A bicycle odometer (which measures distance traud)m7x0* booejl, j)- kdcne1veled) is attached near the wheel hub and is designed for 27-inch w 7j)b1kx*lj modo cuned)0-e ,heels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angulkenyo.2 iwt/4rte 8vba) ,;plar 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 eithr8. y;vptabto4 eli w2 ,)/neker component of linear acceleration change?

Could a nonrigid body i,lc7q 4bcf6dbe described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert arek *cq f5wt-tu-*9rn 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 wit 3/nb4va jss8 +hyen8gh your hands behind your head than when your arms are stretched out in front of you? A diagram jb8e va/hsny +ng3s48 may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel a2iw/+ 4qhmm h s21syxand three at the pedal cranks. In which gear is it harder to pedal, a small rear ah2m i2q+ /ys14xhswmsprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender low:vcke 1cpi0n *t71b gher legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, :gbkc*e v17pncth1i0 explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, naga5- ;wmhx27( vyo voc9yvb-t1j0rj qrrow beam?

If the net force on a system is zero, is the c t 50vflnqn-2net torque also zero? If the net torque on a sc5 2tv lnfq0-nystem is zero, is the net force zero?

Two inclines have the same height buk,qjfl w8+ 4gp:vms)c t 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? Expla+v4fc:mgj q ksp8)w l,in.

Two solid spheres simultaneously start rolling (from rest) down an incli-gogm3o:6u ( ieln z8 n9+4z nyilnfp9ne. One spherelu8 gzn ynf 3+(6z9oom glpi94: ne-ni has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the sa mvr r,y7cxy8*me radius and the 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 bottom? Which has the grx,rrc8y7*y vmeater rotational KE?

We claim that momentum and angular momentum are cb; 8j 0n*w)s xlmwzef746ti fsonserved. Yet most moving or rotating objects eventually slow down ;jltw67w*si) n e80zxf4fbms and stop. Explain.

If there were a great by7 oh56e2vrzmsy +n7migration of people toward the Earth’s equator, how would this affect7vy +5em n2hr6yzs 7bo the length of the day?

Can the diver of Fig. 8–29 do a somersault withouo1 xgpt ed;mcaxen ) do:.l6t9okw*, 3t having any initial rotation when she leaves th;e l :gxmtexot w ,9kad)n3co.1p6*ode board?

The moment of inertia of a rotating solid disk about an axis through its cgo2m.)/ cnw1a s z(czzenter of msozcz(c/1z2g )n wma.ass 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 stool9;d,xay.t q s0/3rcm)rzrvol holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity ivlro30z9);s .rdrm / ayxq,ctncrease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Hok9sqso7 ;a3ktwever, one is hollow and the other is solid. Describe an experiment to determine which is whichk3s9 at s;k7oq.

The angular velocity of a wheel rotating on a horizontal axle p/j+rf,nfg- g+sf q:9rqgx , nn2tzh(foints west. In what direction is the linear veloci9rgf t2 sz+f,+ rx(,fggq/nn- h:fqnjty of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Whfg91y9j 33awn9sdw.p6-jn1ivqu oa k at happens if you walk towardy.inf u3kj9 paw19wavosg3d 9-jq 1n6 the center?

A shortstop may leap into the air to catch a ball and throw itq 0r*;9;jxw xkmqe+fm quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that *0qmk ;w; 9xq+xef rmjhis hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservatinwi2nd;4;jwc2 q x t; 8gng9skon of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stknq gj n;9 wis gnwcd;x2t;428able.

  Express the following angles in3cl*3jx an)w) mw5ivv c2cmc:z9 z5tn 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 amazing coincidence. Calculate, using tho 0r(8t1zld+ )hnadspe information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moondl0a+ot pr n 18)(zdhs, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges czbtlyj*d +46mmin72 at an angleb*24ydml+6 ct7 znim j $\theta$ (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 rpmkle ii0izey/z 1kkua/-bw3 w h9a:/g /. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slo3wkzeyizkl-w9kiu /aa0:eg/ ib 1 // hw down?    $rad/s^2$

  A child rolls a ball on a level flob*.lw:pqh1 d 1v xps1eor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its di1epqdhv bp x 1l*.w1s:ameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutisf r v.5( zykw),a:joeons do the wheels make?kvs oz,)jwae.(5ry:f    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calc(ly9 kxmc gj h 889brsc71rk:yulate its angular velocity ib(78:k9rjrc 9lm1hgcy8 xyks n $rad/s$ $\omega$ =    $rad/sec$
(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 izjntr5f j ky;)x2ui07n 4.0 s (Fig. 8–38). (a) What is the linear speed of a jkxt r5fz7j2u )yn0i; 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 orbik 23yca54nq48oviac vt around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point lpnccka;9a ;6l: klbkb g-(d,
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from th 0 xq5qgwau z5ig yelr57+fa-3e axis of rotation is to experience an accelerrz+-exi 3g al5 af5quyw0q7g5ation of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its h.7)sejt-i*3zzp h jacenter from 130 rpm to 280 rp )*j-zhzj3pae.7tis hm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu a sc18/x+t13op ztispjnf0jib0 jr,)s $R_1$ 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 (r )m*a5(ji dow vw7luru7 )btMoon, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distributeju(7 5rbudw)wt(rvol*ia 7 m) the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from reslq n m;bmty cl-v8,54ht to 15,000 rpm in 220 s. Through how many ,y;8 blhc5tq -mlm nv4revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculx: fgx2mtb 5.km/,q zmate
(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 fl6 jd;c0g6l mn7v6 taajs)i fw)ying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its ffm ls6 6c;jn6a)td 7 vw)agji0inal speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.5 2z(vcjly*8n b s. How far will a point on the edge c8l vn2*(ybzjof the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runniirb87: n+dj0v jyfy-c ng at 850rev/min It turns 1500 revolutions beforej0 vf+i dc:ynyb8jr-7 it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reducesuj.: 0nc8rti 4 88 iokvgsimx- its speed uniformly from 95km/h to 45km/h The tires h-sujk.808ri n:im8vtgi xo4 cave 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 tve,-ff/l+pq lhe car reduces its speed uniformly from 95km/h to 45km/h+ll pv-qff e,/ 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 pks))kl 9z+h wxbi (a6uuts all her weight on each pedal when climbing a hill. The pedals rotate in zhik (6 askx)ub9)w+l 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 cmla ow47e /gc7c wide. What is the magnitude of t/o4l7g c 7ceawhe torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39aqg knl(d2a 19yfvxw:uo )+ tatm+,n7. Assume that a friction torque oxl+ a tm:ywf ,qvgn+1t (o29)7 duaaknf 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod7t m8 h; vj-u st.ga3wfxah9,d 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 syst;9,m jgsu7.8d w-afthxta 3hvem.

  The bolts on the cylinder head of an engine require tightening to a torque of g:gwp( ,wgda 038pw:(,w0a gd gg $m \cdot N$ 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 spherf a ch(l*ky*k 4.ux:tgo/,x,mlv8rc we of radius 0.648 m when the axis of rotation is ut:faw hx r k8lyv .,l(k*/g,4xmc*octhrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm 4 0yyniiq/u8 npn;qgi iq9c,5in diameter. The rim and tire have a combined mass of 1.25 kg. The mi p;0n iqq, uyignn5y i48/qc9ass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotat ox qqn.rfqbyk:(9sj o67y( 3zed in a horizontal c3 yj qkyqqof:(6zn sor.x 9b7(ircle 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 potpw 1sczffy9,b3+un ; hter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 13b1f y ,u phz+fwc9;ns.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 olm+/x lrl zg1 (kalhr*w(: x2sf the array of point objects shown in Fig. 8–43 aboutr/lx m*l rhl+21 glxwa:szk ((
(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 ag)y cw/gy5 o )8.n 0/dzjhcdetotal 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, unifo c:(ujz *gnbw3wtl xikq47laru51z9- rm cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass ofzn1 b(7twgju-u4ql 3r zx5*kw9 :lac i 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 cylinder with a radius of 8.50 cm and a mass of 0.zsx:7e;k b8pzbipp rr( 8 s0x6580 kg:b70rxr zpxzispe 8sb ;86(pk. 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 / sl+vm(sx4 n;bj,a bebat, 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 sf64vn qh pb dp*5viv(+mall 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 edgepdv bn( +45vhq*pvi 6f. 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 rotat87 tu/yb 1n*qo) njdcuing at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torqdqtu7cn* )yj o u8nb1/ue 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 accelerax 6z0+jl7otuxz 2hq2ezf2p8gtes 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-kiicd y y s:kxnf0pq ;44bh,)8vg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the t4 4 )8xi hbpycvkqnif,ys:0;driceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be g5uur bnygrtr ;8mh8.fi/5j 7considered a long thin rod, as shown in Fig. 8–46. m gb75j/5rurf8u8nt i .;hrgy
(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 consiswe pf (mk ,cznqw3-54mts 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 full fw utedy1y;:x kv:,zl li20 :kturns (revolutions) and releasef xw2t 0ey:l:1 dl,k;:iykzu vs 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 momen/og6ju3kbwpe x(-s zo 2jb*z6t 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 jc2p+ 4yh+l9:y) b2bdccn hr+a tz+ ii$m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg andyy/r: :e mg+hbj9x3c,19dfg7 i bnm rm radius 9.0 cm rolls without slipping down a lane at 3.3i: j 7199+nfy/brymdm: ecxm, r3gbg h $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with res m bhs4;ure(c6-z(fhfpect to the Sun as the sum of two terms fs4fbh(z ;( r-muceh6,
(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 muchhsgwx 5 -7a-tk;f +btaipz s-. net work is required a-hs.xft7wk g-- p;is5taz b+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 mas+7.ow8jeof 1gkj-e7g(oe wxx0 y o4 pys 1.80 kg starts from rest and rolls without slippinggoo fexe4ejy+g w(.opj ky7ox 0w1-78 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 qz0biyg7j+ dio1m 4n5 -x 02occb ld,obalanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of tz,bd7n2+lo5 xjogdiyo-c i10m 4 0bqc he 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 0.2;o:adamdch 9r(hu:al 7oa l/ +10-kg ball rotating on the end of a thin string in a ci:hhldo+am c/ :l9u(ora;7ad a rcle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg un* 4 .ns usqn5b2i,drydiform cylindrical grinding wheel of rab5*ni.q rn4,d 2s sduydius 18 cm when rotating 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 side, on kk(*54mtxhaeo1j m+pd 9 ,if ba 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 9x b hdi, f+je k*4mp5t1mk(aorotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the on4 kd2nn pe*:wi ; )ml8ilws2tje shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed (nlm8tkiws 22e4p;dwlij) n* :$rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation u 1o17y(jeohp,l)au frate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3 hyjupul1ae7f(,o o1) $rev/s$ 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 aro06(+/fu p( iyhww xwnzund 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 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 centerw/u ihnxyp6(w( 0w+ zf 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 s./d v2 4avoxnfigure 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 momentum of th v3(ecy; emn g qa.l5ix9gob5.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 2 2hzd.cmh8u3 cc 6fradisk of moment of inertia I is dropped onto an identica2a8hc6fr 23zu.mcd hc l disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns abp/+ru:d,yk rn7lq2(ou5 lypt 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 centqt- 99drwgaw1 d q3p.lew)h-m er of a rotating merry-go-round platform ofawrdw-e w lpd9)q h-gm.q 1t39 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 5l)4vwo1 hfkx3oo 9 rorotating freely with an angular velocity of 0.xfk rvo lo4)h93owo 158 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half its mroaxab vas4 s42 9p)s;ass 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?(rour4;sb9o aa2) ssx avp4nd to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of gy6bi(3 7r-exv df, ea120 $km/h$ 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 c 6zosm8hezp63i me5; $ 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 freely 0w0/6yx sttbp,.qsgh without friction. The moment of inertia of the person plus the platform qyp0t,.t xw /g h0ssb6is $I_P$ 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 diameter38b--a*lor7ua p njzp merry-go-round turntable that is mount-aubpl 3 o rjn*-7a8zped 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 with the end of the rfob. g8nqi,tx, kbe j*d26ls8ope lying on the top edge of the spool. A person grabs the es lnfgqte 2.i,xo b8,bd*j68knd of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same itqm -(fc ifu9*(xtxx- (+etoside always faces the Earth. Determine the ratio of the Moon’s s+(t9t--c q xxeu*xit(mifo (fpin 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 accelerates from rt*-grcipfk82qdcw .x3 lx (:t est 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 cylig 6zk(spmi+ixt) * *umm7u l0knder of radius 0.20 m acquires a rotational rate of from restx +7mtgpm s)kiu* 6l0u*(zik m 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 twmdxrz 17ce9 q7o solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindricdrq1 cmxe9 7z7al 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 rear wheel. tc w(2rkp9gd.ow 1zb ($\omega_R$) 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 wi-h a d /q8l;otj1vrf39s1rxk2z yn vs3th 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 x9voh-sntk2 3j38f/;r yz rsq ald11vkm, 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 l8sr.4g6 hher; b ykuv0ow-pollution automobile is for it to use energy stored in a heavy rotating flywhe; ye0br6hurgh . ks84vel. 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 illustra1 vd;h9wg;cvu tes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal sur.ucl7q aqdb;l* 3vg 6xface 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 lengt/mc rsm9mp gpx,+jc;7 0a:me rh L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]prm; 7psge/r,c mjmc:m+09 xa

A wheel of mass M has risbu x;vcz9u3a:66 czadius R. It is standing vertically on the floor, and we wantuxs:cv636ab9c ziuz; 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 has height h, where h

  A bicyclist traveling with speed v=4.2mln.mjb9 :b0mg r 8,xam/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle lrb9 8mg.m xj0 ,a:mnbare the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 74ns v 2lgcd3vm 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 torqu d2gvv47s cnl3e required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid +4t8os pu-aur 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 a o8s4u+ upr-twith outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plate a2+pt)y eu5uwsz4 d;ls, of mass s)24 ;+lpz uwdyut 5ae$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 kb)+w93xju z xradius r rolls along the looped rough track of Fig. 8–58. What is the min3wkxju9 zbx )+imum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do noz 6io*o bpg3:yf5xd ,ht assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions37f xeone/ / ff82nawz as the car reduces its speed uniformly from 90km e2f/faxzfe3o nn8/w7/h to 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