmk0t7vtime?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcu9g17x d90g,;idne qlow04erf fgip w)late
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in wfx s/90upiq;a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions i/; 0xqs fup9wbefore 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 diamk z35dq+ bwbc.icz;4on e qwhn5-li+;eter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How fao ;35l n.ck icbwi5+hb z;-qwne+dz4qr will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off w.etr3n +24vr d8m pjjbhen it is running at 850rev/min It turns 1500 revolutions before it comes to a stop.4jmrjr.dvbe t3p +28n
(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 revva)ylxw/cgw c4rh20 hh dv5z.7nw i23 olutions as the car reduces its speed uniformly from 95km/h to 45km/h Thevncw2z 2w)l h w7 40rh5diah/y3xc.gv tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reducl0 ,smx09 i,o 0dsmbwr68rhxoes its speed uniformly from 95km/h to 45km/h 8,0oix msmwl9 b0or6d h,r0s xThe 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 h0 a1jn xa9zxw:er weight on each pedal when climbing a hiljx0 :1 xnwaaz9l. 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 jon u80-fqw (xof 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if0xqnu- wof 8(j 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 shown in Fig. 8–39. (8gb 2nqls m7hj( *skcyne8 ;x29m zjlAssume thaqjm8 g( 9sj* xl2n8 (bnych2ls zekm;7t a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the endsh0s *eiajltxhu9rv h)s*9: ) o 2seli3 of a massless rod which pivots as shown in Fig9 hh :iijs3*t9la)sx sl*v0)r2uheoe . 8–40. Initially the rod is held in the horizontal position 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 tightening to a to3grchk clz3qp . 7or*4rque of 38prclhok4r3.7gz3 cq * $m \cdot N$ 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 o6gc2t 46-w sebvq,4m, m sggbuf radius 0.648 m when the axis of rotation is through its center.g-264sw,muvbggctq6b ,s4e m    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. x4ckfn4;bqcn3 )z ru77 hc) uzThe rim and tire have a combined mass of 1.25 kg. The mass of c zqrcx)c)b nuzf;hk747nu34the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizo/pazz:iog ql 8f ser)(: r6.apntal circlsae or8:)qizg (.6: r/fpp laze 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 potter’s wheel rotating at constant an+p8ng 1rr **e/ 3 k,oeddopfcqgular speed (Fig. 8–42). The friction force between her hands and t8p ,d 1p+*oeog3cf*rqndkr /ehe clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of p8p7zh4bu wqy z/j:,wcoint objects shown in Fig. 8–43 abo:8y,jzp uc 4qbw/z7w hut
(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 whzqkb+ rt 3r nn 0k3wv-2eelz:(ose 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 spinningn 9 2coa74ioxzdk kogt*8 .*fe at the correct rate, engineers fire four tangenko* 82 nxckg*9.z7o f4 tieodatial 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 :mq3xj5lc f, tcylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calcullj,tm3xc5fq : ate
(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 swin o zjnwefit5-.6r2af: gs a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangential(2 mh6fa6p9w1h ytc-zei r 4tuly on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. -f2ihpw(tyhem 694c6 z t ra1uCalculate 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 rotat t9,t w fwnp.o.vi-1zving at 10,300 rpm is shut off and is eventually brought uniformly to 1wf pv.vzowt9-t.i ,nrest 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 blit0rd (-60q/gyqm: ,b llouy all at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball lp6zium;cb85 is thrown solely by 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 uniformly from resi zbum;pc58l 6t 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 be7 f8jqfzq */h 8)yddaubo3p2 e *y0ifm considered a long thin rod, as shown in Fig. 8–46j*8 f8e qba23/uy0 )p 7o*fddzhyimqf.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of t ,gfktzg0 8oe(wo 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 thebbi;q6y4syk.* q) dyb) bk0i,k fhf)r hammer from rest within four full turns (revolutions) and releases it at a spebif) ,qisk;brkk.y )* by0hq6fy)4b ded 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 ofez(bevff-f*/ 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 ovp0 evi.js ,+r tn:3ca 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 witzl )4d/vya kb;(k7dv uhout slipping down a lane 7 v/zd; u)kab(v4ylkdat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic enenqiem*kic fuh sulv;/ (r0h1 ,isd37;rgy of the Earth with respect to the Sun as the sum of two term31e mivn;s,k 7l*qchh ;(/fuidisu0rs,
(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 muc)o4x n sckb6 3a;9ujx q;vm1msh net work is required to accelerate it from rest to a rotation rate of 1.00 revolution p 3vsx ;bxj kms9c4n qu6a1)m;oer 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from resc9mo)+w qyc m- (faq9nt and rolls without slippo9c)9nw - cmyq+mf(qaing 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 .)( g*bdx nyr2ymqx u(tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before ygmu(n(r) dyx2qbx *. it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular mo3g gbjosre)n( 1k; e,ff7h9jkmentum of a 0.210-kg ball rotating on the end of a thin string in a circle okhkg )e31, s;ef7gjr9ojb f n(f 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 cylindrical grindinggm agc6/ 5mw/d wheel of radius 18 cm when rotating at 1500 rpmm aw/g5cmgd /6?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side,6fw/ fcn8l 9it on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal positionwlt8 f/ f9nci6, 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 moqcey-c+e u5/t.9ipa zment of inertia by yztau+cpe.5ic e-q /9 a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation m mo(s//*- n nftgsgcwxy +34prate from an initial rate of 1.0 rev every 2.0 s to4-gsty(+s x mwc3g/*pfom n /n a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vx*pf fil)9j3nuxo/zn qp4u + 2ertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The pun 4 x3lnp*fxi )qou9jz/ pf+2otter 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 ofzp 8uqsr)m +2w a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular )fj)3+jcwft m 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 idq4 cm/noyv:0 xentical disk rotating at angumcv:y4o0nxq / lar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 :d9 cg4my+iq4lqgy)e z7 .o rt$rev/s$ 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 rotaz0y,cdex9,vy bn ju)r2hl t1,ting merry-go-round platform of,y)r,z02y,u v1n t xblc djhe9 radius 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 acu9,gjx ,ob/cn angular velocity of 0.8 9,,jocgx c/u b$rad/s$ 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 dwacy3jcxbzn6m4h /wjl r n18a).rf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carrix3m. lnjz4cn r/8hy)ja1b6 w ces 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 involveobk1n:71nas x63tde o winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass qxs n(e4k .lfwe-/;ln $ 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, that can ro(hun559,jl . dfkg+gwao6 nen tate freely without friction. The moment ofghu6 ng.dw9 5n (+f,ea knlj5o 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 6.5-m diameter merry-go-round turil,j( p;drcdb t)*1wintable that is mounted on frictionletw jdi)i(pb;r 1dc*l,ss 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 with m, b6l pknzif +0d-or7the end of the rope lying on the top edge of the spool. A pepfr,di0k+zn bo -7l m6rson grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth u :d*plm)j5o vsuch that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentom pu*v :l)5djum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from r2:fnf-mm z+s gj3z6skest 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 4gf19r6 pvd :k67thr90si k2oknbfi;gu i ez*shape of a uniform cylinder of radius 0.20 m acquires a rotatioknkbr1i7*9ie ; trszvp96gihkfo 2604 fd: gunal rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two so bsygmx slb,vemk4 404o :49filid 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 0.010 m. Use conservs,:mks4y4i 94l0 bbgv f4emox ation 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 *muq4 k , -bpb6*a ugrrx9w9y p1excc.the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, wereb 6+o2pxh3snc k7xhu+ rotating atk6+3xh ux2 ch +opn7bs 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 mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is fo7h1u/ dea7n t.-e epxzr it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform edxez7p1h.7e / tanu -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 an v16ogyr cjw;- $H_2O$ 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)ro(u:7mhnr4nwa1wv r*a a;w8 r : vc-e is rolling on a 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 ,( l-ke3q27kgrjgi sv(i.e., we ignore friction) about a hinge attached to a wall,3g l, k( sevrg7kqi2-j 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. 8–21g.]

A wheel of mass M has 9e:j4c0n wllrradius 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 a step againslc nler4 j0w9:t which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s y l7 etzteh3mmg28-f/on a flat road is making a turn with a radius Th -eg7fmlm3et28yt zh /e forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock in/ gk v8seq-3p)bpxest nkq+b5t9 m8 7bto a sling of 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 required to achieve this fea -nke)xbg5v 79m+st/p38pebs qq k 8tbt, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, mak0h6-*u;, a3 0wsxt2nrkd p v rzcgmse(ing reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a rknep02uz,-rtg 3s mdcs;v06 xh( *awspinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical clg-ay/--wp bt gpa,a3x8ojsib6 r3: plates, of masyat63g3bis8, -rpalpj- :/ob -ax wcgs $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roulzp9de2vk )f6 gh 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 )9z l62kf dvpehighest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not 5h1d5r6oq.eg d i4m uy( y ..fsgd0zbzassume $r\ll R$ h =    (R-r)

  The tires of a car makev1fcs l )h,x*a 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diametvcsal*x1f), her 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