A bicycle odometer (which measurptw7;g9nr,6w w 4z ;ufvyv3u yes distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What hapu6,9nvwpyvw; g3 ;zwr 4 fuyt7pens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poinov 7u)i cqh59ct on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/o7ocq 5c)9i vhur tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describxxtbj qwn5q9x 9k254n oo9mwz5di)4u ed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater za)s xblpivxb; /2; )w kwzg 7g6qm*c.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 hands behix6x,u5 sirv a3+nw5y end your head than when your arms are stretchedyw e, n55r3ivxs +axu6 out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at th36a;ch*ai*uaovp-t )twk ) d be 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 frcaa3td;) tv *ia)-bkp6uoh*wont sprocket or a large front sprocket? Why?

Mammals that depend on being able to run f ho* 0zhw/u147nqofxe ast have slender lower legs with flesh and muscle concentrated high, close to the bodyh7o1f oxuqz*0 /4ehnw (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers xm 57 efbk*:ca(Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torq :w1 c:cf62 o7cqk4ljmvf+ys bue also zero? If the net torque on a bcv m4:qs:+ 16o kf2y7jcwflc system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizon i.1 jylhow08tf 3hon3tal. The same steef w8i t1 ljyoh.on30h3l ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultgc6cpai*ado-5y u. 8 il;hxu) v h- ksi,h.q/taneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass opa.5iqi ch-u*th /y8kil sx)v h.gd 6-auc, o;f the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same rmxo +o bzl9h2o)a 6ed,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 grea6+ )xoo 2he9d,mzlboater rotational KE?

We claim that momentum and angular mome ku4o9l qh9x)mntum are conserved. Yet most moving or rotating objects eventulxh)k4 9qmo9ually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wouwnn4/ dphvk b3u) i4+u *co:ruld this affect the length of the 3i4*h :)+nucupwdo /b u4vnr kday?

Can the diver of Fig. 8–29 do a somersault without h n1jmxumx.h ldl 2 /2,x*b6cslaving any initial rotation when she 2 */lu dlclsj6x x,mnx.1mb2hleaves the board?

The moment of inertia of a rotating solid disk about an axis through itg0dhnt +m5; u (b ;phq7jrea(ks center of mask(hdp; je gtqar 50bu+mn;h(7s 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 outshgu0lu1y ./e ltretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the sau /ylg1uh0e.l me? Explain.

Two spheres look ide*z z0j x3(6zvat)xqh(qck* u qntical and have the same mass. However, one is hollow and the other is solid. Describe an experiment qv*3 q*uaz)xzqh06 ((cjzxtk to determine which is which.

The angular velocity of a wheel rotating on wd9;b, qro yow (.w af1:h8dqfa horizontal axle points west. In what direction is the linear velocity of a point on th;18wwohbdaoyf(9,rw.qd: fqe top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotatins1md,5 tivqcw*.5yc zg turntable. What happens if you 5.s51mzdtccq* y ,v iwwalk toward the center?

A shortstop may leap into the air to catc qn (2 6yx27e7ltato jgb4ar*nh a ball and throw it quickly. As he throws6nl 7tao nge7 ax (br4q*ty2j2 the ball, the upper part of his body rotates. 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 momentum, discuss why a heli 0ayrucxi2g7: sxh52z 7 pq,l1-c analcopterp2a0alyxsh51lczxiu7 q a n2:, rcg7- must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radiu ) jepn,n)y-a4rvj9xans: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculatwxj lsv 9 yniio:s0n752 b95kbj gyi.3e, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on E 90ws3by2sn x7gi5o:jj9bk. i viny5 larth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 3ow y2i zj*5p0z80,000 km from Earth. The beam diverges at an angyi*jp2wo 5zz0 le $\theta$ (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 hhmn2v2-f my6d; l 5cyrpm. When the motor is turned off during operation, the blades slow to rest yyhmnd 2h56flv-m ;2 cin 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 anoth 6p8uv .fhfu*qer child. If the ball makes 15.0 revolutions, whf 8* qufv.6hupat is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How mand . 51/rxhr j-ztdl /l2hsbb4ny revolutions do the .b -/1txn/lhdzj2br4rhsdl 5wheels make?    $rev$

  (a) A grinding wheell/x*dzpb mpenn979 .e 0.35 m in diameter rotates at 2500 rpm. Calculate its angular velocity7n n p.zd9peb/mx el9* 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. 8–3ryo.;wfddty(fj)g1j m 3o t0 38). (a) What is the linear speed of (03 fowt)jddm;1t 3 g.ojyyrfa 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 around the Sun0k9f 1dnh a0 9su-yori/pb (an93rgjq    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pointrc-j. 0rkxw;d nz( mi-
(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 j2p2b2sfs qige +8 m n-bqfjnq7p1s -:centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experiencebp s qq2 s7b+gen:-m-1fsqfjj2 in28p an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center . xy ym.m5qju-from 130 rpm to 280 rpm in 4.0 s. Det um5. qyymj-x.ermine
(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:h w+d/5b gqge $R_1$ 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 A5 v(5jl vw8cpcpollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of theirlpvjv5 (85cwc trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly fr9obf s7n (t v)awe5d6gom rest to 15,000 rpm in 220 s. Through how many revol7b fgwve (6 )ad59otnsutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calj-uo96d dk)suwj z*-vculate
(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 :7qr)dzw-e vwe)9t ra stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 med9t- wz e rr7vq):w)ain 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 unif./t*s0cej+scdrvzh;sv2 il.ormly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travei.;hs.0jlr*vcd2esz / + ctv sled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min Iv;p 4ighxg */lt turns 1500 revolutions before it comexvl;4hpgi /*g s 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 reduces its speed uniforml435)gp pjlk 5)mlsdsyy from 95km/h to 45km/h The tires have a diameter of 0.804 pmkp)lldyjs g)s 535 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 sck;ao x 8np-gj(nv bz.n;i h13peed uniformly from .h;bi(xoa ; n-g 38vnncjp 1zk95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puj( mrp (iucl3z j,u1z/ts all her weight on each pedal when climbing a hill. The pedalsmcpj/1u,z (r 3j(ul iz rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a fone1*so r-6(pggi j prds.1 v 73bu6attrce of 55 N on the end of a door 74 cm wide. What is the magnitude sen 1t6*r36opa rvj .pbtg( ds-i7g1u 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 ther - -wja(+inme wheel shown in Fig. 8–39. Assume that a frictiom +j(an-r-ew in torque of 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 masslesd) 0qi3z* 3utjg *doi41xoeg 6c:5laip9kf mzs rod which pivots as shown in Fig. 8–40. Initially the rod is held in 6pfoa3)kt0q1 i cgzx j4 o e*ld:g*i3d5ziu9mthe 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 eb5ljsk.hw3 .g jz 91uwngine require tightening to a torque of 38j.9w .wj zsug3l15khb $m \cdot N$ 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 spherejvysjyfu 5v .te :w7ety/)8 l4 of radius 0.648 m when the axis of rotation is through its cenfj t uyv / )4.jt85ysel:wye7vter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle b;0mrom0sr2pf h,+ gu wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass om 00p2mgr,s +br ;hofuf the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is r9uon a2g mayw/j su*.(otated in a horizontal circl9gna .umyw/o*us2ja (e of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotatinzq mei ojj80k.d6s +i:g at constant angular speed (Fig. 8–42). The friction force between6d:ezjims 8+ o qk0.ji 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 obje-vh vy9h62 oorhrogjw wo* 659cts shown in Fig. 8–43 abo hor*2 -g9 ywhrvho65o9vow6 jut
(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 makv9 a/uh+v6i 7vn8mr, /a96rp po ycsass 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 cylin22zciz h (p:0b ydbz8*kei(d ldrical 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 toy(hl d*z:2zzb0 k(8cp di2bie reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass g2q0.b ;3xg d o1bf8lrkkvv.fzi+ xs8of 0.580 kg. Calculatigorlb;q.k8b0k2gfxfs.3 x1 vvz8 d+e
(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 frof:sfv:2cu8c.cky+ d r m 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-driven merry-go-roun5jq )en(v3tfsmk- bo;d 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 ) koj-ev5 m; stqfnb(3on 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 io -2uj:v9ycda pt5u y)s shut off and is eventually brought uniformly to rest by a frid p)yjvyu 2tu5c -:ao9ctional 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 accelek(jsp w su*3q ij(..ihrates 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-kgp +a:43jr)wbz.r 1cdv-ro w7ewpmp3 c ball is thrown solely by the action of the forearm, which rotates about the elbow joint under v: r wcao w3r4dc+j1 be3r7)pm-w. ppzthe 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 Fig. sua4vihpn ci 0/ 8 empv*4 n8., e7prx;gkeva;8–4pv 88hi,4 vuas0agn/pk r7cpx;e i;ev*e n4.m6.
(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 consiadx/ws v v.tag-k5r58ut i.. ests of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower acc6-khp-oh (vpqelerates the hammer from rest within four full turns (revolutions) and releases it at a hp(-po - 6qvhkspeed 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 ine)j :g d vrosmh5y-kj 72u)t6mxrtia 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 enginea,,xaexs,uxjh6 uai:1 pu ;1t develops 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 :+51wg.d*1qruljn dowe 0mvt 9.0 cm rolls without slipping down a lane a5nwtjemr+ *1 ulwqdo1 .d v:0gt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as:j9w+ czgxk* qp7 tdo8 the sum of two te:t78 9zcwxd*k q+jpo grms,
(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 ays 88 uo)ii,ljnd a radius of 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? Assume it is a so8jioy8s ) liu,lid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wimu .4q:zmqyl /thout slippingq:mq u m4.y/zl 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 st6qka 1iw:yeq 1l.dw s4arts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just bew1 4wde:aiq1qsky l6.fore it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular n /;/9wi.8wcoyznvotmomentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at a8ww/9nvoc/ion ;tz.y n angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2qt rr0qyjfspxo ),0,wt+;uv+.8-kg uniform cylindrical grinding wheel of radius 18 cm when,ry+jwpfvquq)s,+0r 0x ;t to 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 g.h4bbm7j5j jl8gsmegvx0m* 1ub(g 3 rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation d jg*gbx0g( b1 j7mumhv .m4j3elg85bsecreases 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 inepobf*6 i*mcr2 mk++w 15qbmkbrtia by a factor of about 3.5 when changing from the straight position to the tuck p5 m bfpq+ w* crkmi+bmo1kb62*osition. 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 d23oa9qht1 nv8k5pl*m cmmr-initial rate of 1.0 rev every1-omh 38n pdmmc v*kl 9t2ar5q 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 vertical axis w o8 ei7 qb73(obgvcbpe (w+*jthrough its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximac3obq7 7ji8(e(b + wpgeobv w*tely 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 figw((1tks t8 dpcure 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 e,e9 9axsbq5h of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an id2qs u:lqqq)jz6n7f )zentical disk rotating at )lf)6qu q:2qn j7zzsqangular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns(mci dn 6e2 f,i*utsq)l 0pe(w at 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-rv 8vcdb jhb3j00ziwa*3+ .gygj 6qh8 gound platformgjjd0a j8w3 v vhggqb0 *6 .i8z3+byhc of radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely rlwvb(nr+swpawe2 p,2 *8t l:with an angular velocity of 0.8p8wlpt(2b , r:+l vwws*2a ner $rad/s$ 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 intowl 18+ujpntgz-k)lg 7;8u iby a white dwarf, losing about half its mass in the )+nub 7t8 y1glu-wj8klipgz;process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(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 f-l7 j1m+ab -kavhb-a*+xv jpexcess 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 *msl q )e;se+hd7/* caw bp.vg$ 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 l5ei,79vp rd mcan rotate freely without frictiom, rpv e79di5ln. The 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 di:0q eyw1bys f/z:e.xrameter merry-go-round turntable that 0s :ybew . 1fr/eq:zxyis mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lyigpem-c ;36r5n mxvqq )ng on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the pepg ;n5-3rexqm)mqv c 6rson 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 9jmv sfv:oz 4x/r8.qpthe same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its qxvr/ojs.8:f9zm 4 vp orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ro xc5ddeu;.0e ate 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 sh)jebqg nu (y b/01yy b9fee9.bape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6..(e)1 je0u9y b e/nbg9qyy bbf0-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 ogw *dxwh+4gut bma1).f mass 0.050 kg 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 energy to calculate the linear speed of the yo-yo wh.wudm4x+)a tb hwgg1*en 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 ang ihixe rz:iabu*0a*pat3jj*.(q -rw, ular 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 8.0 times as mthmi6n(:kyau te,* + great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravi, hmy k(mu* etain:6+ttational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy r8jiw7r,t lgckl)hs.w, - p*sstored 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 anlg ,h *sj)cslt,i7 r.k- r8pwwd 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 illustrateszgx lq8u42l 3fe,flg9 an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surf-r48wcq 8qyjw ace 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 ly8*c .a gah;2fv+ccj .8pewb., 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 angular2cagc*wa8. p+.lj ye;8hvbfc acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is smv()8jd ju6lm;gq w 3ftanding vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests 6 wq (vl;mdj8mjgf u3)(Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road ibdgr 6vp sq wc1:m/b-0g;)riys making a turn with a radius The for:m6b0 ibvrpg/1w s;q)rydg- cces acting on the cyclist 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 slinfl/7 lx4gft1447a lq ti,fxzvg of length 1.5 m and begins whirling the rock in a nearly horizontal circle aboveq l7fzlfa /,7xf lt4x 1t4v4ig 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?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as yekfu 2; xi5ggl q:9v;thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angqkuy lg;5: vxi ;2f9geular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consist/g 4sc)elgy y2 3x8bsgs of two cylindrical plates, of mass y8 l g2syeb/3cg)gx4s$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 b-ifb9 z+)9ghwg4u2ad.c qgq Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it isigq4fzbua9- bhgdcq+.29 )w g 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 ass.lzpyw8kj g4 / koo a2qp4b0m+ume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces itsph;q cnordoyik28 g.b te53;72ftl d8 speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What wabd e g3ri;ncto8hk;t8 7qp2fldy52o. s 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