A bicycle odometer (which measures distance traveled) is attached ny,zsg2 ((/) 5kayl;n izbwzknear the wheel hub and is designed for (s;y5gw2(n)/zbn, klkz aizy 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. pzp m0 b*-g 8+y; rft)cmfiel;Does a point on the rim have radial and/or tangent ;ytfzr0lc);*g+ - imbemp p8fial acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of x5n +cvi 9zqk-the angular velocity $\omega$ Explain.

Can a small force ever ex4sl.. (e /3eq3adpdulv-e svuert 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 do a sit-up with your hands behind your ho1h/qx:xxhuf6b s(mz -, q8ab9x 0cvaead than when your arms are strv /mz x8fx6o, -0sqbhax: hbx (1a9ucqetched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the ped)(gun7h br *nz/bdhe zynr: *04c +aclal cranks. In which gear is it harder to pedal, a small rear s*nyug 0*(znn :/hrr c7+chlz)b4ed abprocket 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 fleswfzalmso9 4 0x,t*)f uh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explauf 0s,*)xowa 9zft4mlin why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam? dhp zr jzg4 (c3*(-rh9cbupa3

If the net force on a system is zero, is the net torque also zeronxpppkau89xokm 7 c/z 87 +b:oz4ap:y ? If the net torque on a system is:pb87u +m7 opapzcx8akxz/ n p9y :4ok zero, is the net force zero?

Two inclines have the same height but make dip5ggrp6w;59rvx63z k7 t8xm fn lzh1m fferent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at t6g9fx6 8h7mkrplgw1 tnzpx 53v zrm5;he bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an ie tp9h05j ,vifd)e2 mincline. One sphere has twice the radius and twice the mass of the other. Which reaches the bot h eptm,d0 29e5v)jfiitom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. Tht)0d3cg pbx*o8q1 omerwgmz y9() j,i ey 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 kineticpw(od1 qgimzgt) r0mo8cebjx9,) y3* energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserve ga7 w2*qdmsu)d. Yet most moving or rotating objects eventually slowdwm)*uqa2gs 7 down and stop. Explain.

If there were a great migration of people t/+l llz3f,/uxr3xd7sx 5 .oqq rk5ogzoward the Earth’s equator, how would this affect the length z s,xxq+lzu5xl /7/5q r.fo33lkod grof the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatiop z *rdt6 -88rzk8q3f 7dnek*o myr0zyn when she rtzz-odf 0en*8 qz r6k*87 mp3ryd8ky leaves the board?

The moment of inertia of a rotating solid disk abo2e wx pggg*(, ))nlbxcut an axis through its center of ma(x* )npgg2 l wgb)xe,css 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 holdinp,z (oqupsd6qn.0di (g a 2-kg mass in each outstretched hand. If you suddenly drop thei sppd( (.uzdqn,60o q masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howev /ty1:5j,: lfjyndiy39pm jla er, one is hollow and the other is solid. Describe an experiment to determinef ajidjlm,y5tyj3l9n:1 :py/ which is which.

The angular velocity of a wheel rotak q05o *uzyiz(ting on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is 0iy zz5u(koq* the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotauzt 3 yly:t+xok* x.q+vj 6y4dting turntable. What happens if you walk toward :xjlyotkv qu+z6 yyd.*x34t+ the center?

A shortstop may leap into the air to catch a ball and td ghiwcfazn;628,0q qhrow it quickly. As he throws the ball, the upper part of his body rotates. If you lookd;08qfh ,wg6 qi2c nza 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 angular momentum, discuss whyf /(9t nbrva h;y4qpl,n(a8o b o4rf;r a helicopt rn rb 4q ha,o lftobv(r/f;p(yn849a;er must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) u2 suixnqn9k0v h*- y930 $^{\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 becaulcwam l6w9t,ep*tnu df; ;37ed ad1y8 se of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) oaaml3wt;1ded ,twu76 e*dn98py;c f l f the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at t4y3t/pd k:r1ke huyqt+:.tw che Moon, 380,000 km from Earth. The beam diverges at 3tc.k1yy/+ hw4 tru :tq:ekdpan angle $\theta$ (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;h pf 0kb .y ononfdv-)/9f:xx at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What i:.0yno/x;nk)-vfd ph f bxo9f s the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on wkrh skbzm/8 fr 4cb585lo(4wa level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its dizhbrlw w54 c8fr5m/k 4o(b 8skameter?    m

  A bicycle with tires 68 cm in o/zfc)y)px)j diameter travels 8.0 km. How many revolutions do the wheels ma) y )jp)f/oxczke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcu0,sl epnca* w 4o.upd0late its angular velocitp0dp,oeus an4wl0.*c y 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 revold9uhmb iq5 t7wyja9t. d wb59.ution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the centtbdiwq 55 j hy7 999bta.mu.dwer?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of ttn. uwnjqgek :)b8t7tvp6./b he 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 p8 on*p4v6sm-gp1um nv oint
(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 part j(,gggmktk0eun(u8 f9s;f;kicle 7.0 cm from the axis of rotation is to experience an k mejfk(;s (f guu0tnk,;g89gacceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abouoli,7z . 93*+uk-whl rxlm3hjsyvdc5t its center from 130 rpm to 280 rpm in 4.0 s. Determin-ldh,m.yhv wls *i9+73ujkxozc 5l3r e
(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 radiusx gvy1w j0ncn;b.q( g7 $R_1$ 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 sp 3pn14vmcd..6y**udeeyphb p acecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rh yyud* p .v 6nc1d*b4.epp3emotation 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 from rest to 15,000 rpm in 220 e1wntu1;11s9 kseph ks. Through how many revolutions did it turn in this timn111t ;p ku9e1k esswhe?    $rev$

  An automobile engine slows down from gj (fxo:uq u n.xux,1 :bj;ns34500 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 f bav ,w)-d6ynt)k ehh)lying highspeed jets in a whirling “human centrifuge,” which takes 1.0 heykwb)h6 - a)d),vntmin to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rm 3b-*sxgqd5jpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in ms *5dxqgb3- jthis time?    m

  A cooling fan is turned off when it is running at 850rev/min It tu, 8xs9+u kyxxnrns 1500 revolutions beforen9 x8 y+ksxu,x it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly*mo)c+u*cg 9 ,kcdhik from 95km/h id9*kgcm+c k h,u) oc*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 revolutionsivkmawdqa6lg :fzc7 (1 ;0 d2e as the car reduces its speed uniformly from a g:1d7adkivqlw;m2 zf e(c06 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

  A 55-kg person riding a bike puts all her weight on each pedal wna +-ngp6t 8 z(3nxvqbhen climbing a hill. The pedals roqvna (863x nzb+ntpg-tate 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. Wha pgx2oz0:m bp5yf9cj5vru:r(wv ;0ef t is the magnitude of the torqu9 mfoubpf:vpy rjvw05z0:2r5 (c; eg xe 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 g 2ag9xr/mqd; about the axle of the wheel shown in Fig. 8–39. Assume that a frictir/ mdgx;qga29on 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 o:3sk k-g46z3qbto p lthe ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calcul:skk pzb4t6 qo- 3lgo3ate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of ap-z uh(p :2gykn engine require tightening to a torque of 38:gh2z pp-k(y u $m \cdot N$ 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;vu w+ ucusc3;.8-kg sphere of radius 0.648 m when the axi;c3cu+w uu v;ss of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a b8dbdttdu -q),icycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of dtq)b-d ,td8u 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 in a horirq1ydnxe h -ru,te2 (9zontal circd1tx9y e,rhq2r-une( le 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 wheen i* m7+5dmq:bhcyl7pal(d4j l rotating at constant angular speed (Fig7d(dblhan* q+:mjmcpil 54 7y . 8–42). The friction 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 inertiax8(hu5 o z3api of the array of point objects shown in Fig. 8–43a(h iz5po8 x3u about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mass isw 6:t*ujers 6uh+t2 ;fvw-pontz 5zb3 $5.3 \times10^{ -26}$ 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 yf(8uh4lk1r6k7v7qg; fcf k qrate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 360k;ry qgffvf 77kkh6c1ql(48u0 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a masskpt y -kk*f9x, of 0.580 kg* ,y- pkkx9ktf. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest toj /po*-ivy 4dc 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 smaylq d7 6gib8veu9.-xy8jd9k( u xa )pxll hand-driven 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 mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the e ilv7 6yduj9(g au9yk8bep8q) -.xx xddge. 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 even 7;+ yv8 ebgkut0cjemr6v,)0r x1n rtrtually brought uniformly to resmrruv0t+ne jg; 7cevbr )8t 1k, rxy60t 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 accelerates ag(f6aoyj xa8. 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 o;1tstsj vm9f cx,-j*vf the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from ress1,tcv m-9vsfjj ;* txt 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 can4n2w4flcxis f6.qa:l be considered a long thin rod, as shown in Fig. 8–46. :l4qli6 xn. f2cfw4a s
(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 fuphbm+c/ (;tntdn8t .i5, x wmasses, $m_1$ 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 four fulnizcl6w(f * f6l turns (revoluf(fcwi *n6l6z tions) 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 has3. ai3p*zh mcx a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque ofq6ij0,c2ne9hghs) tm 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 rd5s gazja(qfu3diu+1 ;,89sve syj- bj+r )zpadius 9.0 cm rolls without slipping down a lanqsus p;ayr szjjb+9 53 gfz ju,v)(1+iad-8d ee at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Ea 6mk2dz:1o-k8vir 8ougwix()w h6el prth with respect to the Sun as the sum of two term izi h661op xdw-(kv88u:)kowr g2elms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much nn7e/orm vaa k5(wv:: zo ,rq+het work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cwn m7 hvr5zov a/+re:k o(,qa:ylinder.    J

  A sphere of radius 206s8: 3xty awvw.0 cm and mass 1.80 kg starts from rest and rolls without slipping down a x68:ywt wsv3a30.0 $^{\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 verticall8v3pyaw)xr xet fc:/u +-5lqx y on its tip. It starts to fall and its lower end does not slip. What will be the speed of thlpf)q:wr ctv8 x-/ x+3xu yea5e upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-l lmdefy-p;;dpu.fxvf 4 qsli)p:g/;g 84*d hkg ball rotating on the end of a thin stedl;*mqilp;fs4h 4 .-f8pdxy:g/g) ;pvl d ufring in 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 mj2o (91coqse 2.8-kg uniform cylindrical grinding wheel of radiuco(oqm1 29 ejss 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at hi/b7ds ,dxvspz8;6tjts side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal 6,p ;sjx8ztbvd/ 7sd tposition, 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 inerti4 ufn6p. -+gog:xpwdka by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angg.wd:+fug pn-kx4o6 p ular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an -3vp+x lt p,kih-um5j initial rate of 1.0 rev every 2.0 s t k m-l-h35vtpxjp+,i uo 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 center 4olk( nt8ur7xlsv4 v1ps k7 -iat 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 after the clay sticks to is4 vniu7sr87vl (o1 ltp -4xkkt?    $rev/s$

  (a) What is the angular momentum of a figure skate-zfuw53 mrm x,1tun )ds2aesqm(;0jsr 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 of the E/z mbi5: wwtn1f3)r/ l 6fvsuaarth
(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 dropped onto)2)2wl*qe u m4fgbck u an identical disk rotating at anu)b 2 ec wfqmu4g2)*lkgular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.*.h,-w ,oh6kcku eau vylo n:+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 g)lyt) q*jo;ppw01zg kg stands at the center of a rotating merry-go-round platform of radius 3.0 m and mopg 1w o)0 qp*g)t;lzyjment 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-gl9g*/gwpk 5:zowvl 4bo-round is rotating freely with an angular velocity of 0.vw4z g pl9:og/lbw*5 k8 $rad/s$ 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 white73k 9jv0k i (aq.fxhm uuttfp k1;q31q 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 fmk0 tkkat 1ji;qv xu13up(7 .9hqf3q?(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 4o ppb):a 9ckmefo;exezu1 8-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 p2c8 j(erohi 7$ 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 platform9( zq o8xcx,ne, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform is zo(,qc9xen x 8$I_P$ 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-m4/tf7jd6w )e dgvhte0lhq+-g)h v e 8b diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of i760 ge t+g8 dht)-jvqd)fl/ eb4vewhhnertia 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 witht*/ 3 80+o dp-jyvwhbsz w3hun the end of the rope lying on the top edge of the spool. A person grabs the end of the rooh8y-30zn+ hwbv3sd tpjw u/ *pe 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 the Eart we0eyr u6sx i(2n,57v )nknsah. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum.k6)use nry5e0s n2vnwi 7a,x( (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 m/(y8d+ff( iawhen.z*mtf4 o4f$s^2$ 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 0f2e yvss d+n1el)72b) jwqw bik0 3(zz.20 m acquires a rotational r2sbesv1fdyz3 7jw0e(wk)z l)qnb2 +iate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made o81gf ur:c-vj/d; mjr mf two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical ;u1/fr m-gm:dcjrv8j 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, how is the angular speed of the reaul/p7ue4o gh( r 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 Sob i 7iu6ok48eun, 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-quarter6i4u 87oebiok s 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-pollutnqu 4xsrmg g7: )npb4/7ermm (ion automobile is for it to use energy stored in a heavy rotatimg/(n gern: 4mmr sb7p74u)xqng 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 “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 a0b4( vxuhl2 ipm3z) man $H_2O$ 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+trbpi6 cwq-2xa4+, zpd g6la 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 and length L can pivotb66vb aomq7i+ freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of thqv66abo 7b im+e rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on a5id:u:qa. 3qzb dqb6 the floor, and we want to exert a horizontal force F at its axle s bduqa:5aqz ib :63qd.o that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on axceutg a(a ot3zk o3u :11++ji flat road is making a turn with a radius The forces acting on the cyclist and cycle ac1eo (iatt:3 oxu+1ju ga 3+kzre 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 lengte f);-gvgod98 5gqc.3udfkd ph 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, acceleratin)o . c;9ffdq8dg5-ek v3gpgudg 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 bodyo*+f-oak h dn6 as a solid cylinder and her arms as thin rods, making reaso-h*oak f6+ nodnable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylind 6bhv*ohbmp4/ia.z c 5h+aa q9rical plates, of mass c6ahpi bvqha/*4mba+.z95ho $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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/yfsu*/n1w k h the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Asf wu/h1n/ky* ssume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do notp/dn1aq:7w/t;t zzil /rs0 qc assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car redag7:ap2 s ej3 tc:pdds*,5 fmjuces its speed uniformly from p: 2e5sfp: dagjct3*j dm7a,s90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s