A bicycle odometer (which measures distance traveled) is a+ i6;2jdvyyhphc n.sdz)9 c h6s.p(f1j ez s6sttached near the wheel hub and is designed for 27-inch wheels. What happens if you us6s2 6) hnc v+6hy phc1.ds(z.ysdfjis9p ;jeze it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does amgx;o7n (azvjc/2a+i 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 whichag/ m;7vz x n+i2jaoc( cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the ang*b2l w5k..p eugwa- fpular velocity $\omega$ Explain.

Can a small force eveaw y (4da6e6uar exert a greater 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 sit-up with yoo: *eww 7fxk pp:9cjgcb)j, 3m: 3su)3jnud asur hands behind your head than when your arms are stret c3j,u 3j:sp7kf3 dxmowwp:u*jn9acbgs)e): ched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets ah gkxig3ou+20 t 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 sprocko3xguhi0g 2 k+et? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on b ik:(0jkn; xp0z mzo9veing able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain 0 vkzm9k0ixj;p nzo(:why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry 8uq t(5doj8,r9qhi rxbb/d/d a long, narrow beam?

If the net force on a system is zero, is the net torque a *puf iv,d1;.xmz-gg nlso zero? If the net torque on a system is z z*pf ,1x;n-.gvm gudiero, is the net force zero?

Two inclines have the same height bh2 fqg p)z *y3sy+*mpnut 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? Explaifh)* zmp3g* +sn pqy2yn.

Two solid spheres simultaneously start rolling (from rest) down an incline. One dqtxdbdyo/0;ko)/j5 sphere has twice the radius and twice the mass of the other. Which reaches the bottom oookx bqj0 dd/)5d/ ty;f 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 radi ko8b9( lf fffg ee(yg--;se.6(pq xezus and the same mass. They start from f8fgesfzl o;-(.9ee-eg (pb6xq fk(yrest 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 bottom? Which has the greater rotational KE?

We claim that momentum and angular momenx)2u * cpe7lfstum are conserved. Yet most moving or rotating objects efp xc*2 7slu)eventually slow down and stop. Explain.

If there were a great migrat64kw0gzypvu mb5o2 5vion of people toward the Earth’s equator, how would this affect o0524w gkby5 m zvvu6pthe length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatio 1fij)ag 7z ,4sy8*pzow2n 4pjstyvn+n whe+21jgs4zojpt )n fy w,a4vps iz*n8y7n she leaves the board?

The moment of inertia of a rotating solidt6isr wr, 3v ,3rnecw9 disk about an axis through its center of mas,w3,96rrte3 rv nswics 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 outstr v(bmxvb70oh.+s(qc u etched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same?mhou7+scbq(x (v.v b 0 Explain.

Two spheres look identicalgdw/*dhwzu /or t,v ,8 and have the same mass. However, one is hollow and the other is solid. Describe an experiment to detuwr//vo,w gh*dz t8,d ermine which is which.

The angular velocity of w6x-8aop:loz a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a8 wzop a6:olx- 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 increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating tuzgzd3dn;9m me;s 6ri.wtsd * /rntable. What happens if you walk todgs te ;n3;/ dsw6im*zd rm9z.ward the center?

A shortstop may leap into the air to cat)c w+:kwwj-powp1: 2c d*rnffch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you wilp 2ww1ronwd -wk: fjccf+*p :)l notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of co,jb 3n6o l*dgznservation of angular momentum, discuss why a helicopter 6g3d*b,j nl zomust have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radi ;j+ (mwuo6b:c ;pzxcqans: (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 becaus)hpl908g;( i4quswy 0lz2qj r ke eq(ce of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Mo(2;ecwh )4qkzqlsi( jryl 8 g0peu9 0qon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The bejz:qg m jdn9)n 6ckh k;k-vfi3h0uc1,am diverges at ankzqkvn kcm ,h 9un0d- g:)i;h6 1fjj3c 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. Wheg stx9(ozz*7wpxss 0 9n the motor is turned off during operation, the blades slow to rest in 3.0 s. Wha(0xoz9 97s tgzs*swxp t 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 chi4 hv-u 1njh;z )9i*bfoe1 tdxcf7ny:old. If the ball makes 15.0 revolutions, wh1;hv 9nt14fjezohfbdo:n7u c x)yi*-at is its diameter?    m

  A bicycle with tires 68 cm in diameter travj. -t/te m ( 6.ip3xkhfmpig6mels 8.0 km. How many revolutions do the whe et(/tiig.m x. p 6hm-fj6pkm3els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates ai-:ij6 pg,0suwzw :ej t 2500 rpm. Calculate its angular velocity iw-j: i pu,j:sg 6e0wzin $rad/s$ $\omega$ =    $rad/sec$
(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 d e /tw6ivzy++0git .cmakes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the liy6de/i .zi+vgt 0t +wcnear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit ar) dvk scunz(6 -;mav*lound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speedh,vs*r;zjj 2 cjh)ba2 of 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 :qe2cf1 d4wmea particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,0:fqw2 c14dmee00 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly ab3 xqfx-h1g, ymjyr /8ii09wxsnk+ z2iout its center from 130 rpm to 280 rpm in 4.0 s. Detm jh xii289w-yrzskni,+ xfxq0 /y31germine
(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 radiusqk ax0wetv1 -5 $R_1$ 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 spacez cs;b pm0slll .fq;6ar-x6z3 craft 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. Des lxl6q;m ;0.b szpca f3lz-6rtermine
(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 unib9bnx5 1zp 6kmo .-9 hklhcyl0formly from rest to 15,000 rpm in 220 s. Through how many -hy1lzcl09ph.9k6 xn kmo5bbrevolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm i72zj z2f-g -rs;hl0hmrb9k c en 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 highspeed jets in7e*6dr cdds7 ,w bf)1at x:pze a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final spef brdw 717ecdp,dsze* )at6x :ed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.5yom (0c*7cd uc s. How far will a point on the edge of the wheel have traveled iny (* 7mc0ucodc this time?    m

  A cooling fan is turned off when it is running 3)cq2je)zrh9r-ze g dat 850rev/min It turns 1500 revolutions before it comes tj qz3zecr )e r-hd)g92o 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 r tso 1vz+)6omx,n7t25ghbfw pevolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.8ovtfpb z+)t,67wog5x2 sm1 hn 0 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 sxr9o( uz 7:fvngz,e3 npeed uniformly from 95km/h trvu 39f(gx :zne on7,zo 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 lf ;g3kkd1gr. nb75x+zlff/eeach pedal when climbing a hill. The peb +7rgn;ff1zflkldxk3 .g5 /edals 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 wide. What is kv/m)4zfn tzt;c9g 4l-lwu u*qr y swly: 3s/7the magnitu/w 9l44qkgyt*lmt nvu):f ycur/3-;lwz7 ssz de of the 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 f(v gbx37 q*.hun)1f pmjkp/ythe axle of the wheel shown in Fig. 8–39. Assume that a friction torque ofu)p (fbhg7jk.m x1q/n pf*yv3 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 endw.f46hsfzgb70ssmrq l -,dv 4s 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 net torque on this system.s0bhlszmrq ds.f7wgf4,4- v 6

  The bolts on the cylinder head of an engine require tightenin5tyh- tkro,.e3x0t .zh mng4 ug to a torque of 38 ek0 nh.t3xzy tu-or.4h, mtg5 $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius irm6*g :)cahbpksy 8 )0.648 m when the axis of rotation is through its center.cyi am) :hpg*r)bk86s    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyctm1z 4 :izj;dsle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg.z;jm sz4t:i1 d The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball og6rpy *s28.iy r ayyg+n the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calcuyg2y i 6s +aypr.yg*r8late
(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 pottjc(o )t znjb7a/ jsfn ubt: mvec2ah +.0t1i46er’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her h+na2 0bt7 ja zij61n 4svou.m/:ch)t fjbtce(ands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shzrpgh0.u 2 d0h fmtxhdx- 106yown in Fig. 8–43d1mu 0hdr6pt-x 02xz.hg yfh0 about
(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 a5wb) h(fjadi 3q1nu/ptoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, engintikfqqtej 9 ce+mjy.(.em( vs96 7n4weers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a rv mecq(k6eqst 7f(n 99m.4jjiy+ etw.adius 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 cylinder with a radius of 8.50 cm and a mass ofwxf3qr1pp:(x3k/ f; qew:v g1wwa( xnkpn+ : d 0.580 kg. x:r+p(wq x3dw/wpx 3 (wg:1 pk: fq1avkfnne;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, acceleratingt8z3 lld:h( 8 /qj2 .al ujpjmzll9;rl 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 hanb)wty* 8m )qqgd-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. Calculate the torque required to produce the acceleration, neb8)g)t w q*yqmglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm/hdxk 1t5gt .f is shut off and is eventually brought uniformly to rest by a frictio.xghftk 5/1tdnal 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. 8–46i+pwlqs fo s8 d 9cw4c86j*od6yd2c r5 accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown8an g )k30eq+(fo q.rvt3/kdt pot9pd solely by the action of the forearm, which rotates about the eldfg3oq0dak3. pt+ nvt8/oq9rk)(t pe bow joint under the action of 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.8t0 d pastr p+r7i9tx can be considered a long thin rod, as shown in Fig. 8–46t.tp7 8xtpa+ir d90sr.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masse zd1g.ry (1jfer5sec; s, $m_1$ 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 full turns (ry i zh+mw ; aojh22/8+njeetv7evolutions) and releases it at a spenwmhi+z/jy7eva o2 8h+tej2; ed 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 hakmb ymlf 8,,m+hin 1e0 nmz*o*s a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a toea/+h4qq 5wn wrque 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 without slng:(j8+n j qj(xiqpd7 wz1qe;dq/r 2sipping down a lane at 3.3 qwqjsn7; pq 2j(r1g(8i+ jdd/ex: zqn $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of tommvkexi1tm; * r34(zwo temeo k43t 1m ir*m;(vzxrms,
(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 radiuwe*pd g/hq6 8gs of 7.50 m. How much net work is required to accel d6ew 8*ggpq/herate 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 starts from rest and rolls wi spw/*k)0; 0fmv, ;fdtmtj srlthout slipping down a )jt;kdswfpr*svtm0m f;/l,030.0 $^{\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 balanfs 5n )an0wiosjzh4 a .vuuerm8)- bxn5f6.0cced vertically on its 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 it hits the ground? [Hint:-bixs5). no.0rw u h6)5efafjnuaszc vn 40m8 Use conservation of energy.]    $m/s$

  What is the angular mom+frlsk*zt,y5j x +au ,entum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at za*t,, f+jr5 lky xu+san angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheigg .3k:pl9 uqel of radius 18 cm when rotatg3 .:upi 9lgqking at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his d urs lobs**)3h ckys b24x((i/6luy jside, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of r/3ou i)y4hjr lk* d( yb* x2uslcbss(6otation 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 F0-bgji6p e dq)ig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuc0qj-g)i db6 epk 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 avbt2s*2kx ( ov9rvkq *n initial rate of 1.0 rev every 2.kvrxko22 tvqv(*s9b* 0 s to 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 rota3omn03n 9xzq nwwx .zp .aju/fc2 4+gfting around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and f w gjonzcz.. wx+n2m0uq/xa39fn3p4 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 kyqyksk6w+p8kk8)(e5caf upae .9t. of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momeis a8 k cov,s h70pew9dfu l6s5 /mhyb355qi.untum 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 dr:kyb8 yk sfg) pfqn,s2l4l ;6eopped onto an identical disk rotating at angularsyklb:;ke sq2 )486n pfgyl,f speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2,oryxh es *nuj;u*5v3.4 $rev/s$ 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 centerhj3 *wlfhscqqk+j0 ,9 s k7)xf of a rotating merry-go-round platform of radius 3.0s *kw l)sj0f3fhj9,7hqx+qck 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-rib k;lr+z7e*;56/ sns 0c3oinj mccq mound is rotating freely with an angular velocity of 0.8 ;c730kisbjrq*m m56le zsoc/+ nnci;$rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing aq6x3l,z v9jbubout half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away vqjb,93l z6xu no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve wifyvck: , b(h+.aogd* 3c)z nhonds 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 aetxup*6ua4qs.* d) d $ 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 rotate fr,i0:uh q5gqi.k nh46dnifu) q eely without friction. The moment of inertia of the person puni.f ,d5 hig: qihku nq4)60qlus 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-igf e6q1 z*krf. *d-nlm diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of ing fe*fq-z6.n1lk i*d rertia 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 the end of the rope 20ze+tbg/pfi lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from tf/ b+0t2pig ezhe spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that e 394c8w j1nkgll asc.the same side always faces the Earth. Determine the ratio of the M.gk84sl c9jn ea 1w3lcoon’s spin angular momentum (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 acceleratesl6 sq4z(,e /frmquz/g from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acqz8;q xt+cgu)+r -qfqbuires a rotational rate of from rest over a 6.0-s intervalc) 8+f -tq qugzbr;+xq at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two som/fd+ q:kl ,m3 wsk:jylid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrkm/l sfk:dm3,j y:+q wical 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 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 re(g+p0oye w z(gar 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 o. utrzvj 6pq32/r tq ,kgl*3igur 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 undl3 v k uptj,qi6/*.2rg3rtzqgergo 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-poll5wyl2q hat7:j+ 46ab0josfxi ution automobile is for it to use energy stored in a heavy roaf7x q6jy40b2il5a+sh :t wjotating 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 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 anrys *u dj9w2z1h9rht / $H_2O$ 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:e8 d*g*5m llq2ubqa lp7h;km horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore f s.pbm6kih:3-t8xuefriction) about a hinge attached to t6 xi u.:8 -pbse3khfma 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. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floq.c:j-niiauh* g5p4 zor, and we want to exert a horizo4:.ziuh-j gcqp 5in* antal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is makin9kd ss+atqs5r )5w5dv6c c+ ahg a turn with a radius The forces acting on the cyclist and cycle are the normal fora5+wcssak s9v) hdc56 r5t+d qce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 5use14m j(bkxn ey( ; jgzrhz+58il k)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 r jjkhs iu(xe8(1lm5n +;4rgzb)5z ykeequired to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her argr (-ldkah:o 85r;n d ,ween1bms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angub;rrkndd5e g1a8(hn, lw:e o-lar speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindril1 ze )z-4sou xxt7 px u9t2q9/m-lfamcal plates, of masz1x2 l-ml uu -xmq4a9tspx)et9z/fo7 s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rsz -waci*io(8 rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leavi8 i(* iscwoza-ng the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, butkyya2y9b n+1 ) gpxxf; do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces itsz 8b+alt*fqcpycq2 l9n+ ;19 8stpwco0dyc y 5 speed uniformly from 90km/h tofcw y9ayzosptc19c ltp c20+58 q qdn8l+yb*; 60km/h The tires have a diameter 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