A bicycle odometer (whisz;(es65m jxv 1kr91vqo ci/nch measures distance traveled) is attached near the wheel hub and is designed for 27-inch( x/5;j c1ikqv6zen1mv r9os s wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Doe;d sjpd f-d0/vs a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point haf-;sdp0 d/vd jve radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the an/ lv9f)f z*mbugular velocity $\omega$ Explain.

Can a small force ever exert8da)lx vib r;8 a greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to (m0ey3p cqh-rdihwkvf 1y/*8, o v*gb do a sit-up with your hands behind your head than when your arms are stretched out in front of you og, ( yv*fhvr8*0/h d 3ykbec1wqi-pm? A diagram may help you to answer this.

A 21-speed bicycle has sevbzx,vx. e-( qsen sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front se bx.xv-zs,q (procket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slendzsr26 g4m9tgw )l /tvm.;b5my ybzf;qer lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynam/b y;mgrv2bzg;qm 9ltsz 4 .fty65)mwics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, n are0r(.cfa +earrow beam?

If the net force on a system is zero, is the net torque also zero? Iy:c, )z)akr-(m sbt8kn;v tqw f the net torry-,tzbaw qmkv) c s)kt(:n8 ;que on a system is zero, is the net force zero?

Two inclines have the same height but make different annk: wt6pc-ce-gles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the botttpcke-c :6 wn-om be greater? Explain.

Two solid spheres simultaneou,s(37fg- -bc :9qr demmrc5xm ct;zx asly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Whi(,-gm5ax;9 b cq7m r sem -3xdzftr:ccch has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radiust(xb tp g0h;6t 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 th06(t xtp;t gbhe greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum ans*jpha4r 2sga0h99ie d angular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Expgse 0ih9p4a*r js2a9h lain.

If there were a great migration of people toward thtv fxbe lb-9 awi*9q788r88az) vqerze Earth’s equator, how would thisx e9iv7laa8tqz b 9rq8rfze8 bvw *-8) affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any i k+8ql,/zas3bld*+p+l /jthevwoq)h nitial rotation when she lea vstp jo+ del l,+8qhw/za* l3hbq/)+kves the board?

The moment of inertia of a rotating solid disk about an axis through its lsyy 4-/y:kp/j-tr-0 k2: du alpkvez center ofyut -y/:4k2l-kzl pej/ s- vk:dpya0r mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holdi.swx7 o;fm74 b8xzogp ng a 2-kg mass in each outstretched hand. If you suddenly drop thx8 ;fbxwm.7 4ozpg7os e masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look ide jpcic;7: +parntical and have the same mass. However, one is hollow and the other is solid. Describe an experip+ai j;: crcp7ment to determine which is which.

The angular velocity of a wyx vgz*v7(x+n+x5aq2x kg g (qheel rotating 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 pox* ggqzax5n+ x(v2v7 xq+gy (kints 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 tur terd; ))ce(uhcfxa.( ntable. What fec(ute .(x)hc r;)a dhappens if you walk toward the center?

A shortstop may leap into t+ e 846iglbzx ;l9cxuyhe air to catch 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 zuy+c8x; ix4gll 6eb 9hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angulbuh 9j4obcc;m: l /g1/i8 xrwaar momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second prope i:9hw xcracm;8bu1obl/j4 g/ller can operate to keep the helicopter stable.

  Express the following angles i.dc9k3a:vdzf jn,w zn 2)c v6qnh(ytizo-;-wn 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 coincidence. Calculao zywzpzg 4.jzs 3k:8u5.3e wkte, using the information inside the Front Cover, the angular diameters (in radszg eww.3.5kz4kojp8y z 3: zuians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earl8d0 npg oz,i5tnb :..ca3 hvith. The beam diverges at an a c g:tno8pnd,.i0hb va5 l.i3zngle $\theta$ (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 thee:7hob/8lr cl3) 8erdpw:hye; r y;po motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bo rb p: d8);er/ eo8;plc3e h:7yrhlywlades slow down?    $rad/s^2$

  A child rolls a ball , 3yxy4 ipiz/a)eu9 hjat,j)dwu9m;n on a level floor 3.5 m to another child. If the ball makes 15.0ty 9nh)ijdu/, w9um) a;p4iejxz3 y ,a revolutions, what is its diameter?    m

  A bicycle with tires 68 coch 6 7t3le74)cjyduo m in diameter travels 8.0 km. How many revolutions do the wheels ma4uc dh73)yjoe6t oc7 lke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rp 1x3 (obggn*vmm. Calculate its angular velocim3 1 og(*vgbxnty 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 80y) l )k5xsg 58oqmrivokj1x.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the centevlk)q xmg8oyi0krx j o81s5)5 r?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity o z d- g60gezi:;esowe,f the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sphfpd+vh3lt;8o3y mi xnm ,q. -eed 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 t)-rlbq 8c z4p; nadrr9he axis of rotat- rcrqprbnl8a) 4;9zd ion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformlu(c70j*d,t7kxs3hgc y. wan iy about its center from 130 rpm to 280 rpm in 4.0 s. xwtd jah g(nyk70scu3i,*c 7. 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 radiu i(k.r2 j+m*.axn 5c9eomyvj0h:xd dis $R_1$ 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 thf/af. e3xbkwo i71 *1k5elaxeemselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they acceleratedf3fe xka5ei e7l11 obxk./*aw 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 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 frooz 5iw7 hr;qe/1o- wznm rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this tim;7w/z r-5ewiz on1qohe?    $rev$

  An automobile engine slows down from 4500ruzx-55.u) qdpd3 t ps 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 ftj 0rr+(tala.or the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its lr0 aa trt+.j(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 bo;(6kv 6 /xv/n jntwo8 r8txp360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in /r6vo8 t(xn jwt8n 6b /px;kovthis time?    m

  A cooling fan is turned off whexlc e4y)0),z9ya u oejn it is running at 850rev/min It turns 1500 revolutions before x9c0)az o)e y4l,jeyuit 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 revolut,mxp q8iv)v+x ions as the car reduces its speed uniformly froqp+8miv,vx )x m 95km/h 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

  The tires of a car make 65 revolutions as the car reduces its speed unq7w pc6nd6)baiformly from 95km/h to 45km/h The tires have a ddq7n b6cawp 6)iameter 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 +inxu.1q)wtlcn)dp2bike puts all her weight on each pedal when climbing a hill. The pedalsitx wq n+pndu))l.c21 rotate in a circle 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 of 55 N on the end of a door 74 cm wide. W;y.fo,p( lg5kubk:has .+ c iihat is the magnitude of the torque if the fo:k,ifh; +cabpio. gsy.k( 5lurce 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 t ;nd3)li edl,vhe axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4 d)d i;3len,lv $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a mb mkodhg 5v/k;7-s 2ff/xd bo-bjbp:1assless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the -gfvomd1 :ph7xksb2 j/bd;f5 bobk-/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 tighteninhyva5 ks lzh:v 83sry+) cp6n8a1dm8n g to a torque of 38lpn8v)h: r8v3kcdms1ay+ has6yn 8 5 z $m \cdot N$ 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 sphernqxk 9hc10 m,we of radius 0.648 m when the axis of rotation isq0,h 9m 1cnxwk through its center.    $kg \cdot m^2$

  Calculate the moment of a,pkq4nr2 htl/f)j*.2 e okdvinertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be igno)*2o 4lke. v 2ajkt h,frd/qpnred (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontac5s0tk 3n0 /iedzk ; 9wpx8ulil i zc 389k/pni5t 0uex0w;lsdk 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 wg5tq 0 1d1yyad-4yzncheel rotating at constant angular speed (Fig. 8–42). The friction forc-tczd 401qgn y1 ydya5e 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 inerl vchr;nxg);:tia of the array of point objects shown in Fig. 8–43 abou c :;ghx);vnrlt
(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 cons ekant5,mp:x r t24i4oula;0 cists of two oxygen atoms 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 cylindrical satellite spinning at the correcwdvw otge8j r:6p3b m91 z1ly;t rate, engineers fire four tangential rocket:61 rw83mvb y ;p1gj9o zltdwes as shown in Fig. 8–44. 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 cylin e2;j2/y hn;t)k4 :xdlpwf bdlder with a radius of 8.50 cm and a mass of 0.580 kg. Cal:hwllb;4 2 e)pn/t dyx2j;fkd culate
(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, acceleratin1 hkjyph34: ck4f;l2 l(ikmky g 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-drivendn ctp7 fq( ah,n4hn06 merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a masnh47n6 c(,hpfnq0tdas 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 10,3x50aabr x/ nukh,j(d/00 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.da0b x/(hr,5/xuk jna2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at 7u(o )nh 2(ce xrddi1 dpa g0)p9c,ldt3 $m/s^2$ 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-kgx1m(eyw3 -vbh6t 0uq c ball 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 uh-e63b vwtqcuy10 x(mniformly 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 ) e- p:le8ssi ec+ywv0bn v)0clong thin rod, as shown in Fig. 8–46c eeb-w8:yl0p+sv)sinv)0c e.
(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 consiste22 ml::j4ah:cl fl1lxlbnpn xp:;vfz2k1 4ts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within f4mq6d+)dl pcrgaa al*: 6blj- our full turns (revolutions) and releases it at a speed oq+amj * a6ld)adll:6-cpr 4bgf 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 in53+hqsxk :3dzfxq8 ftzp eirq5./l0xertia 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 develo0fdg ;zwi 8r:ops 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 *c 1vh;u j9z-jbd(lgy 2n,c zc7.3 kg and radius 9.0 cm rolls without slipping down a lane at ujz9 d, lzv-cjncb ;2h1*ycg(3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to t lyv4 4b na+wq13aza3ehe Sun as the sum of two term3 4y4 an1+lb 3weaaqvzs,
(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 g0a(fd+s1z tc mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rot0+t(fas1c zd gation 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 rjt+m*xon 5c3e6 lbz nvjao hi/32 /3mkg starts from rest and rolls without slippin+c tm /heaz5jj3 o*vxb 2n li/n633romg down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and its v sgu)lf6,v0w lower end does not slip. What will be the speed of the upper end fv l6)sg0wu,vof 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 en ,iwp nnwgj++okv)z w2+jsc3+d of a thin string inw)on wpciwg2++zvs ,j 3j++kn a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical gri bkkt+ y;uxz/(nding wheel of radius 18 cm when rotating at 1500 rpmxtykuz; +kb(/ ?    $kg \cdot m^2$
(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 plak do7cxb q6+ra(gy ,x8 owocx636.cgg tform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotatia g(xcko xxb qrdwggc6 687+,c36ooy.on decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one so:t1ke g )10lv+rmhg5 ue+ha zogcc0/hown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position tgtg :1mek0+rvh1l ) acc/zou+50hg oeo 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 rotation rate from an initial r;0earqkt 3v isx )2-jcate of 1.0 rsv)axjr -e0 3q;t2 ikcev 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 ve3xgc,8qgod rr5w r8t-rtical axis 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-kw 5-xt8r38,gcgqrrdo g chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater cmv*;i x1uj.tspinning 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 9-.4rjazctrq the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dr-+ia oseqougr,d 76ka4p9 + mqopped onto an identical disk r+7os9a- ,6urp gm+edq4iqk aootating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns/njvbg 73m:lu a*/w8 x6fc.eu f;sl jz at 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 kn;6;q cu2qeim g stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment q2 6m;ueiqnc; 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 rracmn w. ,fe)ps yx93,otating freely with an angular velocity of 0c3,yw x.nf rps,)e9a m.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 eventw4xnjbi5 (( dzually collapses into a white 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 the Sun’s new rotation rate be?(round tz wx(ij n4db5(o 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/q xl(3ut(ecfa7u; yw 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 h3qfz4buw4 wvexp5rw t(5 t;8$ 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 plat :wtx mfyqncg1+lb -1.form, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the.g+tc bf :wyqnl1m1-x 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-mheov85vv6or76 :r iqpmmyk;,y *x4 ob diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 17me4y;krpmo, h v8:v6yo xv5oqr *7ib 600 $kg \cdot m^2$ 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 lyin)ijbc3)u8 b fr,jaj. og on the top edge of the spool. A person grabs jr3uj bj.cf8a i) ,)obthe 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 tfe1ua76 y2 pw6x3*rl cnrkn ay(q2g*y hat the same side always faces the Earth. Determine the rat*q ea n ckp1nl3u*arg67 (r22y6wyyfxio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 mqg(j7/m-q v89ihmamc 0vn9t u/$s^2$ 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 radiushyhjb)+x63aynx uz/ +myb9h ; 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered bh3b y+m/hnb)xjz ;6y9 x +ayhuy the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0o pg)bt+11 .;ufh b8h+monnyh.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-ybo1 .ohf;b +t y8ghn1+hmp n)uo 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 m+sl. kb2:axl51s pckl (f2lf of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our somny pa4g5 mx;e*8zpl ;c;x5 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 gps;;m5p x5 4y*x 8lmanec;zo 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 ht9cv jc+ )8w0 ho1foifor it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spin8chih0f)vjo 91o +c twup.”
(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 illustranq+ 89n wojho*ao)-q+uuk-8wwrc: ia tes 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 (hoop4tm,3rcpq* jy) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M andlfvesf0) +u sxo;/ 7n/idryaed7w/ n0 length L can pivot freely (i.e., we ignore friction) about a fuxf7dn;n0ew/ +soy/aeirlv )d / 7 s0hinge 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 iu8+ie rgfbs 8 ibp;+s5s standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a b+gp8 sfu+ersb 58ii;step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/fz j:7,iownevvld2 8fp, h;ra5 .dvl1 s on a flat road is making a turn with a radius Thf;d.n7 8jvdl fp1 5rh2lv,avizo :,ewe 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 rockitb.ow z/ u,p0mn8es9 into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle abovep9s.un ow /t,bemz 0i8 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 ; s1ifl xix 4 feeu9cw(z,i3x0as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretchedcswi30 x(fu ;i9il4xz1xfe , e arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which bm 9nex+ t3r2dconsists of two cylindrical plates, of mass me2 3dx+trbn 9$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fig. 8–e p.- nu638m+lhxveq j58. 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 th6n38- uvm l+qx.epjhe e track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumx(i :se *be6dopv1 k.vhw, 1zfe $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces itr/nb/d kd in1d3f7 j2y;hw 9ios speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (;1bni/dd3wi yfnhd rj7o/ 9k2a) 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