A bicycle odometer (which measures distance traveled) is attached near the wheely(bob-x. t 4xg0)sxf l hub and is designed for 27-inch wheels. What happenlog(bb) 0xs tfxyx-.4 s if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. (b 7ehpi ue2ya6 4zx)gDoes a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?6bp u )zg4aiy7(2he ex

Could a nonrigid body be descri/ ; s512w6y9ww.dlpwl9 ox-qwjgs tdebed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque tcg 6m6bzj (km/han 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 lrcy)3 x-xjq) a sit-up with your hands behind your head than when your arms are stretched out in front of you?l-c))y3rjx x q A diagram may help you to answer this.

A 21-speed bicycle has seven sprocketdxp ped/+86 zhs at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large h8/6e pzdp x+dfront sprocket? Why?

Mammals that depend on being able to run fa) )r 65:l:zqrdssyxwxst 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 distribut:w: sy65d)r rx)szq xlion of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrwyk yz1od* )j4c)bro :s.xe (cow beam?

If the net force on a system is zero, is the net torque also zer/u ;2i9c onf9qi(5tc+ mf jilfo? If the net torque on a system is zero, is the netj2 ufiq +tlof5 ic/cinf99m( ; force zero?

Two inclines have the same height but j:)u: w0clu7 g 3dqufymake different angles with the horizontal.0:f:u7yq udwgl 3uc )j The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneouslyn5ga.5(kaax .8/7nr mr e dmoq start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Whie xo7/qmmarag5k . 58nrd.(n ach 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. They sta*cgub4ji4ov5 rt from rest at the top of an incline. Which reaches the bottom firstoj vgbi4u* 45c? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most movitlhz ssd c(7;8jcs8m3,i8 wq/ g1axgx ng or rotag ajg3 sit( xmwc8s,csdq 7xz1l/8h8;ting objects eventually slow down and stop. Explain.

If there were a great migratuvqvgj* . qh64ion of people toward the Earth’s equator, how would this affect the lenguh4q .6vq*gjvth of the day?

Can the diver of Fig. 8–29 do a somersault without having*1 iehln +9s-mo*a9m4mos ab;voh tf ( any initial rotation when shom-hvb 1in;*t*+4seaom h9 amfol 9s(e leaves the board?

The moment of inertia of a rotating solid disk about an u32*de8fd co2 rwsgr; axis through its center of mass d3se; 2f8 ruo*gdwcr2 is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each ounxy j/tw3dg63l0zyr*tstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same?djyl3*/xr 36tgz0w ny Explain.

Two spheres look identical and have the sam5 t *:w-kd5lqost6o2v3bbms y e mass. However, one is hollow and the other is solid. Describe an experiment to dv 5 t3ymt2*:bqso 6 k5bsdow-letermine which is which.

The angular velocity of a wheel rotating on a horizontal axle mi il*v -8+xu)ilmi(upoints west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of -)+m8i xiim*l v(uuilthe wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the lhb4x* g-ls7p jx qr7uya*ln w9b3u;,edge of a large freely rotating turntable. What happens 47lq7-uluxlh ;*wsya xbp*gjb3,rn 9if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw ,s*i.nt2 uiyf it quickly. As he throws the ball, the upper part of his body rotates. If you . t*s,ifiy2un 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 con6 :(yh/jnyr:oxhw4 mejx, 5 rl )(uybjservation 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 keew :(yyhjbn(j4 ) r ,5exo/h lmjxu6y:rp the helicopter stable.

  Express the following anglgd t n344l1n l)nec :o1f.j ny7kn-jt*jlmv4 jes in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coinc2l/g0qccog-h20sh cj idence. Calculate, using the information inside g2 q s2ch/0l0cjoh-cg 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 at the Moon, 380,000 km frokj6vwudqp85ei67f: gk c0.ey .i o; qlm Earth. The beam diverges at an angle lpuge;6j:.yki0oc qqvwfdki758.6 e$\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotatel4ti*/d +b 4tp aozmg67jpn*z at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. onmi td* *6+ bt7gzpla/pz4j 4What 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 vp* dtkj4f53x:(sxrnjx2ofah. l*: m another child. If the ball makes 15.0 revolutions, what is its diametlx(:xt f* k: nm sfdv4r3xo.25haj*pjer?    m

  A bicycle with tires 68 cm in gg7g p0kdozmb-;0o1r diameter travels 8.0 km. How many revolutions do the wheeld- zg7ormgop10kb0;gs make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Cabft +o z:wom7.lculate its angular +obmt 7 o:fwz.velocity 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 revoluti*ql9ug y b/2bjon in 4.0 s (Fig. 8–38). (a) What is the linear *u2 yg9bqjl b/speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit aroakec*lkdw4) 3t*j5aiv,o wyu(eo -w*und the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed vn.if s;e 0.e0pv5mxgof 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 .q xs*bx +i(pvif a particle 7.0 cm from the axis of rotation is to experix. (vsx +q*bpience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about itaie6op0 f/n 2us center from 130 rpm to 280 rpm in 4.0 s. Dete0fe / nu6oip2armine
(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 m /s g6js u.nrk)l,6rq$R_1$ 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 M1: diosw o9 o-vfihb5d u-9(nsoon, astronauts 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 as a cyli-wvhfdo ( 99bs- 5nd1o iio:usnder 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 in 220 s. T64wl (q .wtkdvhrough how many revolutions did w4l 6qv.dw(k tit turn in this time?    $rev$

  An automobile engine slows down from 4 *vgw 63cbnw5s+cn- hw- irnn/500 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 flyb mnn pq+sm /:mr35r2fing highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions 3m+: p2/ snq bnrmfr5mbefore 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 accelera+* mcrg l z6n+jjycsg.+6hw0ptes uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time?gw6 l r+ + cs*pj.hz+06cmgjyn    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revox+ :k vyy lfmfbi(f3- 6oe7b/olutions before it como +fo 6ikv/x(bylmye7-:ffb3es 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 reduku.did7 ts49wh/1o bd 6(ka wgces its speed uniformly from 95km/h to 45km/h The tires have a dia wd4dubts6ia.wd 9kok1 /hg(7 meter 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 tiib( k7jlut+l/y s2a(uf(r2o he car reduces its speed uniformly from 95km/h to 45kflytui2 (sl(au o+bi27(/j rkm/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person ridinnmn8 b; xct4qcx6c ,3 m2 g7mwfinuz:,g a bike puts all her weight on each pedal when climbing a hill. The pedals rotatm;ixqbn :w67cn 2ux8,3cf 4cgm nzt,me 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 forceh :zua5ck kkp u8-8y q;m*(drt9 xq8nkctz(:x of 55 N on the end of a door 74 cm wide. What is the magnitude of the torqued(8y;zm * hprtk:-9kcxt qu xn8aq:uck 58(z k 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 themb56:oykur,rxnc0xjp* uu (o + l1ar1 axle of the wheel shown in Fig. 8–39. Assume that a bo *k(rr15rp1 cla :y xxuu,0+no mj6ufriction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass l p a)w..3deztgh2h:p m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially:dtepl zg3h2.p. wh)a the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightefxp o3j 0/vxz3m:yshrd q y+8;ning to a torque of 38m/83zpy:dy +q 0vhxxsro3f ;j $m \cdot N$ 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 t8kx20bupw4brbr+ s76 5u jke-kg sphere of radius 0.648 m when the axis of rotation is through its center. krsb u 6rwx b4e8 5tuk270pjb+   $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel t5k 8o ua 4iygg d8b8,b/phd,g66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The 8 5uyd8gdtg 8o bapihb4g/,,k 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 ro )1h4vsvkeemhzg ;u ssk +to2j7+r.j+tated in a horizontal circle of radius 1.2 m. Calcul1.osjez+sgt esmu7kvk+j ) h+2h;4rvate
(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 coxy;5.7 m leaagnstant angular speed (Fig. 8–42). The friction force between 5 gl7ymxa.;ea her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fidc:6l(gpv y 1zr, ef:og. 8–43 v6ld : fr,( :yoecgp1zabout
(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 o*neg7.7ek:vr /bye (,ckt hei f two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite s1 oohkj mn..d(pinning at the correct rate, engineers fire four tangential rockets as shown in Fig. j oh .(d1nom.k8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and ane/ep fnzg/onn 9 ibe:3;07ei mass of 0.580 kg. Calcef:g;n e/zn e3 /nopi0ib7e9nulate
(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, accelerating it from rest g2-xtmq4w kvdi 8:u.:yoz*j x 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-driv: 3(ay7gsx rem3:yt7h dsw s/cen merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the me3xye7(d / tc:7gm3h a:wssr ysrry-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 r dq7 (ud,xdb5fpm is shut off and is eventually brought dqx( 75fb du,duniformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball af)yo2i,q 1vw8uvb af6t 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 by the action of the forw/ 1,xbe3-5e1 *,p fsmq: n ynuwkyc cavy.+bzearm, which m:pc* en wvz+y3fc1w,yn5k b-q,y1 sba/uxe.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 bm)h3ee)tzf c - /qwem(lade can be considered a long thin rod, as shown in Fig. 8–46)me( -c 3qezm/ ethwf).
(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 okkduq1m , .ne+lcb 79pf 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 accele2pyg-dk x npdl;s*o2 ;rates the hammer from rest within four full turns (revolutions) and releases it at a speed oo; p 2s;gyd2xl* pkdn-f 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 9nid7r oh9q9tw rb-2omoment 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 de2sxgy7ac 7 (nx 2h gltaa.(j/(v; hxexvelops 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 slipping dow0(a dv,4 e5+ll fwto:/npp( tr2nvgwin a lane at2np,/w v(:li4( d grfo5awne0lt p+vt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of tho- ;s cx)i-phv0s ,yipe Earth with respect to the Sun as the sum of two terms,o- 0s;px,yhi-)pvc is
(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. vp ezz5mixel5o+0-m 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Ass 5xi v0o-m5.zmzp+eelume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and r9h/m5hs2 b:km)tcv dkolls without slippid:hbv k9skc mh /5)tm2ng down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall ano* h8-gjae bz9d its lower end 8hagb zj-* 9oedoes not slip. What will be the speed of the 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 bi4mxcq/xl8vum 3j o*(all rotating on the end of a thin string in a circle of vu x4oclmxi 3q /8(mj*radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylin9 72 )raou,a mbac;6qgqud+rtdrical grinding wheel of radius 18 ur aqbg r)6a2qmd,;o7 c9t+uacm 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 is rotating aton;1ftbt*vhl3-m9)lu pz ; xk a rate of 1.3rev/s If he raises his arms to a horizontal po uov -bh 1pn9m;lk3t*l)zt f;xsition, 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. 8–29wfa86( qmsxte(.: idi) can reduce her moment of inertia by a factor of ai. (m(f6qdia x8sw:etbout 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an 8yu:ca zw/r4x initial rate of 1.0 wzya u:48c/ xrrev every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertis 2/fgft*8eh bcal 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 clayfg * 8tf2bhe/s, 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 moment nuz/v5k2e h8ryc f;5tum 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 the Eart yvz9,igkrx y+r 52,ilh
(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 2)3k+0yu bls *mskwxiis dropped onto an identical wl3k)2kx+0*byimsus 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 at 2.4 :ub)y) zi2bak:hq;x a3j vs2f$rev/s$ 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 rotat v dlp (v1/m5rv:nekb0ing merry-go-round platform of radius 3.0 m and moment of inertia 92vb:dpv50e m rn /lk(v10 $kg \cdot m^2$ 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 merr7th 6o 9(q,ze frs/ci x8z.w8qa 59gntcjn,hky-go-round is rotating freely with an angular velocity of 0qnrt6 fc /9tk8(8g,i7nxao.,z9je 5c hhszwq.8 $rad/s$ 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 halfii3*)rne4mf r8)xoap w xuc6/ its mass 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 woul)wer8xpr *i inamxo f)36uc4 /d 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 winai id2/-4 :l(0hzuf 9hpbcg1zkexgi*ds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass ) 4jvft*3fe 7p4nn20a lea vxs$ 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 platfo 9sc qdz8h)a8 ko07tbz36 trcqrm, initially at rest, that can rotate freely without friction. T)sco87k9bt0q6ct daqz 3hr8z he moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m df wxhiwzin+6k1,.; o fiameter merry-go-round turntable that is mounted on fricii1x whzk,f6own .f; +tionless 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 gzn)i e95aq+ xchow 4oooqb3gv9i 125 yround 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,4qz)oq32 xa o ghwo9yneo955c+ ivbi1 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 Earthg:i xmeg35x+ i such 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 momentum. (In the latter case, treat the Moon as a part ei 35:x+gxmigicle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fromw hcw(a)yf ckef,zo4,1v1nj2 rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20mow, la10niiz5z9u (m-i5 bdo m acquires a rotational rate of from rest over a im159a -ol(zo,iz i nbu0mwd56.0-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 mass 0.050 kg and diyv5x2f pgz9 :aameter 0.075 m, joined by a (concentric) thin solid cylindrical 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 reacz yg5pfa:v x92hes 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 x/50fh buwh ,ris 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 sy.;zb4 q6 rhgbize of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a 4b;6by hz rqg.neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for t2cqt 43gqbl74 8oycb it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mab4l3 t7c4y8o g2bqctqss of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an wja;t(j+w p6gh b ;3n pm3y2ck$H_2O$ 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 horizon6 +(gi xr p-yn 0xtfy31 vcf89bmvqd0wtal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., sujeml/09g*v:+pu sj 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 acceleratiem*ss/j v:0ujgu+ 9lpon of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and we 7xl7rx1xl9b f want tl r7b19 l7xxfxo 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=4.2m/s on a flat road is making a turn with a /cqw;,q t6kkp radius The forces acting on the cyclist and cycle are the normal forcet6;pq kq/ ,cwk $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 :, c+;xco y9tty;5 edragk 5jza sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?y9 : 5a 5zj,etco+ydrtxc gk;;    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thq (lhuamluw7v:ba 1-: in rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and wi:bw7u l-hv a:qm(l1au th arms held tightly against her body.   

  You are designing a clutch assembly which conjr 74w8a s r ;/oz8j,klmc4gjfsists of two cylindrical plates, of m84 cjfj 4;/omza krgl7 j,8rswass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ra1iltau;lob6 xa(:xp* . p-crrdius r rolls along the looped rough track of Fig. 8–58. What is the minp-p.a (6arctix *:ur ; xblo1limum 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 not xxsmhe5kv*ba*0 g (d:assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as 95f 1kz sw6ptwthe car reduces its speed uniformly from 90km/h to 60km f9sz16twk5 wp/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