A bicycle odometer (which measures distance traveled) is heyqv d+,4af6y9i z t,attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheelt+9d,4azyvf , 6hyiqes?

Suppose a disk rotates at constant angular velocity. Does a point on the rne 4fe0 5eimt9rd(wu 7yf ;d0zn9wjd b;r s.9dim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangentiad .9 bnr9un7tsmydf 0d; 9e0ew5rj;z4( edw ifl acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be devx5 ko(1hsdw9scribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exertgtl nq*:02knj-(fjh jrkni 5( 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 mi kj2o.lv04vet 2c 5njs:.y)5oa iqvto do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer thmy tq vi.4ole v2sk j2o50:)aniv .5jcis.

A 21-speed bicycle has seven sproc*ltc/ b4:xcni41in khkets 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 4 /: bnh1*cik ncil4txfront sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowb)(o ipu- 9mxper legs with flesh and muu)bpx 9-mio( pscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–3 8 o e-8wi0+8jlz ,zhtmupqi3z5) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If;t:jyug90rq x6,uf w3 sc frv, the net torque on a system is zej,c6uwf f,g:vt;0 r3rq9ux ysro, is the net force zero?

Two inclines have the same height but make different angles wy d,a y3sd:m py0ej*(with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of tha*3j0: dwyysyd,(em pe ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclinv jv (o ))ki*kaf1f;pxo;ne)fe. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy1o f(kjxk* ;fnav;ivfe)op )) at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start fro+hx gggryb*s0ul1 d. i:zj b:)m rest at the top of an incline. Which reaches the bottom first? Which has the grea:lg usgxiz1:+yrg .*h )jb d0bter 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 mo*cq v4h-qalz,:,zu hcving or rotating objects eventually sa-,hcuz, c*lvqq4 z:h low down and stop. Explain.

If there were a great migrationd 18zdhz(l ykbpl3j 3) of people toward the Earth’s equator, how would this az8 dyb3lz3l1k(j)dhp ffect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotation wdak 3w9e aye c3eaj68,h74 .wsnlm,i when she leaves the boardycai4,6m8adka9w.en33eel whwj,s7 ?

The moment of inertia of a rotating solid disk about an axis through its centerf3 jy* mdef60rst-m9g s3fg 0 tm9-jym*d6rfeof 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 rotating stool holding gml ,i:(w/gfg a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the smglgg: wif/( ,ame? Explain.

Two spheres look identical and have thg9h5/9 h.tda-.w0wdw7jrdq z11gr(wdn q zmqe same mass. However, one is hollow and the other is solid. Describe an experiment to determine whiwq9h 1q1wd7 /5d-rr..0mwgwtg jh(zznd 9qadch is which.

The angular velocity of a wheel rotatz/y7u 4d5(pgu2m xskring on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angularz 4gumus xpr(27 5k/dy acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntabl gm-u/ytaqb3 igvb m;*l, wfb)pz.- x8e. What happens if yo yb-g- *zfmiu8 ,mxw/gl)pb v3abt.;qu walk toward the center?

A shortstop may leap into the air to catch a ball anj2 du k 4hvxumms*5b2k47 g3hqd throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rot3*4j 527g4umskukh 2 mdbxqvh ate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of admhwv2 4vgx1t 13 -:bqdnsk:r ngular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter st v4:gv32brk : 1snwd hmqx-1dtable.

  Express the following angles in radi*ek 9 h7*utu x:fhftlni,*( tsans: (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 ,gz:f4.rd hokcoincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and thz4.hr ,ogdkf :e Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divi-rpgxy/2mo a/ tk/c 1erges ar/-itaxcm/g po1y/2 kt an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotatxpm3m0k4 xyq.qq3:b gb2zd( se at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blams. gb mydx:pqz2x3k43b0q q (des slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m 0 .d)lyd6qkkia1.s pbto another child. If the ball makes 15.0 revolutions, what is itsik k)pa0yq. 1bdld6.s diameter?    m

  A bicycle with tires 68 cm in diametrnat.4 fw0yr*er travels 8.0 km. How many revolutions do the when0*y4r.ta fw rels make?    $rev$

  (a) A grinding wheel 0.35 m in diame6q;9vvv /dzaqlmaf- ub8,.ds ter rotates at 2500 rpm. Calculate its angular velocity inlfa-;/v v ds.u,b9qzv 8qd6ma $rad/s$ $\omega$ =    $rad/sec$
(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 revolutionjp8m *5tm0/nmkkr6 v* br f6tb in 4.0 s (Fig. 8–38). (a) What is the linear sp*m6 ptb6rm8k fk* rv/bt50n mjeed 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 velocityvl ;t0 2iw:v3jpjkvl0 of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speeds+hydq iei8 kok jb/k 79)ll9:v )vuu6 of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotatcgs a-taoy4 3+e if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,0003a-goya4t + sc $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerate*is 85xtci* exruq,:7- nhyzu s uniformly about its center from 130 rpm to 280 rpm in 5e sr7yz-* iixq8xt:n*uh,cu 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 radiusqf2ej4ptejwm n5z,x: :; imoi *+tv5r $R_1$ 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 Moo wzmgim,x; jos-5uj-7n, 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 cylinder with a diameter of 8.5juz; --ms5w7j x,mig o 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 220e 4z(t(l,67z *ol sxmucg5nww s. Through how many revolutions di oe,zgw mn6(s 4wll(ut*c7z5xd it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2q6mytk6xi3 w4. moh o92ipfk+ .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 flying highspeed jets in a4e 3c.pk p1p12izcfccoi9gmj/ l . u4e whirling “human centrifuge,” which takes 1.0 min /l2ci. gp.c 4 k4ceuom31cef9i1pzpj 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 x xb tqpfq8wi5hj)93w/g.tf8ormly from 240 rpm to 360 rpm in 6.5 s. How far will a point oni9 fb5thj8 /gqq )tp8fwx w3.x the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1504 bf8,l k34dqhrl4fpsy 53 okg0 revolution qkff84bpkyh34d5l, rl3 4so gs before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make z502/ ikdn-ike w8ehy65 revolutions as the car reduces its speed uniformly from 95km/h tkh -i/iz082wky 5ee ndo 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

  The tires of a car make 65 revolutions askc .,hi8c q6yp the car reduces its speed uniformly from 95km/h to 45km/h The tires have pch y8.qc,6kia 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 puts all her wei 6scgvf)a-.y1dmcm t6u(h.e sght on each pedal when climbing a hill. The pedals rotate in a circle of radiu6-)ga (mtvc.s.cye m6fdh 1sus 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 , c+vwpqv m:0kny*s2w of 55 N on the end of a door 74 cm wide. What is the magnitude of*2wpswm, :k +cv 0yqvn the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fijqp x,myw.fq (m5 07kzg. 8–39. Assume that a friction torquem(,5pj.zm qy7kf wx0q 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 of5n;.l zc89ey)wgz m 2 7zqlfbf a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this systemfb; z582)9elz ym7nql.fc gzw.

  The bolts on the cylinder head of an engine 5sed f er0n.a3e)6fgzrequire tightening to a torque of 38 z0n3 6 a)sgeefed.rf5$m \cdot N$ 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 rbqw(rkk (r rt2wb/+, vw :re8sphere of radius 0.648 m when the axis of rotation is through:wwt vr q(kwre28+r, r/ brbk( its center.    $kg \cdot m^2$

  Calculate the moment of inertch1*1w)ueo79vvn 4h, nbuv ce ia of a bicycle wheel 66.7 cm in diameter. The rim and tire*)1uvwcvo1nb ,nech e 4 9uvh7 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 f/0.vm8xldnf on the end of a thin, light rod is rotated in a horizontal ci 8fnv0/x .lfmdrcle 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 potti:)sw4 pap* bner’s wheel rotating at constant angular speed (Fin)ai:4p*wbs p g. 8–42). The friction force between 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 poin yy/i;4rxl odyxz683tt objects shown in Fig. 8–43 i8o4z rx6lyy;d /txy 3about
(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 4 q9b kxg03v7uvco1l9g zqtx. 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 spinning at the correctvdhh7 bxfi 7 co-o7;n, rate, engineers fire four tangential rockets as shown in Fig. 8–44. If theo -b ,;7nv77chofxhid 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 a masobaeu17 x0ef pj/sh -6s of 0.580 kg. Calcul 1 osep- 7efah06b/ujxate
(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 resh -eo )fds729x,yj,sdw i c8unt 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-nb0q b*usd (w0go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round iq(w* 0d ubn0bss a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is es -s/qhfv q u,n*c/v)yventually brought uncq, h-f)// yvn sv*qusiformly 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 d0b41e9 cr iwuat 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 im5;ecinq2a ; the action of the forearm, which rotates about the elbow joint under the action of t;; i2mqca5n eihe 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 lo6xhqq i z;kt0k0 /vgd1ng thin rod, as shown in Fig. 8–46.kqd0v;z6 k 0/qxi1h tg
(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 - 6 2sy-z kvjedbs4lbm9cx(z-consists 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 acceig0f+2hyeowvn 5x;e 9lerates the hammer from rest within four full turns (revolutions) and h5g+0xynoe29 ;f weivreleases 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 ine5yq .t cj5xxx/rtia 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+jw9m+8l o2 g9vjkm qc 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 wc( e7xezzag).6ljwl j79 hpct;kn( 3down a lane at g pwj t;ka7lxn3 lcc9h.w(6z7) (z jee3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as kp.4x-, 42boh wu(a uomcdrq. the sum of two termqoh2k.curm(wp o x4 .au-b ,d4s,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How k);v 1 274lqnkjh ablrmuch net work is required to accelerate it from rest to a rotation rate of 1.002baln1j 7hlv; krq k)4 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass ()wtd :t .vmfc1.80 kg starts from rest and rolls without slipdtc(f) m.:v wtping 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 j o4s-9hv f-.09nqzpzeylih) its tip. It starts to fall and its lower end does not slip. What will be the speed of the upperqn4)yizoephs9j lf 0-h9 v-z. 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 rotating on the end of a thin stxabt vm)nxh/2 g2 hi:.ring in a ci/b:n2 hvi ax)t2h xgm.rcle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform * mlz4+ lgyp4g * 01(oh m79tlfnmnbfgcylindrical grinding wheel of radius 18 cm when rotating at 1500 rplmt7 l( 0fmzng*1+hybf g4mpol4*9 gnm?    $kg \cdot m^2$
(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 at a rc-go /y2y)arsx(a :a2jfmtm( ate of 1.3rev/s If hefm)2-s acj(t(r2y :gaayox m/ 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 inerti6.7* jac yzbgv 6j:cdca by a factor of about 3.5 when changing66* :7 ccgdavzcbyjj. 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 incr3h /-vm/ x4 0fyw1aos uxv:hlzease her spin rotation rate from an initial rate of 1.0 -l01sy/a owh3:h zu/ vvf xm4xrev 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 vertical axis throughal 9* gagf6v9kc k-yc9(j3ny h 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 po(y hjncaaygf9gl -*6c9kk3 v9tter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure qcm0x.uv.v )l 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 ofs,r ,j(y1anjz 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 ou y bl24y,7 n9ock7l 5msj3qyknto an identical disk rot 9,2bl7msy 7lokyjqyuk4 c35n ating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.6glar0 i 3odrzi,)8a o f4nk llp+0,vg4 $rev/s$ 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 ofw/hly8 c yn,oj fjs(zg -z.7.k,ia*eg a rotating merry-go-round platform of radius 3.0 m and moment of inertia 920 o,i(shn,ey w*y ak7 /j.-lgjz8fz .gc $kg \cdot m^2$ 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 rotatmkbxlz. l.2 3bing freely with an angular velocity of 0.8 3. 2l zbx.mlbk$rad/s$ 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, loh ;(n)9itbxr ising about half its mass in the process, an9hi)i;rbt(x nd 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 excess ofofnh(bk nq)x9j0v:7p1 h 3of l 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 8ne1jn+ mvf4x-uua 8a $ 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 platv m+ vb3+3 stfx(zp :jc juxc):a1rt:nform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform: pbrs+jx3vu:c xaf(t+:n1vt3cmzj) 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 6.50/ga v4 qvhlbvc90kji2;)k or-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a m;vkhc4b)rg l29qvo 00vaikj / oment 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 groundzps*ufa7;z czp3 5qz* with the end of the rope lying on the top edge of the spool. A person grabpucp*qz;fzz3 5az7* ss the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such (4f1rhzr1 whf that the same side always faces the Earth. Determine the ratio of thef(1zfhw r r41h Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a r*(xuztvj qb9w6 xx*yd4 *pm- 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 unybm 4/0+cvfeez9 1 jsgiform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered byevcs9 40z+y 1fbm eg/j the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricarjov3 gs0bc-2lt 8 wq0l disks, each of 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 yo0t0- ol8 j3rc gb2swqv-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angulu3us)+xey .dh- -ilmkar 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 w z7k ckyhsrq/3i a3+7our Sun, but with mass 8.0 times as great, were rotating at a speed of 1r7+ k 3k/wqc7sz3hai y.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 mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for mc q4o233 duiia low-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diamet3oud2q i m4c3ier 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 hj ao1,a qglja xe i: cj+e:2*5o*qy*p$H_2O$ 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 /+zt-buibv2b on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L c(rq9p;1fokfwz/7ywo1 zwkjdsd+z; 7 an 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 re7kodpzz y;;(+w7/ w9oz11 j wrqsdffkleased. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radib+)- slujsnswf p12r+ us R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The ste b n l+s)s1frpsw+u-2jp has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn with pm;997ty6zz7gr rk (2anboez a radiuot 6ape7yrn( brzm z9 9z;7kg2s The forces 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 int) -cys9q.d jnw *suk9mo a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circl yn*c-.9s usmd9 kqwj)e 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?    $m \cdot N$

  Model a figure skater’s body as a solid cylug42: yh2fmwwinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly w w24hgy2um f:against her body.   

  You are designing a clutchuz +y/5 kackwt --z6bx assembly which consists of two cylindrical plates, of mas-6xkzy5-+ /u bzcwakts $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fmn) vnnbw/+i*tvv i7eo2:4th;7arz w ig. 8–58. What is the minimum value of the vertical height h that the marble must dro4o+vne;:rw7vb 7vtw* nm z ii2t anh)/p 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 assume *:e*ei6/pcv9 l loazv$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car rex0z4v/; br.xx, zd))3 mb5dmbospikfduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of v/4pz bk;f0 , xb5z)d xx)sibmod.rm3 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