A bicycle odometer (which measures distance3 qafvvlum dsi ,k9+ zm-u7)g+ traveled) is attached near the wheel hub and is designed for 27-inch wheelsm uuq kai+gdlfs9,-z37vv)+ m. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does rw/t ;za.1nq zijj.f: 6:nh qca point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial rj6cn nzz.;t.a 1:q/i w:hqjfand/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the anl9q mw qcm)g1,gular velocity $\omega$ Explain.

Can a small force ever exert a greater tv imoqgu/) 65sm2i v(borque 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 behind your head th-j:a /f)q qt- y8b;rqryks+hban when your arms are stretched out in/jf qq;sryq -h)r y:- b+ba8tk front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wovnn.la: 41hkqa33b l heel 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 sprov1balhnl q3:.o ak34ncket or a large front sprocket? Why?

Mammals that depend on being able to run fag z1eph v0/* sibbrsbk))cxv e2-w+y :st have slender lower legs with flesh and muscle concentrated high, close tz0xi seye bs* cvwprgkbh/:) 12b)-+vo the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lon86ki)h twtlm ,*cd*y qm *jmi.g, narrow beam?

If the net force on a system is zero, i5 b5+ cuctkk3ss the net torque also zero? If the net torque on a system is zero, is the net fork k5c +bcu5ts3ce zero?

Two inclines have the same height but make different angles with p16k7xhvsl89ba 1ko e ,0zgqkthe horizontal. The same steel ball is rolled down each incline. On which incline willaqk eplgz9bk6 x1s17 h8v,o0 k the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start ro yn enj6g0uk 9(aez,2olling (from rest) down an incline. One sphere has twice thegyn60jz k euo2n(9ae, 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 energy at the bottom?

A sphere and a cylinderlo2q,fxpwb2jvh8g xgz ;0( y 2 have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational plb2y(j,f o8h ;q2gxv2xg0zwKE?

We claim that momentum and angular momentum are conse oqo q )umw0yfc;*:ijqu+ )nv5rved. Yet most moving or rotating objec5 0imju*o uc+foy) ;vnq: qwq)ts eventually slow down and stop. Explain.

If there were a great migration of people toward the Earthu xf u33xri0fbu51t1p )u* crr’s equator, how would this affect the length of u3rr)ur1*fu5u 3fctx 1xbpi0the day?

Can the diver of Fig. umhj5qbsy3i5 d;;x *k,c qj9k8–29 do a somersault without having any initial rotation when she lebus;kk mqcx,j*i5 j53 ;dh9qy aves the board?

The moment of inertia of a rota8z(j5v gve2lb g 6,lssting solid disk about an axis through its center ,lj8glz 65( vss2bve gof 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 a 2-kg mass in yhnu0l,x l0sj7*yth. each outstretched hand. If you suddey*hlu.0l n,70yxjh stnly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the skd 6w4dwv:s( pame mass. However, one is hollow and the other (:4vdw pdks6 wis solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotatin07 igzcziveu t9:x9 hd) ;8ipoqt+ +oeg on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of +h 9czi9 ;o0+zv8itgu) xi:oeptqd e7 this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing tflv 9bt9y2-o on the edge of a large freely rotating turntable. What happens if you walk toward the cey lvf9- tbo9t2nter?

A shortstop may leap into the air to x5r)m5 ih 1jkacatch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his r155ajhm)xikhips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of -pg utuf +0dn5f)hab-conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or fdfu h)-+gup0 n5bat -more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in r5u 84 ippg.8oudp 6ffiadians: (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 becausfz18 t 0e9sgbte of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen 1 tzf0ge b8ts9on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is dire-ky/fli/:z 2v 2 efmf 2iq)epjcted at the Moon, 380,000 km from Earth. The beam diverges at an f p :-yffm)z/l kj2 /qiev2i2eangle $\theta$ (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 ratei(;um*w ikc()o 0eqt r of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acqi uc;(kwim0 r)te( *oceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a le i/5(h3uh9t nj6cgrcbvel floor 3.5 m to another child. If the ball makes 15.0 r9i cr5ghn3t/b6 h( cujevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutio-9qau*/y:r/;ql7xhgk vge srns do the wheels maker-gg e: 9/qv;hr*sk xyaql/u 7?    $rev$

  (a) A grinding wheel 0.35 m in diame4-- kor2r7j* tazjaglter rotates at 2500 rpm. Calculate its angular velocity7- r*g 2lktraj aj-zo4 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 r zeol pmnt45 kiy9 ggrn05q),+evolution in 4.0 s (Fig. 8–38). (a) What is the linear speed g pnily0+ z,o9kmge 4nrq)t55 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 yr l)v74jf+e v oof-c-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 speed of a poinnoj)/d dno. )ht
(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 centrifube:nxm0 8ug s1 1k3pqfge rotate if a particle 7.0 cm from the axis of rotation is to experience an accelerationpq 1xn0gb8ks3f1u m :e of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unifo+0h:*sep y n-rd+ 8zh(y hzuf)8jlijg rmly about its center from 130 rpm to 280 rzip(*hu gyhe8-sf hj :r) d ynjl8++z0pm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius s0+xo4bph4 0- ;s3 hszdxfdin$R_1$ 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 n ut)ne59zvsv;v t.w,vjg a(ub0;o/ u 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 5vu,w; gnva/e)u 9ov0; nv j.tbsu(tz12-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 from rest to 15,000 rpm in 220 s. Through 3hzx-4eq2)alqwo 3ih how many revolutions did it turn in)q3elhqhi4wa xz -2o3 this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.py0/g*hrifwb5we wti04v/ v 0 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 ( )t5iozt wj8as5w(fya whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions befotf yw8t ozi)(5w( 5jsare reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm tk 7qlpe hmi2a vpyfv2m8m8+.2o 360 rpm in 6.5 s. How far will a point on the edge ofv2l7k.q 8mp2+i8mpy ef 2hav m the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runni+r p:nju+kg 9y*mut +mng at 850rev/min It turns 1500 revolutimty: u+ n+9pu j*+mkrgons before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions a0r-vw w 2e6 yqeytx*8.hd1m sos the car reduces its speed uniformly from 95km/h to 45kme0* yh-ey.s w 8wmdt6xv1o2rq /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 as the caglc hax9n(v u-t2+1lj r reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 + lhjl(n9g-vtxa12cum.
(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 weight on each pedal when swwi37ho.j 6 4msp/iyy/d/ x+5b aeonclimbing a hill. The pedals rotate in a circle of y/e56wny oi3.sboh /7xdwi+s 4jm/a p radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm w9fsnysowiw,vi 5ez5n6 j9/v5ide. What is the magnitude of the torque if the force is yfs / vnn5jwvi5w65 ,o9eizs9exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assumie -a8mqv,+zi -9+uy,t bjoake that a fj+,uoybzqa9 ,k-i im+-ev 8 tariction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attache-0e nk)pn)z t9q zc(vn lv)i,yd to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and zzel0vq)9)n ikyp t,n() v-nc direction of the net torque on this system.

  The bolts on the cylinder dt8ls4l 2o-dcb+ nzel5 d:z 1ohead of an engine require tightening to a torque of 38-8n+tod 2 41 ld:lco5dzs elbz $m \cdot N$ 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 sphere of radius 0.648 c:5pr h8bcxeyp.-dcgu 4/t h( m when the axis of rotation is through its centh8rdh/ u x4(cby-p.tcpgc5 :eer.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 6+rbkbxg24rhyj3rjo) w4d +z56.7 cm in diameter. The rim and tire hzrr 5+y kjbbd4)o x+hjw34r2gave a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end o kna;54hc7 f+-wmb gxlpfjq8 3f a thin, light rod is rotated in a horizontal ci3p-k+ba h7xj 5;mq 8c gff4wnlrcle 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 rotating at constant angular spe*p1s+,a mruyp4l mp5fed (Fig. 8–42). The friction force between her hands and the clays *pu1r4+ fp5pmm,yal 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 o jozj9, s9e qw6;hrzp1f the array of point objects shown in Fig. 8–43 1j pow , e9q69z;hjsrzabout
(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 yv2dvd tw;4 (8ipnoem 1s:l0tis $5.3 \times10^{ -26}$ 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 r: 4rutp0gaen*g/v/uspinning 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 radpean ugr0 vu4g/ :r*/tius 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 mass4,re .(b y+du/yhus wu of 0.580 kg. Calculatewyr by s(.eu+uu ,4/dh
(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 4 :ld8va mm.swxnz(s *c4*fhd 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-rounmpu6j /abzfzjr 7cw;+6 y.q)hl 88af0 j+ bykmd and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional to 8ka hyy7 wru6;bz +8fp mljam6jfq+/c 0b.zj)rque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut ob *q:be6kw3i cff and is eventually brought unif6ek3q * bbi:wcormly 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–fwxr4 ,zfj7* f45 accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the acvorm: ,s lv1+u fg(d6ztion of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The baduz( gf1v,+s r:mo6lv ll 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 sho t*gwa*rwa0 ojvfzbi +50x*5ywn in Fig. 8–4 a+f50vx*b* yawg50*wzoij tr 6.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two edu8oi34v.: k ainrr ,masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within b*s,ydrq(lu sx 9rn .l*xof/, four full turns (revolutions) and releases xqdb9lnl*rr,f *xu . ss o,y/(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 tfheh74x84k vr xy q,iqn9h8q4i 0p3ea moment 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 eb e7f;z ;im9lnw )pc.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 9.0 cm rolls without slipping down a lawe88d k/wyek*xq-/mgq 9ue4 b ne at 3ed84k -8ewqgx*q ek/u9m wy b/.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as9cbd) rz9 kg,b the sum of two tgd9c 9)k rbbz,erms,
(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 t9.n6bv:eedfzj r/s s:- g xf5a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from restznff.s:5sv r:e6xdt/g e -b9j to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass v:ugd )3yhm+ksef1h 3*q5x hh1.80 kg starts from rest and rolls without slipping down a 30.05kfydh3u1q *e h: +mhh)x3vsg $^{\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 and do( 8 x8v1( ebscbr*fiits lower end does not slip. What will be the speed of the upper end of the p1i bbr(fvxs oec*8(8d ole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-gd1picaw.t793 lmb:f kg ball rotating on the end of a thin string in a circle of radius 1.10 m 1f.9bp: twca7m gd il3at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindo-9y)-bh u mizing wheel of radius 18 cm when rotating at 1500 rpm?hmu-- i9by) zo    $kg \cdot m^2$
(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 gr:pfrr1 0 ryej*92s krotating at a rate of 1.3rev/s If he raises his arms*9 fpkr :2rjgyr 10ser 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 inertia byvh6q*)rh trj m1 m3,duvb 4wk8 a factor of about 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 a 6kvwrd*3m1tr4 8h ,j)qmb vuhngular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of kdx 4cr l8m*b/1.0 cldb*4xm / kr8rev 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 e j/v l/va9h1svertical axis through its center at a frequency of 1.5rev/s The wheel can be considered1hv las/j/ev9 a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum id zvkoz+18/l/xqcp, 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 7 hf k++sqiwprl9g1q 0momentum 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 inerts kp861arihq i4 uc.3cxx00,e 28ft5jndcze oia I is dropped onto an identic8rzchcejd t61a u qfk20xii.8 co3p,s0n ex45al 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 atq hm/hiv4:r- i :ol2jv 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round pl7gpn258 enepy atform of pe2ny ge78pn5radius 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-roz v 1q,++bmfemund is rotating freely with an angular velocity of 0.81+ef+ zmvmqb , $rad/s$ 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 collcr3*6ygpj 5j3sx1w mec:l lg 7apses into a white dwarf, losing about half its mass iljl 7j 1:36xc rg3* wgecpsym5n the 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 wixote yun1q /oefql+d9 f6- h1,nds 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 v)- /*ufiyqb y w4jtwxb)+us 5 saxx+/$ 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, ie:f9rx(yw9 w wlenc (u+ e*b;/qoju u9nitially at rest, that can rotate freely without friction. Thnjeu r(of/9ex c*y(ulb;w wu99+ qew: e 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 diameter merry-goa*uq ud th)hg6 g+5nl9-round turntable that is mounted on fri6u+ ltuhqa5ngg9*)dh ctionless 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 fdra3 9 ikk- 9ncf2jg5of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. 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 jdif53ck-9 krn a9fg2move?

  The Moon orbits the Earth such that the same side always fhvj) o*9tcx+ kaces the Earth. Determine the rtjvo9xk)+c h *atio 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 particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate ofdva,+ z6 pyi8y 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(,8 ysmz0 kom5nwhs boaubr)e q;q3+; radius 0.20 m acquires a rotational raty;eq n uq;s5(+)kszrm0m3 ,8ob ahobw e of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mh.isyckb 2 ykh/w, .a-ass 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 when it reaches the end of its 1.0-m-long string, if it is releakih -.2 byayks.ch/w,sed from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular j / ;k g3gro* lgepdnqg3s*5l+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 sizem( mg zc/)lgsp/h 3l+w of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 day3gzc +sw )/p mhg/l(lms. 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 a2h7f8 lv j/b1h x4spuc 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 diameter 1v shx 4b/8lpcujhf17 2.50 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 illustratdstwo /(wro8 jnu51 b5es 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 surface at speed pe8lcz:wk4 y4v=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 h0zmvkc**q) mcy3b0j c1,eh iM and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the ang1b*3z c0ijm*ev,hm 0 )khcqycular 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 standing verticall ( )t6iko(kgd+nntm s75(xad vg1d;tiy on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step agati(a7dd 5( dm6k 1t)nn ogkxs(v tg+i;inst 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 roaxcl2yzbqw/yx+,zo 7a,w 4)upd is making a turn with ax+),obx,a l/c wuwzz7py y24q radius 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 into a sling of length 1.5 m and 6txktou b:p9 5c ;cx.vbegins 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 frompk ;9cot:vut bx5c.x 6?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as tk kzhs:.c0 htoh)br//hin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with t.bz)0kcohs/ k/ h:hroutstretched arms, and with arms held tightly against her body.   

  You are designing a clutch asso*okg)y- j 8is g9iio*embly which consists of two cylindrical plates, of k9g*so ioj)-iyio8g *mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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, *,p4t m*o7vcakf s+gvjl4tm r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drov*+fo4m,ck 7msaj*tt 4,p l vgp 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 ex 4yp *uq zzc7e:j/v1not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its s7nb o0+0apcvb peed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) 0bv07c aonp+b 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