A bicycle odometer (which measurh*t g(b4pv7tt0e oo/des distance traveled) is attached near the wheel hub and is designed for 27-invepb 4ttg*(o t 0h/7doch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at consta 311a,isw az-nfvao+p.oh ;ch nt 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 a afa ,1iz vn3 och-spwo1+ha.;cceleration change?

Could a nonrigid body beu d6j,iru 0zi m(tno umlf*9,+ described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explabjp+g (,l)bb7or x 2s3sba px-)mp /auin.

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 behi,d6h v xkrik gm.oq)- h/)p/z p,lh+lwnd your head than when your arms are stretched out in front of you? A diagram may help you to answer thklipo, z-gr/qd+ h lm6/x.hp , )wkvh)is.

A 21-speed bicycle has seven sprockets at the0m:x:wvo 6b26euwz:9ggv c hgqdq 48n rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small r4 h0vgdq:o6zvw:8:96 b e mg2cwqxnguear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fleshvh ;w, ;oqrjaofy:)1id+/ nglg m4 k)g )i+qao,gg; w)m rl 41oynfd;kghj /:vand muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beaa7oemtfup.njl 4 )h((m?

If the net force on a system is zero, is the net torque also zero? If tn,rv 6st. k-f lp1nim8he net torque on a system is zero, is the net force,lr 6vns i m8nk.p1tf- zero?

Two inclines have the same height but make differejepm6z9k. b t0nt angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? p.jmkz6 0tb e9Explain.

Two solid spheres simultan0bsx 3qir6pk9eously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Wkq3rsxi9 p06 bhich 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 radom9:2q,rx, a zi)e lc;e(jwp6r5 mowm ius 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 energae65 ;j oezm,2w,9i) (rp: xow crlqmmy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserve fyyis,9c 500vlbuh+pd23hq c d. Yet most moving or rotating objuv 0cdqsfc2i h+,hl35y b 0yp9ects eventually slow down and stop. Explain.

If there were a great migration of people tow7 ,rox)l6 c1x7jtv/x /feqhbnard the Earth’s equator, how would this affect the length of the darje6l)7h/qx/vc x t fn1,xob7y?

Can the diver of Fig. 8–29 do a somersault without having any initial rotasuc +ao0f wzpvk em5 iy28q:,3tion w0:,ewqau5s pkyzv2f3o8c+i mhen she leaves the board?

The moment of inertia of a rotating solid disk about an axis fzhev,ethf6 2y a/+ a7through its center of ea,v hf6ye2a7+ tzf /hmass 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 holdwgbo 0 j..-max.ba*biing a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angulaa..w bx.a*-bj bom0 gir velocity increase, decrease, or stay the same? Explain.

Two spheres look identical an-a jw7ttm0 *t x76hfwid have the same mass. However, one is hollow and the other is solid. Describe at*6h- mfjit77 w0t wxan experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle poj0mq8i7,cj* k9 oenej ints west. In what direction is the line0*konje jq7j8e9 ,mciar 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 decreasing?

Suppose you are standing on the edge of a large freely rota m5f2zbq 70tzf1.jcc2j*e )i+-flydzeb 1rd uting turntable. What happens1+z 52jbfld -furt1db* .cezm7y i f)j0ez2 cq if you walk toward the center?

A shortstop may leap into the air to catch;2/sg oyjpghy 2ef) j* a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If yoy gg*22efos;yjjp h/)u look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angulu7 4z nb3g(lfsar momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicoptez( nu3b7 g4flsr stable.

  Express the following angles in7xpu6h0b cnskv*ux1zh d4:z jrem 0/5 radians: (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 est:0w gih2 .culbo-,f4qb k/coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun i o0w/:b .hfqtg kl4 ,bc2eu-sand the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divrc r vk z*snu86/zc.(jerges at an angr6 /cvr ksjnz*zuc. (8le $\theta$ (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. When aj4/ cd sy( (n;bo6sdethe motor is turned off during ;cd(bsjans(e4 o6yd / operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level 8b:+he6 y*mljzpu8n sfloor 3.5 m to another child. If the ball makes 15.0 revolutions, wh8*l8 yb6+zj emsuh:pnat is its diameter?    m

  A bicycle with tires 6d .3l;f7x +oknu l7vmm8 cm in diameter travels 8.0 km. How many revolutions do the whemk.f d vom;xn7u3+7llels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates 0nymaf n +uz,23cq3qdat 2500 rpm. Calculate its angular 0da3+ uf32nq, yz mncqvelocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s ((du (:l yub2fwFig. 8–38). (a) What is the linear speed of a c(u2wb fl(: udyhild 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 thsy:-f o9rkr6se 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 y3 uuwezqn(8- 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 parti4*+crt fcuaonj c09n8 cle 7.0 cm from the axis of rotation is to expea j8+ r ftu0co94cn*cnrience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center o-q7v2gwqa*8 u bwlwzfzw*(y 2+avr ,h gj 46dfrom 130 rpm to 280 rpm in 4.0 s. De8zdqb -gql4fw6wzavuh w( wyvr o, 22 j*+g7*atermine
(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 radiu2 vavodas+7/n s $R_1$ 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, astronautsnv*-ov0c t n.x aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 .0nxt-* v cvnom. 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 unifos2. w6cgpixu *rmly from rest to 15,000 rpm in 220 s. Through how many re6 xcipg.s*u2w volutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm br1dgw) hg8s:m1owo v38zy4p 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 jets in a whitkl f-;o e1ac4rling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions -41kl; ef ctaobefore 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 tumwlc11k)xr,( pe,4d hrl:u ho 360 rpm in 6.5 s. How far will a point on4eupc hm1whkldl, : r),(1xur the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when itp rbo,4soz/:u qleh 2edi bm 0/uuz*hj(jw:9 2 is running at 850rev/min It turns 1500 revolutions before it comes to a2:w sbe:(e9li upru42z,/dqj/mb zju h 0*oho 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 uniforgy/i c.:ho1+s5xy)cwzx gg9 *fsh-xkmly from 95km/h to 45km/h The tires have a diameter of 0.80o1.+: g9wzyk/)hig s* f5xchys -xcxg m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car r2vx s;nc9 nbgl.h7y *teduces its speed uniformly from 95km/h to 45km/h The tires have a *nbg2vx 9. 7nl yt;schdiameter 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 weightq 3 9jifhoke6jzrw7pl6*q-d1 on each pedal when climbing a hill. The pedals rotate in a cif1h qw6*9dj-ej k3q6z7or plircle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force +c,.i4x,kppi9m3wr 7vs r oau of 55 N on the end of a door 74 cm wide. What is the magnitv73 u+,srpwoici.p4marx, k9ude 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 shown in Fig. 8–39. Assr/p(mq tq6zw5 yp dcba;+2j(z ume that a friction toa( cp z;t5dw2q+ 6/bry(mpjz qrque 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 mass eaeixk eu4-6l;wx(;7g cyxt/less rod which pivots as shown in xx7wt l 6k4/;eegxiuy-(ca; eFig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torquemzfs ec5oa9bbb0wjr i f4t,o3v/+ 81b of 38jec4i ab ,sbfb3/+5mowzb1o8v0t9rf $m \cdot N$ 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 m whb xrq; dfo2fvoz1x;( 3en the axis of rotation is through its center. 3xzo2;qvd(;f f rb1o x   $kg \cdot m^2$

  Calculate the moment of inertia of a bicy2fdx:0zo:;d lxytd 2ycle wheel 66.7 cm in diameter. The rim andd;x:l2zxd tyy:2fdo0 tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in2qyq/cd(kg f , a horizontalc/qgfqd, y2k( 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 bowl on a potter’s wheel rotating at constanrdqjm)9 zj j*(t angular speed (Fig. 8–42). The frictz(d* mjrjqj 9)ion force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of ine;pi9-+yk io oprtia of the array of point objects shown in Fig. 8–43 abo -ypi9ki+po; out
(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 4b/)c) ku kcgrtotal 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 rateg )p xousbqh203. dris5u9p+s, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0pu2sr5g+o u39ix hps)d b.0s q 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 z9d6y58wjdxt(9(dc eao r3gcv z89)g 2ttusv a mass of 0.58adsz2 xg98c)(yut 68e9wgd tv 3voc9zj(rtd50 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 o2 k* d19,ge aix c1x2kvpnub1bat, accelerating it from 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-da i4a j:dqqh8l84o8 edriven merry-go-round and is able to accelerate it from rest to aoq8alh:4 dq84a jide8 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 torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rot. +yrje/ zi.veating at 10,300 rpm is shut off and is eventually brought un.+ j irz/eve.yiformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 acceler cq/ sy7baz6;hates 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 byk xve0+ fcz;jpu5r,bg *zx/j+ 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 unifozx+e5/*k cj0 bgju+p,f x;rzvrmly 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 l7qoo l, quppc7yf/9 (ucg (yu-ong thin rod, as shown in Fig. 8–46y(p 7-lpqcc fg9 uyu,o/7qou (.
(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 masses,9t1g7 e3x td ispq:4ao $m_1$ 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 acceleratem-wgd,( wbt/65o as lfs the hammer from rest within four full turns (revolutions) and releases it agsw6w, b/adto fm-( l5t 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;5r w0 q9znfd(zu .hao 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 develops a torque of + s7 .qmf*ye*qbyo7xl280 $m \cdot N$ 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 down40 i8yk yv ump*c lb,u19pz(nn a lanic,n8z nmky4 90l*(u1p vbpuye at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic un,yhyt n1vmn0d;*r5 energy of the Earth with respect to the Sun as the sum of two terynmd150ny tr,hu *;nvms,
(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/ip9e ter8bx( 4rx z nox8dl65 mass of 1640 kg and a radius of 7.50 m. How much net work is re 5rzl t68 r89(xbidepnxx4eo /quired to accelerate 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 stap h,i3vq+ ;skwrts from rest and rolls without sli ivq+,3ps hkw;pping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is bp-p)vazd/ x 4calanced vertically on its 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 ground? [Hint: Use conservation of energ -zxac pvp4)d/y.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thpk+jvm xj 6:k*ae:dx3in string in a circle of rapaxj+mk k:evd *xj 3:6dius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical gri1 odw8by8k.a ftecl6(q ;z:ed nding wheel of radius 18 cm when rotating at 1weo1ltq:6 .8d af;(k8ycz bde 500 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 .mxxfw3t3 h: n5b7fbjw0 dfei2.myu3at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his armsx n:wfh2f 3du7m.5xi 0t ywmebj3 3f.b 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 b4ta0z.l d;fj0 a vm)oin Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations i fav0d0blamjo)4 z;t. n 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 rotao wmv8u ia+t a:zyyt2j 1/fw08tion rate from an initial rate of 1.0 rev0y1mtaf ua /j2+8twyv: oiw8z every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical a(zwi sz fo8qr:k9 *xt)y; wv6qxis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, 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 aft8roqw *qw6(:)9x fz;itsyv zker the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater sku szn 3ni0ia.or,+ 9ipinning 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 of thi)ut.0hxwffgn4 01o . t/ caope 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 cylind bznang/b/5;i9r; lq jrical disk of moment of inertia I is dropped onto an identical disk ro5/ nriln;b9 ;a/b qzgjtating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 1zxzd .7jpf.k 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 xyiiep)*30r k merry-go-round platform of radius 3.0 m eykp*ix0 3i)r and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an anganl1u n ucq)z) ghf bk:n6a41.,e i*kjular velocity of 0bei )nn1:ahkc u6)4uz* .klaqgn f ,1j.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 a : u2 -u4xvw(g8e1p0 dwi rexvxwhite dwarf, losing about half its mass in 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 thu xx21w 40rg e pev(-id8xw:vue 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 ocn;19/w lpd maf 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 v1, 6h /5flgxk .zolmc+hte v*$ 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 f/+3 o/er2tukbme,off 1tpy0rest, that can rotate freely without friction. The moment of inertia of the perso/kbe+f2 3p ,tyffmu1ro e/t 0on 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 dx9t2zv9ots- mr u g6c5 /ka,kmerry-go-round turntable that is m - 59 trkx,ckzd9go62atmusv/ounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying va y+fsv:c0* con 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 p+cacs f v:yv*0erson 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 sao2ara /d5p8 1wxunys;me:/t5e: o ukq zy*ak 9me side always faces the Earth. Determine the ratio 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.) ya/8o 5k 5;uq2se d w:mrypno xt :*9a1akeuz/   $\times10^{ -6}$

  A cyclist accelerates frq6b03zm rv4le5d:3w* vyjyhj q) o ligwj04 6wom rest 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 th v3 nqcz:m4/mbe shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.c4:qbm /n3vmz    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, e8kx6qplqk ht +2;q2oul kc5 3gach of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed ofhq c5xt +kp8 ;uqq2ll3k6kg2o 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 wheel (mbc hm( hn(a)9eld,6g$\omega_R$) 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 mak -kt7-t qmsb+ss 8.0 times as great, were rotating at a speed of 1.0 revolutio-km-q b7st+tkn every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it x7 x1dpvycx 7/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 1.50 m and mass 240 kg, and should be able to travel vp y7 x1xd/7xc350 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 asww+wl4mnv1w5 e ;u xhidu b 3c4.m(9an $H_2O$ 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 v2*aqhr/2hdk 4u-s s / :mxppbn=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot f s pyuq5og0x3lgtvuqv p:yhzg)q 0-c:b8*- 2rreely (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 angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that tq8*g)qz-0h pr3gl-u20vg u:yyctobpx5 s vq:he 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 vertically on the flosr ufu1z 5qa h2c-,qp:dkg.j-or, and we want to exert a horizontal force F at its axle so that it will climb a step againstacuuj:d5-zp2- rq. ksh1g,q f 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 road is making a tba0,+r5bw u c:x ovyv5urn with a radius The forces acting on th,5vy0 :cbow5+vbx aru e 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 /ons 2lqo 1:ubw *g2qo/gkq) xlength 1.5 m and begins whirling th g21wgq :snk/*q) o/2oxqo bule 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 from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, makio /fn rd5or;e0ng reasonable estimates for the dimensions. Then calculate the ratio of t o/5;edrrfno 0he angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch asu;bl ml9ap o(7toy)o6 sembly which consists of two cylindrical plates, of (yoobo7l6apum ) 9lt ;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 r rolls along the looped rough vw ) twx0;zfr ,f7cu,( e7z: (juenoantrack 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 highest point of the loop without leaving the 0uzf); c7ewozrntevw(u a(x7:n ,fj ,track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not ass .uj6pss*x w/kume $r\ll R$ h =    (R-r)

  The tires of a car make 85pjpy ,4 b.gpr1 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of ea.b pjppg14yr ,ch 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