A bicycle odometer (which measures distancer .a3nhq8s xb2v 6yt*c traveled) is attached near the wheel hub and is designed for 27-inch wheels. Wh3v6s28*t.nhbay cq xrat happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim hw9j5n;r3h j9pz4x zw8yilo , fave radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cfy,;i l 3z4zo8w xj9p9rh5nj wases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velociy*1 ii 4 2px*vygh.bhlty $\omega$ Explain.

Can a small force ever3h )bth0 im0 bjzsm ;n:a2g(bn 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 your handsflv p-jf*+yvve; 5k h97ru g:q behind your head than when your arms are stretchv *u:;f vkyq+7l-pgf 5ehv9 jred out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven y j7kkl jt+2di 6 0mwb-y1o,m u/wc9vtsprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In whic9o,v yw +jmck2t 0j it7bmd 6wk/-lu1yh gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on be3fke3o/mqmge(esq5 njam ,jo q ,322rtvo,)bing 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 why this distribution of mas,k q,,3rmego o3/s b5m nmea(v2)23qqeojftjs is advantageous.

Why do tightrope walker /z; y;fv7nryekk)jp:z v *v/qs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system icf (ts ;,)z39ivm fey/4 dacd(gz)ns as zero, is the net torque also zero? If the net torque o/39(mci,z4 zsg edf vyas;dt)c(an) fn a system is zero, is the net force zero?

Two inclines have the same height but mam bs8eoxe;o)c*l68ha ke different angles with the horizontal. The same steel ball is rolled down each incline. On wbo6oema8he); sx c*l8hich incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down aa ci.m*puh/42(rs,gm lif, dk n incline. One sphere has twice the radius and twice the mass of the other. Which reaches the b2hmu,kgi. cfd4ilpas*r/m ( ,ottom 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 same radius and the same mass. Th9wi9 ;o*xa tuxey start from rest at the top of an incline. Which reaches the bottom first? Which has the greater s*awix ;t9u 9xopeed 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 momentum are conserved. Yet most moving ospdjnfj8 :uza+7 9 4qqr rotating objects eventually slowd7: s+znu aqpjj84 9fq down and stop. Explain.

If there were a great mil gpuxwmh8gy hm3*k,,0l w,j2gration of people toward the Earth’s equator, how would this affect the length of h wwj3g,pm0hy *,82ugkxmll, the day?

Can the diver of Fig. 8–29 do a 1 5p0a2ax4dsvikcid 59m8zvosomersault without having any initial rotation when she leaves the 2msca vvi5x8i9o1 kp zd4a5d0 board?

The moment of inertia of a (- r4dcqodwz ,rotating solid disk about an axis through its center of ( c,-wod4rdzq mass 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 rota on gw3x7gde 7qo;1)gbting stool holding a 2-kg mass in each outstretched hand. If you suddenly drop thew3oxd qg b;7eg7 og)n1 masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Hox 9r iz-vv9xz m0 gn5op8yvi91wever, one is hollow and th oxpz-1 y9n5rm 0ziv8gv99 vxie other is solid. Describe an experiment to determine which is which.

The angular velocity of a xb3mxg:8utoc 4va6x * wheel rotating on a horizontal axle points west. In what direction is the linear velbx oxmt: ua6g x*c43v8ocity 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 o im*u 7;67u,a iygoowfn the edge of a large freely rotating turntable. What happens if you walk toward the cen67, uug7wmo f iaoy;i*ter?

A shortstop may leap into the air to catch a ball and throw it quickly. As he thy 6q4fdvgj9j 2nri 4u3rows the ball, the upper part of his body rotates. If you look quickly you will notice that his hips ajq g624fv39u jyn4dri nd legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why afvu 5co t0 9g*oe;nm8d helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeo*tovfcm dn8 u0ge5;9ller can operate to keep the helicopter stable.

  Express the following angles in radians: (a)kbcl1c9 bk j.. 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, ynn6xhnp/+ bt0im0 0wusing the informatio/y0h0wnp0txibm+nn6 n inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed a7vecs;im fiieuy/ y* n/7: -rat the Moon, 380,000 km from Earth. The beam diverges at an angle 7n/ f*a7v-y/;ee ir:uicmys i $\theta$ (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. When the m-(0 d1qt0) addozqv6 cdr,n( caqyxj8otor is turned off during operation, the blades slow to rest in 3.0 s. What is 6zny(d xj -,qcddt0q a8r(1vo c0qd) athe 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 b79x h3n( gcdqkcj7cqkl 0h30zall makes 15.0 revolutions, what is it l7 dk0qnq09h cj3xg3c(kzh7cs diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How y o6mtc/9k* 5lyowb -:hbh8phmany revolutions do the wheyc9hoykt *woh- l: 6b/b5ph m8els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 5d8u,u w)chrx rpm. Calculate its angular vecd r8u,hwxu)5locity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–38). (7c0hadpv qjvz qz8475a) What is the linear 54djv70 h7qaqp8zvcz 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) 2f/guoc/ q9g78h./a uini akcin its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of .5 rqgf(xzhl7 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 centrv b0bd;xkcpj )q gwhfl4z;*mtf*r40 3 ifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an3 z;p w4rx*0) tdl0fvq hmcb*fk4; bjg acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cente10 p1xev mz3,pa v8ueir from 130 rpm to 280 rpmme0p,z8vxe va 1 3ipu1 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 radius l+r(q ; wp/pdc$R_1$ 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 spacecraft put theh s-iq 6,h+s,y u0zv5mrjc,zomselves 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 cylindz o uyh5h,0+ jc,zvsr-,6sm qier 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 to 15,000 rpm igzocj,c r.2u1n 220 s. Through how many revolutions did it turn in this time? ocu,1cg r2.jz   $rev$

  An automobile enginefs sd5getr,qyd-.bwyi iw95 2d-f*f- slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flykhj 2-u3v5 s zl*pw0f-5xedjm ing highspeed jets in a whirling “human centrifuge,” which zpx -*lhv2d5juf5w 0s -em3jk takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in c:pjf86sn1dicmsy, 4 6.5 s. How far will a po:4si 8snc1cyfm, pj 6dint on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running abq1na, s( jhs,n*kl+ ut 850rev/min It turns 1500 revolutions before it c1un+ hs*qjl,,s(nb a komes 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 rhtja;wenj34u5gtea*.;e tm+ evolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter ofje ae* +t4g3;mhn5ej; .at wtu 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 xj ls6;x puqu;t/bkvg+6w12 d car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 +j6dwvx2x1 g q ;uks/tp b;ul6m.
(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 alltc0 pojqf)n -o+ w-.pl her weight on each pedal when climbing a hill. The pedals rotatejplnwpc--to 0.f)+oq 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 o-t fbbe q.nm7f+2mdi 2f 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the ibqdtm7e.fn f2+b2m -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 wheelib 6/.v7t;ayjer a f4v shown in Fig. 8–39. Assume that a friction torque ot6 ajevr7a/bv4fi y.;f 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 :kzhz7gsy.b9h g 16fiv3o5qy rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calcus.y96 7hzg vfkqyz5g1:o hi3b late the magnitude and direction of the net torque on this system.

  The bolts on the cylinderalhxap./c sk-/r:i ,h o28qtw head of an engine require tightening to a torque of 38/k. r aahot2x/- ,i8pslq:hwc $m \cdot N$ 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 oo+/f8 yzf0 95tbva5oqu:ydaqf a 10.8-kg sphere of radius 0.648 m when the axis of rotat8ovyz o/a0fq 5 +qub5:d9aytfion is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia 9g7 g ;gavu3xaof a bicycle wheel 66.7 cm in diameter. The rim aua ag 7g;93xvgnd tire have a combined mass of 1.25 kg. The mass 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 rov3 ::p rhum.uutated in a horizontal circle of radius 1.2 m. C u:3.mrh vuup:alculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular spee/wchoa9hw.sqkif26/ed4t;rnxf mn z09d1 x .d (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total.4w /.6f ch / exit9.1kfnqhz0 d xad9;srnow2m
(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 m fcybvulr 90,*l/g0zttwa9 7he1a*yshown in Fig. 8–43 abo/*yya0rt0t 9u*elf w, vabc71mzl h g9ut
(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 mass rwr)e cof;k42 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 cylhpnrtyk6 r304indrical 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 5.0y 3t0rn4khpr6 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.+guf(tp3j 88fvj x1w1b j(n qd50 cm and a mass of 0.580 1+(fgnj vp( 1w q8dtbu3fxj8j kg. 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, accb+w: 4bpr/zt(;doy u*h ,yvn selerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-drivenp3:+qnsupvu; 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, ne:q+3p suvup n;glecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rot(m z2 5ssyslr27eo-n vating at 10,300 rpm is shut off and is eventually brought uniformly to myr ssv (s-5n2e2o7zlrest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerat - fo-z-z ui,mo+bwd-tes 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 thrown solely m/d 0-iin q5qvby the action of the forearm, which v /md5iiqnq-0 rotates about the elbow 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 can be considered a long thin rod, as shown in Ficx pqe31wni rt 0,q000zg 7eryg. 8–4qct13rp0 xeqy rwzg ,e0n007i6.
(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 masses r4-)qy ffpxv), $m_1$ 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 tt)ka9*3dn h72 jldwp4s cf3(nrh d zt7he hammer from rest within four full turns (revolutions) lp k7(32 hsztc4j 7ntndf3a) dh9rw *dand releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertwx;y+jnatb-ys5j x1 0 ia 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 )r+f sm,v5rbqof 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 slipping dof 5h r6m8/aa/va tjll/wn a la86ha ajlmaf5/t//v lrne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eartax 3.3tf/tubz8jl0om dhf cgi5) 0e1oh with respect to the Sun as the sum of two oed 8lhfmt3zi50buc/1a3ft.jxo )g 0terms,
(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 7ipug7-o(p rj j4)e8bi .50 m. How much net work ii 8oej 74jg-)pipru(bs required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rooc(oa 9yqy 73pq8k5lie jm*wg hhykf x:4+n3/lls without slippik hghnjopqeq9y7 :8y(4 m3i/*5c3+wx lfkyaong 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 balap e fxas/phniime3 p v+16*0lc*rj)6cnced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of thef6s xj 0ep*ri1hcpnei l)v+ a 63pc*/m upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating7* qzf/7bd jez on the end of a thin string in a circle of radius 1 beq7djf*z/ z7.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momesz5.y sz3o5u7dn8vhx ntum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 5xz5v nshoy 78zd 3.uscm 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 tha74hhxv : :ksist is rotating at a rate of 1.3rev/s h47i:h:ssv kx If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inr)w*;u w2)yy; nukcdgertia by a factor of about 3.5u;y)wd kc2n)uy r gw*; when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin7syge /h-xmy9 rotation rate from an initial rate of 1.0 rev every 2.0 sx7h-ye9gm /ys 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 rotating around a vertymip5- xa 32xs) n(zn 2(duavmical 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-kgmnz35xm((u aniy pd2 a -v)xs2 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 momentu n5cu*tlmp59q m 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 momentum of t ckmvn7 9x f7jqn+d+7ehe 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)5 g23zileyd k of moment of inertia I is dropped onto an identical disk rotating at angliz)52 3ge dykular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2dkik +y3 acoo021ot:g.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-y q;ps-st+ ty59h;be eround platform of radiusshy9+sq5b t;ypt;e -e 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 rotatingl9b yessydl 5kcq*;v/8s* cd: freely with an angular velocity of 0.5b/d8 *vy9 se*kldlc;qs:syc8 $rad/s$ 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, u(er*47 q3g0yis wsbl losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carrie wrblssu4q7*30(i gye s away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excessdeoxl -1f miz(e;r)09qr 7v )/yuf wdj 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 dp9a3fxmke, 54eqqpbd n 0axp49y 6w)$ 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, in d0o wj2zel82zitially at rest, that can rotate freely without friction. The moment of inertia ozw joz02d l8e2f the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameterq7rs) zbob -vo:lz4x1 merry-go-round turntable that is mounted on frictionless bearings an-b7:v broszx )z o14qld 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 groundx x;eht 0savrr,ca)on9 5.q4u with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fis9t. xhqou c4ea5a0);r xrv,ng. 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 such0f k;q-l:dm1nb 5i95pwo2x . iepcnan that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momenpon10de5fpq 9mw-nxi; . 5b:kiac2 lntum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from +jy5-9ik vv9x ywnido6e(53gcody -jrest 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 azlr1 )gk3x0rzp-s k -scquires a rotational rate of )x0 rrg-kl3p1zsz-s k from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of masseue;ix)qpqa p /,h8p4 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid pqi/ ux,)h q4eep 8p;acylindrical 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 i;qu 3y f.7uajxs the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.00 oe g0/(kst8 vi:6gtvc+ itmg times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mc e+m:s06ktgv gvigo/0t (8tiass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use enernz1mn5kv kl 4fv5o73igy 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 af inv5zl okm7kn31v45nd 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 illustrafd)us np )(/istes 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 horizontaecmwb jb*h044 xu wyq-k4j1y6l 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 Lmrfz y6sua;pk31oe p9) ;o7za 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 actfu7)poa13y;z a6z;k mroe 9pss 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 verticallydw bs9l+yb:ds b7 xudzy 395,g on the floor, and we want to exert a horizontal force F at its axle so tbb ds zbd7+xsw gl :9d39yy5u,hat 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 8 jscr;a4+pkw a flat road is making a turn with a radius The forces acting on the cyclikp;sw8 +jacr4 st and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m 4 z:b t qjopck2 t ;q4qt9,i65-oaxjzrand begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate jbo26 ,5:ttqxq4 krco9 zt;iq4-az pj 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 solid cylinder and her arms as th9og -t ana+:.tk9 e(+ eudzynnin rods, making reasonable estimates for the dimensions. Then calcu 9-yz( n:u.+t9oe aa ndgkn+telate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists od93xiz3*md qof two cylindrical plates, of masz d3x3m i9*oqds $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of vb;.t nhb:jy/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 b th nv;yjb./:track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu gz ztg+gu,62jme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformn :sx; e(*0p ;y;l*sl 2vhbdad*ltb wjly from 90km/h to 60;l(bl:ebh xldsnyd*;0tv;j2ps** w a km/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