A bicycle odometer (which measures distance traveled) is attached near tx ey.rv8z* ;kzj6j(khhe wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheel8kjj*6.z; ye (xkzh rvs?

Suppose a disk rotates at constant angular velocity. Does a point olk11hhm:2 3 foion,uon the rim have radial and/or tangential acceleration? :1oflmihn kohu3, 21o 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 component of linear acceleration change?

Could a nonrigid body be pk .wqoay+f qc66s- ;vdescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Exppbkej-i. *p ea9c 1(1v pyzi6dlain.

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 your hands behind yj8w,wf ;wfm vhi.1 3bt py(6prour head than when your arms are stretched out in front ofwbvm.i(w3 f;rt 61 h p8fypjw, you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the peda,ffe7i. aftyw 7* z1ndl 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 std fn7e z7wfyaf1*.,i procket? Why?

Mammals that depend on being able to run fast:8ktn)hqoo0 (, bhvxm have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On t )q h:oht(v8xonk ,0bmhe basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow b i-ldy5xk5ja ( so51qqeam?

If the net force on a system is zero, is the net torque also zero? If the netdluf 9 5iy ose etos:n*u:5x32 torque on a system is zero, is nei5esyf:5xs out*ld o:u239the net force zero?

Two inclines have the same heigh4;fogsxv ;cb 6 alm(q1t but make different angles with the horizontal. The same steelg;;x 14olm6 vqcb(s fa ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. Ozrj7co+7b g :*w4w 8vjekmpk8ne 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 totakovemg*+cp7z 48 j8 7jkwrbw:l kinetic energy at the bottom?

A sphere and a cylinder have the same ry 5xr -3p+fv+j)vs0a lawz;qo6qszsp (gq. a6 adius 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 greater rotaa.(lsvzx60 ++;qya a)w6fp r3vzspg s-j o5qq tional KE?

We claim that momentum and angular mom t 3ccymu1i6r5f/f 06+mmdwuwentum are conserved. Yet most moving or rotating objects eventually slow down and5 3 u6/u6 d0crywti 1cf+mmmfw stop. Explain.

If there were a great migration of people toward the Earth’s equato -764-mal vrt:aimjvur, how would this affeca v-l-6:vtri uj74mmat the length of the day?

Can the diver of Fig. 8–29 do a somerv9dg,wtku,jf vjil)/zq us66+*17*uj k vvc isault without having any initial rotation when shez vv ,kv jd*uisj)u69vcj7f +wkqi/ ,ut*l61g leaves the board?

The moment of inertia of a rotating solid disk about an axis throug79x)gho bfln. y * 2/x5vbkesah its center of mass ogn/ hak79.2*xfyv5exsl ) b bis $\frac{1}{2}WR^2$ (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-i qw /18opnq/, ucmq/zkg mass in each outstretched han,q8/qzqu c/1onpi wm /d. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howza/*q/b gx 53ct a.9/gkfyhz sever, one is hollow and the other is solid. Describe an experiment to determine whic*sqa.xhgbytc5zz f3k/g9 /a/h is which.

The angular velocity of a wheel rotating on a horizo*h we5i57n ewyntal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the hwwin*ye 5e75tangential 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 rotatinrme 0o39- zmwrg turntable. What happense z9r-mmwr30o if you walk toward the center?

A shortstop may leap into8edqjpc .wv, 8 the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates 8,de8v.wpqc j. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momenuh/wia a4 i84etum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more iu eaha4i/4w8 ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3ga1a:nov*mz9 5+in*9 wisr h(fmht* n0 $^{\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 coinctv+gwuif q6/ (idence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) owi +f/ (gtq6vuf the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed auoy) /g szr6em5ko//7pi 8w ijn owl c-uqh3)1t the Moon, 380,000 km from Earth. The beam diverges at an aimik/)s-epg)or uz/8 ocl1/u 5wq ohj6 w73nyngle $\theta$ (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 ats 6r57p:qhkz : mtxqg, a rate of 6500 rpm. When the motor is turned offrgsqmh,z:7tp 5:kq 6x during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the baioly dk3rz.. a48d g9;opvyw0ll makes 15.0 revolutions, what is its diaia.odz8y43v;w g p0 rl.d9 okymeter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many reyzq9 /rqwm ;5dvolutions do the wheels zm /w9qqr;d y5make?    $rev$

  (a) A grinding wheel 0.35 m in diameter r 55qujs61 jjhxotates at 2500 rpm. Calculate its angular ju1sqx5jj 5 h6velocity 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 compxiitx; /c uv5tah u8c36;ta gu(p /7gvlete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from x p6xiag tc/ ;(hv ut3 iga/7ut8cv5u;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 Es7kp y(s*ns,gc7qc-i) 8je.pgp o q5oarth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speeqm*xx8 hx2-swjjv8iuvvp ssm 5684-g d 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 a particle 7.zldfm.o :w1z( 0 cm from the axis of wdfo ( mz:1l.zrotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its ,*l;x 0p7gdp hb1eiois,r-lzcenter from 130 rpm to 280 * ior7deps lz ;0h ,xib-plg1,rpm 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+jd yspu m/3gjauvcn4+ a814d 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 Moon, asg.ff8kyuk +g :slf+z -tronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of yff+sl:.k ukf+ g8zg-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 rest t 7 vuo8eefat01o 15,000 rpm in 220 s. Through how many revolutionso8av0etf u1e 7 did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm g)yxzz67 +ienva wi-.mtu9 x, k*ss1fin 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 oqt y8u/9id3aflying highspeed jets in a whirling “human centrifuge,” which t9/ty odqua8i 3akes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelepu+x*y 3qqdntfbcn/u* - d.c;rates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled pdq*xt cn u.;d+b-fy */3qcnuin this time?    m

  A cooling fan is turned off when it is ru/z( es:w1sle pnning at 850rev/min It turns 1500 revolutie zes sl/p1:(wons before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as tvg z)1 x, f62nfe7zoqiji:9bo he car reduces its speed uniformly from 95km/h to 45km/hq76jfz, e foin1iv :2g 9xboz) 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

  The tires of a car make 65 revolutions as the car reduces its speed uniformly(p/(iyix m e,f8zt1. hsqsse/ from 95km/h to 45km/h The tis,spqi sx8t if(y /e(.zhm1e/ res 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 aqwak6x*w sm+h-k1qxr3pq/s ) 7 3iamfe 6 ;rpt bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radq 3mpsi76wm+ p)qw arf1;s 3qr6kh x-/ *kxetaius 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 /od zts. y1r,mthe magnitude ,rzymd/tos1. 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 the axle of the wheel shown in Fig. 8–3/gmb.ywuo /* q9. Assume that a frictyg / /bwumo*q.ion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of masy dx; r ,crta:qe50wt(s m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and tht5rc 0:(w,qey;adt x ren released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requirej*icszj.:ed .6)f5*g uet6xe* ipvsy tightening to a torque of 38 s fi.5:d*vsp6je* )tzexi*g .e ujc6y$m \cdot N$ 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 spher l./ dhr/l5rb8p*v f/hxyl xk+i94efle of radius 0.648 m when the axis of rotation 9dk e4lhrbf*+vl/iy/hr 5/ xll 8pf.xis through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicya9md15gw8ss x+ . 1 qfpe(btjgcle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hudae (1.st g+sjwx8 gqmf1 9bp5b can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is roax0/t z3n o5astated in a horizontal circle of rastxan5 0zo3 /adius 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 rotatinauqt 74qikt pfzi: z44k kpkpq. 5,7u.g at constant angular speed (Fig. 8–42). The friction force between her hands and the zk:i,kqfk474 t 4 .5uapup kqzqt.7piclay 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 sh. )g-bc dn7ik;6y qiflown in Fig. 8–43 .b76c )dglyi qif-;knabout
(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 total mabelnwd av dh29+45ogujozuyq 9+9 //nss 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 +tdrm/*nd abvi), nw+ satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 mi d/+wn* b,iavt +dmn)rn? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unhk n5t: gdlm1yzo c)v 42z7kq0iform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. C4zt0o 75k )12 nckgzm:hly vdqalculate
(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 aow r2s(xir8v: 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 tangentially on a small handog4 z br1wa7 p-h5rr)d-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 1w -zra1r5)p7dgr b h4o0.0 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, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm v*k68vaob-,e(r p 5 lf*ra mhxis shut off and is eventually brought uniformly to rest by a frictional torque of 1.2 ,xrfml( p* var86 h5eb*a-ok v$m \cdot N$ 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(s2obcphs ;2u.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 thrown solelyh b y6;7q2vp atkjuh(+ by the action of the forearm, which rotates about the elbow joint under the action of the( ;6j7uav+hhytpkq2 b triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8–4y.ci6/ x)rjyauo k35njcnu)35 .6xaryio yk/6.
(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 tkjg ;qbe3rg(2. i9rzh1s3wdey4ozbtu g/f ) ,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 the hammer from rest ws8tt or* 5pr 2isjo6s7ithin four full turns (revolutions) and releases it a*jrs 5sp6r ti82oo7 stt a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of i+ bu(, ai(kf 789l0z r,wxpinx y-xwpvnertia 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 develo+;8g +voqdra;zd axz:ps a 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 without suey94f gq y9k7lipping down a lane at 39kfeyguq497y .3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum ofj5-d/n1d 8p0ub zpke d two tedp0z- / jd5uendkp 81brms,
(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 of9i .i:)wht(1/lgdit ydhk ui, 7.50 m. How much net work is9iy hihkgu ,dw1)t d:li (t/.i required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and gqs+-no+sz2 c; w v8-havl pl)mass 1.80 kg starts from rest and rolls without slipping down a 30.0gopql)2z8c+a-v +hn ;ws- l sv $^{\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 balerloyli6.y *.hu : aek 1c4za2anced 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: Use conservationcyak4le16al y:h2i. .eo z*ru of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on th5cung(i+hqex;8w. (7 qd v mphe end of a thin string in a circle of radius 1.10 m at an angular speex8.7mp+ gvcid ;(u5ehq (hq nwd of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of cdeuahy6 96ddl3 9*iea 2.8-kg uniform cylindrical grinding wheel ofe 3h *9 adcyildu66e9d radius 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 a platform that ic x m0l+,5r,dzx(rhhqs rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of,c z d+xmr(0xlhh r5q, 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 s esp 96i4piljdmsr(-qi94 wq: hown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 whq6 wml4j r 9:pi9iqss4-pdie(en 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 rlx+pr( g+fspdfv4 *f) otation rate from an initial rate of 1.0 rev every 2.0 s to a final ratp ( vf +)ffr4d*pl+xsge of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical a5c8i gvd7d:k g/kp/9w n.gvff.1ec jaxis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5. g 78 f5 k.gdkvjc1/evawn.9icgf:d/p0 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 center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spi,iz z8(lj ;d -wlvd5ftnning 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 *6g-cuq t q3obthe 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 droppe ojr40a4caen9;(k s o *v+fmzkd onto an identical dir v*afa0m94oje4oz+ n c; k(kssk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a-q:z,bay -hmq t 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round p3-x6bc pjq1t :ob su:: -ah2pbq6w naklatform of radius 3.0 wasxquhj 26-:kbpn-aboq::t b3c61pm 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 merrxng tk):iu1*cg sdot+afm,vf5xi 0* .y-go-round is rotating freely with an angular velocity of 0..xtt:vof nxkufmc1+ ,g 0)*5sig*ai d8 $rad/s$ 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 collapse,2q agxi +4cyjs into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angux+q 4ayg,j2 cilar 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 winds in excess of 1.(dm ool2pp5g) ey)jk20 $km/h$ 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 eio1368f7 0 w ilis8hlrd.xu- kqn+xg$ 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 canwv.v,o r - xs:ye-0guz rotate freely without friction. The moment of inertizv- usewy-xr vo.g: 0,a 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 akyo9 p(u a)bbggk8f -5 6.5-m diameter merry-go-round turntable that is mounted on frictionless k5 (agf9)gbkypuo8b -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 ew c blmn:9txkuy8db x;/*if/8nd of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–ub /xkytlx8m d89w/ ifc n:*b;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 side always faces the Earthz jfzop-f8noh*1 9ze+. Determine the ratio of the Moon’s spin angular momentum (jznzez*o198ho-f+ p f about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at vw)48h. ,.annw/k :zwrb nhxva 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 ggl-qv p6 *f8..zicy yulx/f+ of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torx-g6.zfyi/l u8pyflc . vq+g*que delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 gcs39k-up 1r in rl7kc -v5g3gkg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of e csl 3ic7 -1p3- g9gkn5rvugkrnergy 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 r 5v-y i)ybg ;c1bv*ekz28iwh((nds6oecs a2mear 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 greatyjswi -xty517. vh)r v, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters ojt. v7xys5wyh-1)ir vf 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 idw8 4.yaten*/xr uum 4kia9,gkij4 j0s for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be ab g4y4 0 9tumj8xwkuk*jniera4i/a.d,le 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 illustrad- 006fs7)yazpu ii3kl dr- ogtes 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 )h+ca -njde o8on 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 Moja*ekhyhs.c0u ;e 5/ qfi8 m8 and length 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 esiujh/q 8850o *h; . kfmacyethe 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. ktw; r:z0 j6kol/ ,ud7m.vxlrIt 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 agawlol rr xdkt:7/ z.ju0;mv,k6inst 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 i*xiwy5qdg j;*5bh y0ss making a turn with a radius The forces acting on the cyclist axyb w*;yq5s hi5 d*jg0nd 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 aq-u9 c,nv) p3iftua ,into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from re, ian3-u c9ftvu),paqst to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a soliurbzu lewfk u 49;p ;r8;9u*cod cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular r9oluw9c8ue*4prk bz;;f u u;speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch abk 9 k03ssmt8o9w pxmre)f/(vssembly which consists of two cylindrical plates, of mass vx k /k9 sp0m)fo8rsemw t(9b3$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rollsqpuap./1 m9nu)t593nq zi lj w 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 leaving the tq umi t)3npul95 z/.91aqjnwp rack? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not e *.)gyocb(by assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car rwi( ao swbn9xa g5l5ea )q+w3-educes its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tir-wwa qx5n)lbi 5 gw+(e9osa3ae? $\approx$    $rad/s^2$(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