A bicycle odometer (which measu15 keo. a7kz)mgkrpzaq(e. pjbep 5;1res distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle witkpo jkaz .5a(z7)pmg.5 peq1e; be1rkh 24-inch wheels?

Suppose a disk rotates a/,p0r kq0wn zb5c*brdt constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration cb5bpc rq*z dn/0,wk r0hange?

Could a nonrigid body be described by a si r 2v9rhd,a5zangle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expl5ed-52sck e wz ,tirl/; -ge+genxw7lain.

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 thaw .qp0-pua.k mn when your arms are stretched out in front of yup -aqk m..p0wou? A diagram may help you to answer this.

A 21-speed bicycle has seven sp hd;n ct91j okb9u(,ayrockets 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 smallt99n,ju hc;d1bo(ky a front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower lec,xxfa6 nl, gaeql0 *:gs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotatxcf x ,nae,0aq:* g6llional dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry bq 5-oudc3lssle:q8 p/fff)t*.yo2 c a long, narrow beam?

If the net force on a system is zero, is the net tor0 6i .giee9 njzs2ehf/z- yevwcek ,t2/x-sr6 que also zero? If the net torque on a system is zero, is the net force zero2zhr/xg2ik njzw-e/estfc6- s0,.e 9eyi 6e v?

Two inclines have the same height but makegmz7b9 wun/v m;oc 7p8 different angles with the horizontal. The same steel ball is rolled down each incline. On whim8 z7;bnpvgu97m/w oc ch incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an wd,g.55gwm,xvve k e6z9+ lee incline. One sphere hawld,,veezwgem 5k+ x9 5v6e.gs 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 energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start ;v+-bw/mgg .*mwabgb from rest at the top of an inclinb. -bw/+;gb*mgav wgme. 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 KE?

We claim that momentum and angular momentum are conserved. Yet most moving orzs pe +(mxg7b 436rquh3a :udx rotating objects eventuaz a+3u7p3m xbsh(:qr6 xgue4dlly slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, hojta.h i:l k8a mav75 uhw087ik u)bj5sw would hi 5mtku8 : vhk jjaaul80is)77wb. 5athis affect the length of the day?

Can the diver of Fig. 83cyuj)u.uo rc3 ee/ 3mzx-wcpx.a4 : m–29 do a somersault without having any initial rotation when she leaves theu3/e cz4mccw- a:uy mx)xe..r3 op ju3 board?

The moment of inertia of a rotating solid disk about /yr sah a-udehl/5: 7gxx0j 8xan axis through its center of masyer-lg /xa:85xajx 7hhd s/0 us 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 amu5;ha(q7so 0j :xaqc rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, wilh:;m saax 7qj05(c ouql your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identi c1wh47g,mlz 9q.l jyecal and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determi.hzc1,m97g lw lyjqe4ne which is which.

The angular velocity of a wheel rotaa--) lotga5b.nv ggt )ting 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 this point at the top of the wheel. Is the angular speed increasing or decreasintvo taa)g)g 5lg- n.-bg?

Suppose you are standing on the edge of e3zc 8rjku0-n ixt n4+vva--aa large freely rotating turntable. What happens if you walk toward thetz-- n0c-ix3j8n+a e a vku4vr center?

A shortstop may leap into the air to catcgpby6 c6*phq) 5d*rdh kt* 8smfglo4:h 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 hips and legs rotate in f d :)kbgyrm*o86 pt 65dl*schq*hg4pthe opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discrukprw2)jh* )uss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways tr)up j*wk rh2)he second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (npp*l q1p m*b*jndkf3 -ex-8x y+cvl5a) 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 bexue4)1ii,s9bf bs;f8 fe+ ry gcause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameteu;14 s)f e g8exsi9if,rybf+brs (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, a0nu q;hf 8zl2380,000 km from Earth. The beam diverges at an 02qu8nfla ;zhangle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm.j*z(tf7ntov* ys6b i . When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow dot (. 6nvyif*jz7t*sbown?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child.e c(13 bepgzq ,ie7h *mlnd1.g If the ball makes 15.0 revolutions, ( gqm1 ,e h.3 1dbgezi*pelcn7what is its diameter?    m

  A bicycle with tires 68 cm in diameterls+oz lhebiv35).1npw kfz6- o*n)wq travels 8.0 km. How many revolutions do the wheels mak3zllnh-5b pvw.6oon )+si 1* efz)wqke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates al 1ypx 7m2awrf2bqf:(t 2500 rpm. Calculate its angular veloc m wfp2 bral:y(1fx2q7ity 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 hp4xd5p pm6(pcomplete revolution in 4.0 s (Fig. 8–38). (a) ppdp4 x65( hpmWhat is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit ar:ix g;cwd4 ii3m -1kypound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed sdrzu4 e:j: 1y6xbo(c 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 rotate if a particle 7.0 cm from the axvj1dm-nnn, b1csg)q :is of rotation is to exper 1snvjq,mbgd) 1n :c-nience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acejtg o5f4 sus(o50g-ocelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 (s4j0o5e -s tgguof5os. 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 mg/vozmxnpl85g 3r ,9$R_1$ 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, a)o7zjs gd-e zqj5w,bcrg7s9 0stronauts 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 interva5)oqrb7 s 9s7jzc,gw-ej0 dz gl. 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.qe8wc9 l. 4gfn Through how many revolutions did it tw49ql.f eg8 cnurn in this time?    $rev$

  An automobile engine sl4ik (uf+htpz2 ows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed tt7j;+h6x/b hy c obx2jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revoluttxh 76j ho;2 /byt+bxcions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 36k+gn 7k;r+6 hwsd mq mvbca45)0 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this tik5v+mg6;rdbam+cws 7) nhq4 k me?    m

  A cooling fan is turned off when it is d ck3*c;rybaia00 w:qrunning at 850rev/min It turns 1500 revolukcib;ra:3d*w 0acy q0tions 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 as the car reduces its speed uniformly frohi4bn,fsa+ ,,rwuke y96 u* nyf+c3gom 95km/h to 45km/h The tires have a diameter ofo+syfc9,,bu4 ,ke ry +nng6fu*h3awi 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 carp 3jo iclvinbw166 r5 hax(j:6y,m (cm reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter 6:x5a i( ycmm(6poi,1jbwjrhlv nc6 3of 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 he-in .cwnbj 0kewwq.x 48lt* s6r weight on each pedal when climbing a hill. The pedals rotate in a circle wex.0b k .6tlqin*jw sc-w8n4of 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 of0 ql /iu1llr) ;guz6+kp:jipf a door 74 cm wide. What is the magnitud+fz llu/jkp 06):urgi;qlip 1e 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 the wheel shttfpry 79mo/;36:ik xwit7t g r69dnwown in Fig. 8–39. Assume that a friction torque of 0.4 9oyrd69g:tn6tt7ti;p7mr/ xw w3fik $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are atmf(6q; /vbv1zlu ,sy xtached 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 vyxmulfb1;(v, 6q/sz the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head ozqm ny-/ry;fht-c ee6: c9r e,d f4g0bf an engine require tightening to a torque of 38b gy9 4-tryf0me ccdrh6 ,n-e;fq/ez: $m \cdot N$ 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 sf-zr/ wi7 x-uof radius 0.648 m when the axis of rotation is tr/iuf--w7xs zhrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim 8vm. zmhyuqry**9(dwand tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?d vuymm*.w q(zy9h 8*r).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rcw j9unj2n,x ri:zg 0(otated in a horizontalr2j9ixgz0nu : n( jc,w circle 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 bowlh*w0v/hll ( sl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands ahsl*/w(l vlh0nd 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 ofv., m6 *9i oym4onbpg/a 1igkf inertia of the array of point objects shown in Fig. 8–431igi ,4kny. bmvpm9*oof6g a/ about
(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 a6yv1pe.ozt ) stoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform e a9i zf v00dse6os5t*cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–ee0fszsv 90ia do 56t*44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder witdn k em4gg+wk 2+p*x9ah a radius of 8.50 cm and a mass of 0.580 g ge*k94kx a2w+p+nmd kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it fzyy.3s2l z/xr(zv4st rom 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-round af/ fhx y:4f-zmnd 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 pr4zfffxhy- :/ moduce 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 eventually broughtji,dnmy 69f, +-ct- aly,a pzm uniform9,- 6mnadtmp c, za-yfyj,+li ly 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. 8–4c*3j7)je xg i /sy *pi+my,cfh5 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 eoqg)egi( z 42lp+q q7; gfsc4ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifl47cisfqg 2gq4zeq(+pg)o e; ormly 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 thi0qts0hl lv:i) n rod, as shown in Fig. 8–46.0hl vlisq):t 0
(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 massedi4t d6 y:8csis, $m_1$ 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 foxp- h)w -7i/q9bty ltvur full turns (revolutions) and releases -ty q7/t xwlp9 )ih-vbit 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 f mfou.p n pq823u/tp :mu14jiinertia 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 d3 1h qd318*h4yqnz hiu9zs ikzh ly3f*evelops 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 rade3nzzif+592kv+ chne ius 9.0 cm rolls without slipping down a lanei9+3 cefnzv2e5z+kh n at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eart*s-bua 2pfan9)y jj hp2d. y;mz.h4kwh with respect to the Sun as the sum of two a-.9;fun2hjpa4wp k.yb hyzmd j)*2 s terms,
(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 t;dghkjtce77p+ 9g )q: hir4km. How much net work is required to acceler+q)49h t:gitjpegkk h7d c7;rate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and j45ri,1y7m v46mou xdgq i:5y 2xfyierolls without slipping d6dq7joimmv:f24rxg ex5yiyu 5 i,1 y4own a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts t-f+9tm* )gwuck4jg l vo fall and its lower end does not slip. W)wt+uj g*4c-v9kmlg fhat will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a tdf,p-gqw -vkjl8 ) vf*hin string in a circdq-*vfvlp g,8fw) j-kle 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 kc:cbt8 z 4*:r0hia6x)us(btfut /nz a 2.8-kg uniform cylindrical grinding wheel of radiusn( )tu0 z68ukc:x4b* s aft:zbh/ictr 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platf 1txrvmkum43 3n1yz )qorm that is rotating at a rate of 1.3rev/s If he raises his arms to a hor133zut 4ym ) xkvm1qrnizontal 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 oes-wa6j up7q*6cx7;q vjf7binertia by a facto oe;vjpsqf 67 xj*7a6 c7-qubwr 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 angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rot+qjgva y4)f us42/nt hi2v;ftation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3f fv4q4a vyu i;sjh2)/ttgn2 + $rev/s$ 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 through its centevesrkqy2qskq0 .b2 *; r at a frequency of 1.5rev/s The wheel can be considered a uniksk2 y .qqrs;2 bq0ev*form 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 ofaq:l4 4)c2q.qv08xyha/ q*pqda wrhv t b ui7- a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum n4 c 6m7vz zfa:,fizn.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 disbf op;9p i6;wxk of moment of inertia I is dropped onto an identical disk roti69;bpw foxp; 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 2.4 4 wa-n. nh7,n6rucu cy$rev/s$ 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 kgz1nyv qr++rv4 stands at the center of a rotating merry-go-round platform of radiu zynvq4 1+vrr+s 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 iv x.:,./0g6 er bj6awvyoiygfs rotating freely with an angular velocity of 0 vveo.:gy/.wy0r,g6 j afixb6.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into ap .sf8lw-he*v white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing ra8vw l fhs-e*p.dius. 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 of 12 t(+vywquv) *x4dfhj5 0 $km/h$ 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 -p :tm4-oxnry$ 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 can lzb (zji w1zp3;5ly q r0 k9qess2/ks.rotate freely without friction. The moment of inertia of the person plus tlr/kj zk zzy psi3 02b15l.9qsq(we;she 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-gyma )dppk2 7:so-round turntable that is mounted on frictionless bearings and has a moment of inertia y pksm)2d: ap7of 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 lyia ef96js 42wl5rwe kk9ng 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 unwindr kewwf59j9 ak2els64 s from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth suc:koe:exopw n1:fb 81 kh that the same side always faces the Earth. Determine the ratio of the Moon::1pw1:kfoeoekn x8b ’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 oi n4tjm1/6nfrest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a unifr u72gsm5p4rv. ltwk 8orm cylinder of radius 0.20 m acquires a rotational rate of from rest 4 rstrl57uw2 mv8.kgp 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 cy1y6 yr*vzu ut7lindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub*ur utyzv16y 7 of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheelexjj 1agq( j)7 ($\omega_R$) 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 m85(o egz;tnst d(k- rxass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that thez(xdrt ngsoetk(5 -8; 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 auto/5ugar6bdm dm yg r+2:mobile 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 flywheeubdmr6rgmd +5/y ga:2 l of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates tm1mm;/;bac ih jk69san $H_2O$ 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 knfb n+r(r4,qez n 9 61jetekef *9tor(7odu9 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 gn lqug;u23b.l /vtn r(5v5tqL can pivot freely (i.e., we ignore friction) about a hinge q5;/2(ggtnr3. v5ut vlbulqn attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity 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 i geyqwdd(ukuat 3/ (86s standing vertically on the floor, and we want to exert a hoytdu(6kweu/ qg3 (ad8rizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat r7*7o2rctyyqp:nh z:lo mteo.)g -m-coad is making a turn with a radius The forces acting on the cyclist g 2o7-moco-:*z.rlttnp)ye yc : mq 7hand 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 lh; 9t 6a2u had6r*h nlqfswo37ength 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does th6u7ah9fwld h2*h6rt; ns 3aoqe torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, makp ft6 gb)ka155a lr;ca*nx;pj ing reasonable esaarc51; )xlf; tg jkp p*n5a6btimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consisva(x9featg48as l l*:ts of two cylindrical plates, of mass ags48t9( vf e*x:all a$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loong*x u+;gb i;(rof3wyped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the high go*( nrfyuxg; bi+;w3est point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not a b4f3 e; cfdjz(cwa2tmph .1-sssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car ren,ey 6 g)kp.qnduces its speed uniformly from 90km/h to 60km/h The tirpgq n6ynk.e, )es have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s