A bicycle odometer (which measures distap 9qx6ej74hjs aix 0h()7yvdence traveled) is attached near the wheel hub and is designed for 27-inch wheels.x4d77ia q(s)0jh6 vjeey h9xp What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant an+(irc )k ad*pagular 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 accelerat*ap) ick+adr (ion? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body j4 bv(5n (/nttlq* l.5jplut bbe described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? +zu ikq dd+vwc5 67x,kExplain.

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 difficu9:/-unza,8v e .rgr fblshc/ult to do a sit-up with your hands behind your head than when your arms are stretched out in fua-crv u r,f/ se.8/zb:gl 9hnront of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three v on2uk. 7ww7w- x5zc1 i+ mcnucb*ym.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 sprocke5.cnw bw7+. 1 7wun*yvmumkoxzc 2-c it or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs withos9p-p :7ia exntc)c60wp ot * flesh and muscle concentrated high, close to the bi s-a*e 6c 7:ntpptcx9p0o)owody (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–w n-hrft0+k+wky/ ku z() ddd135) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zer+3lu4d jxq w5jo? If the net torque on a system isx4+jqwd l35uj zero, is the net force zero?

Two inclines have the same height but make different angles wny 5jh89pc(kwque1gx 6wu4 4eith the horizontal. The same steel ball is rolled d5g694xc eeywn1 8ukqj4 wp uh(own each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an innu6-5:rmt3d-8ets eivc* (lsze 7arb cline. One sphere has twicbtc: l7atz*eed i5uv-m8e(r-6sn 3 rse 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 havhvgnaw7m70o -n, cgrsms (j+(e the same radius and the same mass. They start from resv o7ja-m7(ncr 0n gh gw,sms(+t 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 KE?

We claim that momentum and angular mo7sf;zzkjp5o8cc uj j1f lcojm 1:5o3:mentum are conserved. Yet most moving or rotating objf37c1su8jp1zj ojzfjc::5ocolm ;k5ects eventually slow down and stop. Explain.

If there were a great migration of people toward the Eagbtj;h8oa o8/ rth’s equator, how would this agbaot8 /hjo;8 ffect the length of the day?

Can the diver of Fig1qda8wx4 * q6ofbvqod7bc. b7. 8–29 do a somersault without having any initial rotation w*q4oadf.obcw7b 7vqb168 x qdhen she leaves the board?

The moment of inertia of a rotating solid disk about an axis through i+ca; +xjccsa t3.o pw1ts center of mass itco 1x+a ;+acsj. wcp3s $\frac{1}{2}WR^2$ (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 rotatu*8yux-dzqw 7 ing stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your anguyxw7u8*qud -z lar velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the sam3(u ifj3y(.grz y ohhyx8g(: gs1nwxe9dh7t4e mass. However, one is hollow and the other is solid. gw:sid 9g3o 7y(xhjr4x8fyn y(h zgh31u(.e tDescribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal-jxx3xcl/k) f axle points west. In what direction is the linear velocity of a point on the top of the wheel? If j3-kx)l/fc xx the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Wfyn ohs p*mt7l fo1.)*m2nzuj5 f p-u)hat happens if you walk toward thum.o1 l- pn *fftpjf)z5uho2 y mn7*s)e center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he )zsnk7jdh 5*-bwjiq* throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legkqi j)7w* j-*d5 bnhszs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a heloam6 0fmyzb6z6o*; ttw0g7sa icopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the he6mzo6w0sz* ;b 0tomya7af6gt licopter stable.

  Express the following angles in rad.*hiqx 3gau, ve np4i)ians: (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 coinciden p q4mgkvst9km5 k8e hig1(8*tce. Calculate, using the information inside the Front Cover, the kqv9kt m hi4mse8g g p8*15t(kangular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direi8 e99bn+mlbf,o c (jvsao::1i*g pmgcted at the Moon, 380,000 km from Earth. The beam diverges at an a*9 bf (macpgo:j:1 gnem9l8 vo+i,bisngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender r f4 hv2 -0kzxqk6b,hp*r8 xemqotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What ish4xfxrm2q b0zv, eq6-h*k 8p k the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball qvz*s 4:xb.+x u/gky)a(hdsaw z2kz (makes 15.0 2sxk*dhk/vq bzsuz+ wz(:( x4y.a ) agrevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How mwoe1y,th 3f (7,vc(i-j gwadzany revolutions do the wheelswc,ytg dhf( e1zoi-w a3,v(j 7 make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates 3x do/pom- y7jd57 gxnat 2500 rpm. Calculate its anguldx dy-o xm37/7j 5ogpnar velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution ir zcgnz4 *3 c0z2um e7nwe/ejx,j2ew6n 4.0 s (Fig. 8–38). (a) What is the linear speed of a child * w6e zc mjzen7u2 x03e/czre 4ngw,2jseated 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 arounx3 kd: 1y +6og/ coi(9scunaptd the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of )udqtqu 651j/bq 7z00*brypsy;no g va 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 ax/h(:rirtjy g7 9ep9:.jvqz bsis of rotation is e :hv:( / 7ysr 9rjzqjg9i.tbpto experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center fqe2u80 n1ax sbrom 130 rpm to 280 rpm in 4.0 s. D80b qsxn1eu2aetermine
(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 uft.*n;xb r,qu sn/7b$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put tbm hai3e 1*/,lvmrez-r- ym*u9u1oq yhemselves 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 diamohazr* 3-v l mymmui,rye u/e*1bq1-9eter 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. Througsvsgo(59t7ip:r aur9 e :lc7w h how many rs l9ws a7 r(gc5t iu:pe:rov97evolutions did it turn in this time?    $rev$

  An automobile engine slr z8o0uogmfqxwk ,.-t* 8d6anows 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 jet.di)r k-, -e*y 7xnaho;emzg is in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final spe)7;g*ii o kxmnr ,-yhaze.ed-ed.
(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 360 rpm in 6.5r3p 6kjx:uldx1s e36 u s. How far will a point on the edguex k dr6 j6u1xs3pl3:e of the wheel have traveled in this time?    m

  A cooling fan is turned off when-voq8ns- ku- f it is running at 850rev/min It turns 1500 revolutionss--kn8ouv fq- 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 carqcudb*vbd po098g 2i3 reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.*g023 pcod8iq9 ubdvb
(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 carleh:.m8k9c yrjyoa kjq*h73 2 reduces its speed uniformly from 95km/j r 3y2 mh*chko e.jly:78qk9ah to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on eac*cmu 74dehf y4gq +9qch pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm.gqy c7+4cmuqfed * 9h4
(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 cm8o;; gb5 vsfgyk pv8j9 wide. What is the magnitude of the torque if the force 9pvy; okj58 8g; vsgfbis 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 aboutakbweq swck 2*we2c 4pgn2- wq)6b5v( the axle of the wheel shown in Fig. 8–39. Assume that a fric (waq5*6k qc2w2n-w pgwc ekbvb2se4)tion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a masslessl2wb(te ;+cks rod which pivots as shown in Fig. 8–40. Initi+ tkwb l2sec;(ally the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder qktpt3 s ,7x47v/zbwfhead of an engine require tightening to a torque of 38t34/k,xv tbq7fzws 7p $m \cdot N$ 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 rad38wp k6dzb -v/ le(linius 0.648 m when the axis of rotation is through its centere6wd8b/lknz lp 3vi-( .    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm pr u 8w ersb-z)2+jpr0in diameter. The rim and tire have rbwj-e80+ zr r2)spp ua 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 of a thin, lightfypjzgkf..(sly 9mon1 ru7/ b8 e td2; rod is rotated in a horizontal circle of s; 8pglz97j .ek(1fmdurby. y onft/2radius 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 r81b yw2ujkyh 2h9h ww:otating at constant angular speed (Fig. 8–42). The friction forc1wj 8:k9yw yub whhh22e 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 point objects sh*4+sy9 / /wa v:az9b3tj oho0 xdgtmyh;hbg 2yown in Fig. 8–43 yo 9:b4+g2w*ht;v9m/ gs a bz3tdjah0/o yhxyabout
(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 whoa1 oe a.)k dp,wc1ia2kxf* ut1lo+d x9se total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, enw3tq rl5yoj . nvg**6ugineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg andnyj6 uv*g*w5 olq .tr3 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 rad + gd9ixi g3n355csaouius of 8.50 cm and a mass of 0.580 kg. Calculg9 ci 5a3do3un i5xgs+ate
(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 r7ahd0v top l)vy *,dd6est 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 and/xbb l w3+jxr/c7qh ;,j *cdig 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 disrbh*lcxg;,q+37c/xj bd wi/ jk 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 eventual j,5 l5e.3wp6onpv tjply brought uniformly to rest by a fric5 p v56w3o ppt.ljenj,tional 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 w p3v8v8k fb;.x ado8glf-i w1accelerates 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 action of the forearm, which j uekw/f / (kl;st1v8erotates about thetjee(1/fs;k lvu8k w/ elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8,nc/:zmr/ f0 ore3ik e ym3iv9–46.crrkvee9/my3mfi :,0/izn o 3
(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 o y;qyj )mw,5+:3r5kh liuiwaef 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 accelerates the hammer from rest within fouddsjcku) 46o rc2p.8hc vb1y2r full turns (revol)h yo.6jb 4d s1r kp28cuvc2dcutions) and releases 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 inertiwwoi)hcinz6yn.v4 4 :a 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 k-absx 47(jzag y2ek7torque 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 dow8me)hf d ,7ghfggotca /+k,b :n a lane at 3.cgedgtfb+h7m a)g,/f8o,hk: 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the s. n-s.zvf0q gwum of tvnfgw-z qs.. 0wo 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 j4t3(devf4 mc9 z7xkz7.50 m. How much net work is required to accelerate it from rest tojz k47ecz4m(txdf 3 v9 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 rolls witx0*7smjzt gg(hout slipping dj 7gs*xtz m(g0own 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 i j483ut sw6avjmt 7iq/5 n/cz 0xp.xxpts tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the grospxuanw.zx x4t j08 v5j/pqimct6 /37und? [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 t:b y,u 6cz3c:a(ykfabbq7 3estring in a circle of radius 1.10 m at an angular speed of 10b,c:yq3u(:by 3b zfaceak6 7t.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel 3 l*zf obatkie at+in5/jr735of r jtar /en5tii*3b+a35l fkz7oadius 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 4)+4hlxgyeldat his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his armslxh4ygl e+4)d 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 in)mj:f+q ls3bdut ss 0pq4)1qiertia by a factor of about 3.5 when changing from the straight position to the tuck position.q:u0ptms+ d1lsbqs fqj4) )3i If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of 1. :knv() qtij pqc55m7u0 rev emk u5t5q:( pv7 qinc)jvery 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 through its 7mefp,/zut p- center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radiuf pm/peu7t-, zs 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 :*1g hgr c42rkeuela-5u4w nt 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 9jgge+szp no3r:.c73d b i-reof 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 cylindrichp3hrm; c)tg hx4y)oy * l)bn+al disk of moment of inertia I is dropped onto an identical)yrhg)ocm phn*; h)l4x y bt3+ disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2k0c 4fza/ab;)z fu*hi.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 rmewka a3(x+6qr(xfd6 y0cuu;otating merry-go-round platform of radius 3.0 m andfkr( cx(6m36 yxd;q +u e0awua moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velo)+c j/7()erebup gh 0 fjmufe)city of 0.8 gj)upueme 7c h()f/fje 0r)b+$rad/s$ 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 whiteyzrdea6 k m4-wh o5(+z dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius-z yahomew r+(z 456dk. 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 wingmzvu . q-0we2ds 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 n tv(.9cxo(r-f(d:qttm6z jm$ 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,bt8ii(bly*u;og ,.lz v1cd 3g that can rotate freely without oy, b*u8b1( i;czgtli3ld .gvfriction. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge y0g)ix21v*4tx /zq m-irx tf1r4lkvw of a 6.5-m diameter merry-go-round turntable that is mounted on friczm 2x-r* 4xivi)q0wtl1yxtf 1/rk 4 gvtionless 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 rollsrs/d4be kt,t. 8 ho,gx on the ground with the end of the rope lying on the top edge of th.he ,8dt/,xsg4rk bto e 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 move?

  The Moon orbits the Earth such that the same side always faces t+gjvjt8* u-4g4r fyoshe Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angu4ujy8 ov-tf+g*gr j 4slar momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate ofiso.7am))v i i,k40p)dnatta 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 e0n 0uyjhl+5d m acquires a rotational rate of f d+0u5yjheln0 rom 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 njv)nl- ,cqs: s);aja ,rpzf*5 jpnk0two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) n)ajl)rn;p sfza 0:,*n,5p-vjckq jsthin 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 released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how7e 0wvk c9;nd 2nj5w5nbq5us2j* tyol is the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the syu+j dheb92o z6 pk9 cn)4w+etize of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a 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 ndw64y o+j kc eutz+b2)9hp9eat all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stored int 18vqn.0r oza(0ruf zq.hfx5 a heavy rotating flywheel. Su0fx1qrq f8 vo0a.rhntu5 zz.(ppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratim0)9q dab8f ms weu48es 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 surfgm:t0lmk gz nu1x 4)0jace at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivolr4)dhhz+cu , t freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horh 4,rh+du)lzc izontally 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 .y3-3hrh l /kf, t9ajitqkwh8 R. It is standing vertically on the floor, and we want to ew8j-3 .f,i/tk ah3h hqlty r9kxert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2mq8g, 8ekf)voz/s on a flat road is making a turn with a rad) g8kz8voq,f eius 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 1.5jdyu0 m8 x 4 -f;3;jp.s,akt grwfpbl9 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 fe0 w j;mppya b8xgf,9sf l;. tudr-4kj3at, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as tstda +dn.kdi6up 80+ghin 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 h sd+6in8+pd0a.kgtud eld tightly against her body.   

  You are designing a clutch assembly which kmg( (mnpbuvc)/7s- kconsists of two cylindrical plates, of ma g7(kv) cnm-/msbup(kss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 a07an1c3 k3ee gpo7 5xz.xbwvh nd radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical 5nxe7ack13vbhx .wez7 po3 g0height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do n fh-8h3 qaqucs 9s)pz0ot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car red),dw k,m mgtctolr20: uces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) Whm wg2cdm:olk),rt ,0 tat 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