A bicycle odometer (which meaf//sr+i o6c px9t2 g/9nq6ypwvi7iuxsures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What ha9 pnuxpfy/tqis9627cgi +x 6i/vwor/ppens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular v k4+j-p4curit elocity. Does a point on the rim have radial and/or tangential accelej cut- +rk4pi4ration? 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 defbp9k /gtt;/k scribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greatewqn -hy 0-gvl3r 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 do3tq,u) . r9crl51xycvvn3nnn a sit-up with your hands behind your head than when your arms are stretched out in fronr5lntn,9c qv313rn. c yvnx u)t of you? A diagram may help you to answer this.

A 21-speed bicycle has sto; 0gvk* z-)4(d swezw bv;dseven 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 ww;ke ) bwdzt(zv;0s4*odg- v shich 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 slende *8exzl6zsb9zr lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotationa6z*ze9s8x lz bl dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, nar tiohso)*.d f(r4 ln+urow beam?

If the net force on a system is zero, is the nes0vdj ;ln1fq4 yj(if( ,e lzy5t torque also zero? If the net toz s5f ijl lyjnq4,;(evy(01dfrque on a system is zero, is the net force zero?

Two inclines have the same height but make differev- cjg zs ndn26*5cvz9nt angles with the horizontal. The same steel ball is rolled down each incline. On which incline w- j cvdzg2n5*vc6 9zsnill the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclinexpvz8f d.sbh:6z4jb0da t m (+. One sphere has twice the radius and twice the mass of the other. Wh 06f :dxmb8bd h(.v pz+zj4astich reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius ck7n:j2 t.i7 9vlzsz wjlc1x5and 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 energy at the bottom?ctj.zs v:xz9l ic5lk1w7jn2 7 Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most movr w-jfi/yd6rv-. g;cz 5i7oop.ts5nning or rotating objecj5 .6o-ni7 ;dyc/5og rfrznp tvs.w-its eventually slow down and stop. Explain.

If there were a great migrat/z .tmks hy.4l(/v)ohq 5dq:hoez/ mbion of people toward the Earth’s equator, how would this a)z:oqvtqh z ..okm l/5dh h(e4/byms/ffect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having 0zhqb,p ef:-yany initial rotation when she leaves yh0 p:,q ez-fbthe board?

The moment of inertia of a rotating solid euv0qh0zhi17-wx rvx f68k izm5r/. wxx+ pu,disk about an axis through its center of mass is +w7x1h p eux5imq hk8i/-zzrfvx .u,06x0wrv $\frac{1}{2}WR^2$ (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 sikknly;h 3brxml438 6 tool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrm46kblly;k ni83 x3 rhease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow andmpo x71y7 fd 73 zw+qq0tr.caioh lp.; the other is solid. Describe an ep+7q; hxd.0po3qia1fc tzwrlm7 o .7yxperiment to determine which is which.

The angular velocity of a wheel rotating on a v4yf 1) ym1w0xe*t ebkhorizontal 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 f)1v4*t0mky1xew ybeat the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Whath 1;tlxw)+r oh83zq5 * xwdfuv happens if you walk toward th5uwr3 xq+ho8dvl)h z;*xtf1 w e center?

A shortstop may leap into the air to catch a ball and throw in+wha2)6cr16tdjwa22n gxb mkg 9 v : )pz-ofot quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice j k+:ofw2 dbt wca)mxao-p92h1)6rnv 2zg g6 nthat his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservatioujyo5px)et 6 md9 gn.*n of angular momentum, discuss why a helicopter must have more than one rotor (or propee*9o6 d5pj tm u.nyxg)ller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radiad9hgq5- xvdg3ns: (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 col,x w*pw80:ej vogp-)yr eg i(incidence. Calculate, using the information inside the Front Cover, the angular diametersw-vrwe gpjex:)p0lo* y8, (ig (in radians) 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 Earth.poy hl63smntm+q1+7ze) -xu w The beam diverges ae3t 7yzou1sph+ l6 q )+-nmmxwt an 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 at a r f;7i )qwkq8piate of 6500 rpm. When the motor is turned off during opera;)k i i87wqfpqtion, 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 floor 3.5 m to another child. If the ball man9 ,r umj4kbiq.-:s) dvjcxe)kes 15.0 revolutions, wh)b.u)kjm jscix- ,9 :qdvner4at is its diameter?    m

  A bicycle with tires 68 cm in diameter travels kke h8ihkcgj+ cx/f4h;1)6vo 8.0 km. How many revolutions do thefkk4jx g8h 1 )hk/o6;i+ecvch wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameterfyrj (xsaf +y0yl g91,ta,0xt rotates at 2500 rpm. Calculate its angular v(1syax0xr 9f f,tta0l y gyj+,elocity 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-ldi g -rkh203zround makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m fromi2 d0rkl3-hgz the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in ito5p:fimqvj088a4 f tzs orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spee 5r1c :1mul*iqwwbju4 d 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) muhz.( ;mt1q uhcst a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of qzh (.;hu1 tmc100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpk(8kffu*8ob w3dzkacyp,y , s 8 c4m8lm to 280cy8f ydm *o8f4bwku p3(8k k,lzca 8,s rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius 7x0 hshp7*am g( i 5 hq:fnu8q :bf*yul/jtyk/$R_1$ 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 thems) 9tabz+tjq m*elves 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 )zabmt9t+*jq.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 22 dv zr k4.::3dqsob1u;qm kp5fizso4 +0 s. Through how many kob 4.3m vfzq : r;uzdq: k1ispo+4sd5revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 120spq,q xg/pl z/y0a gp/4wsa91 0 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 stressematbcl*tii6r ;)y2 i ) ,:gpjxs5n qj.s of flying highspeed jets in a whirling “human centrifuge,” which t ;iy. g5tmrj)6p *nixsq,jia)2lt: bc akes 1.0 min 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 rpm to 360 rr/bzdny n5hy ui1 3gcz h86n+1pm in 6.5 s. How far will a point o/yh3 nb ngiz1168+yu5dcnzhr n the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min tw+9o0ju9kz f It turns 1500 revolutions before it comes to9tz+0o ujf9w k 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 revo0prwabrq d ja3i ,.u-*lutions as the car reduces its speed uniformly from 9q rrwudpbi03ja.a-,*5km/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 makeovoil7(1c)a2sxrjv, xc; v-f 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have xaor7)loicjxfs(v ;v2 -1 ,cva 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 wei gs; ;2czdt(ei7fnx v;ght on each pedal when climbing a hill. The pedals rotate in a circnizsf 7;vc te;2g; dx(le 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. What is t5bz 2d 83n0w1kuzi mkh p//mnnhe magnitude of the torque if the force is exertkm 5iz/d2 0 n/wknp1m83nbhuz ed
(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 shownp wd* (lc9m0dg in Fig. 8–39. Assume that a friction torque of 0. dg9wm*(c0 ldp4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached toof nu3 u;/pf-tb jik0/-d/u ue the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude andbt/ 0pu-;/u3 -d/ujue k inoff direction of the net torque on this system.

  The bolts on the cylinder head of an enginew fzdp99g3- qf require tightening to a torque of 38 z3q9pgf wd-9 f$m \cdot N$ 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 10hjik03/z r2er.8-kg sphere of radius 0.648 m when the axis of rotation is through i3hrk2 ezjri/0ts center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rug4jk 0tx50w djg4us9im and tire have a combined mass of 1.25 kg. The mass og0 g4wt0d xjuksj5 9u4f 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 horizon;oq 0q12r)x(x: -sip( 0l cwxxuycac ital0(wxx ais;xu-q0cxi p lc(y 12c) r:qo 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 const5 jvzx/22qo3of5-b6b3e+ jje cmfjvz ant angular speed (Fig. 8–42). The friction force between hj j vz+2m 2bf-jjeoc6/fxo53vb ez5 3qer 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 ge ,9*n:iytk2r5ga ui inertia of the array of point objects shown in Fig. 8–43t5 a*2geig9u,y: rink 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 py.k3x/ .mpim 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 cylindricugzkliqfyl zb,zt3( ,r,8x) 6al satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required )g3(, rzy,bq ,lxli6tk8zfz usteady 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 8.5o8aw o1b0pkt3x-:/ahqpub ( y0 cm and a mass of 0.580 kg/qw3k8p0b-a: oatb1 ( h xyuop. 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 to 3ecwy06h0d kb- $rev/s$ 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-drix6ixyht0g*6n: vt wh-ys1b i c5-5jv uven 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 radt 0:h -jib66i5x5x ygy n-uvtswc v*1hius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 1x4l zrg.51 (xpg hyf3h0,300 rpm is shut off and is eventually brought u(lx pg.hy r5xfhgz14 3niformly 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 accelerates a 3.6-kg ball at :2s+o9v iw yex4q4kco8 w-qmgu3- q ydyka*g. 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 afp2;vyre 7 h0by the action of the forearm, which rotates about the elbow joint under the action of t0fra e h;py27vhe triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can bel/1mo.:bai 2c w6imxx considered a long thin rod, as shown in Fig. 8–4 xlc: .12bii mxam6/wo6.
(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 cc z +:ujfzr;e0onsists 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 accelerate)gb7iv-q6 (x.bp g* 6d9 1 dklifxsttis the hammer from rest within four full turns (revolutions)t 9f)di 6 q*x sd.tx(7kbl vigb6i1g-p and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertianmz/qg +hzmq1q6g 3 e3cag;9o 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 dla0l 2 8 cf7eb.qoq*u;j gkdm4evelops 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 7fu11xbwc: i,)oq p htq25iqk7.3 kg and radius 9.0 cm rolls without slipping down a lanefbh5p 27x1qit:,kco qwiq )u1 at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wq4: mv en56e+rc-z: cas k0vorith respect to the Sun as the sum of twrqoz:mc-e e04ns5 6+r v cv:kao terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a re l +:gk) ef.x7f9qsd qai-po2adius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assefspl:+.7 -)eo qqgf9k ix2adume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls withoi.:t25aa ynur ut slipping down a 30.a 2 tnui:5ra.y0 $^{\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. I0+e(2nidedti 1 v)c vnt starts to fall and its lower end does not slip. What will be the speed of the upiidt1(c0 d vv2enn)e +per end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum o y1gsw ;ajojoa4.- or4vl mc8,f0: snzf a 0.210-kg ball rotating on the end of a thin string n ;z-: sgj40so o8v a4wr,cjo.lmafy1in 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 mo+y hcrev4vg;gy u6,s :6 baw8smentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating vrs6;4y:u c8,+ ws gbygvha 6eat 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his sidez tgmdt-ek(8axajo f1 lxro: *)js9((, on a platform that is rotating at a rate of 1.3rev/s If he raisdlo(9saa(mef 1z -rxj t:*)tjkxo(g 8es his arms 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 9oouhnt az- w4*sh0m)one shown in 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 in 1.5 s whem09n )suz-4h o*woathn 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 5 d:) b-xiyrhs7vhdv7m h 42qirate from an initial rate of 1.0 rev every 2.0 s tvyd 5xhbh i4vm :-s7d)h2i rq7o 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 rotag)vi(n v hicpk b,(1g0ad/n:dting around a vertical 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 dn g0h d gb)v(a 1/(ivnckp,:diiameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of al zr(;mgws g.1 figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum5sr c4 i538l1dphtqum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of - q4qr1aok7plinertia I is dropped onto an identical disk rotating at angu-14oqka q7p lrlar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 1 y/ak71a znnub0s7w:ki b7 ekat 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:r(sl e gw01 :efqpe+xv-iq9,bjac: p stands at the center of a rotating merry-go-round platform oq: fr0lp+wbx:jve e pagc, (1q s-ie:9f radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotatecwru1 dqfh k.k o-r,2m-22 oping freely with an angular velocity of 0.8 2k uwof.-1rmhqpo,22e-drck $rad/s$ 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 white dww..eb6 8sjm3yrn en;dw/l01y ip ttc/arf, losing about half its mass in the process, and winding up with a pndstn.yem.; wwr3 e/80 ybl1j6 it/cradius 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 to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of :llyoa tj6v)(zrl/- q120 $km/h$ 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 vbr 3djyxj c93 y5/tswpe(c0l-to$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, or ;7amsi(7ygthat can rotate freely without ria(7g som7 ;yfriction. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person standgbk v3;u zg13vic, i9os at the edge of a 6.5-m diameter merry-go-round turntable t cg3;uv9 b1iv,oizg3k hat is mounted 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 wiubt:wbi; fc1r* / k7psvv0j2 eth the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwindsuwv; e r*k1bbfs pt2 :/icjv07 from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such*9jm*pkts y;plw d,* o that the same 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 *yj dm9;lp pkwots**,Earth.)    $\times10^{ -6}$

  A cyclist accelerates fromr 6b7f hja)yl6 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 the shape of a uniform c aia)e6yvq*4qd( c il5ylinder of radius 0.20 m acquires a rotational rate of from rest over 4 iv5cy)li a6dq*e(aqa 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricaonbc.0iieopk3c9 o y* -2pm0 zo5bf5ql disks, each of mass 0.050 kg and diamocmbiqo*neo9f-. pb5c0p kio52z y03 eter 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-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 wh,.b ypb/j3 4x: -4 l+ayo lpyhvai4mef;j (pfseel ($\omega_R$) 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 mass 8exwec07l 3z5u nn1+wdt 7( auc.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that t5cun ul w3 dx(c7z+t7 w0ae1nehe lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for i+(f ucegjhu/ 2t 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/2j hg+( ucefu 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 illustratesazy4 j6e v m8o,5v(vw c:ede;j an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) csga.j* pmc9,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 and length L can pivot freely (i.e., we ignore frictioxu8w t z+o)nl)n) about a hinge attached to a wall, as in Fig. 8–54. The rod is he xtulz)+on8w )ld 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 is standing vertically onfs vh.) ozb2k; the floor, and we want to exert a horizontal force F at its axle so that it will climb absfz vh2;o).k step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speedmwy(tje0lubjq s. )/ gn,41bs v=4.2m/s on a flat road is making a turn with a radius yej.jlwm0qsgts / b1)(b u 4n, The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0. e(,3,vu 0gkr(uzhx seb5ha;s50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle abovh( ;v,ub3guxak ssr5, ezh0(ee 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’8phjclq6 u ;b1s body as 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 spinb1chu pljq 8;6ning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which cons-nxvpp af 47o ,b2;s sa6:ndyjists of two cylindrical plates, of ma7o6:x j f-v,nn pbp;assd 2ya4ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alongy uw:3+x6)dy shq jbpc 6;vfxflf)1 k. the looped rough track of Fig. 8–58. Whac)kpvwhxl6+djfqx1y) ;: .3bfu6 f ys t 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? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not a4j(-xfaqlx 4)ai y+j ussume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its sp2*z.qr3q faw qeed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a q2q3 zfwq*.ra) 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