A bicycle odometer (which measures distance traveled) is attached nearwteo 00 iwu3ua*x ul8- the wheel hub and is designed for 27-inch wheels. What happens if you use it*u t 83owlu0e0wxi- au on a bicycle with 24-inch wheels?

Suppose a disk rotates at j-g iu+lw;a 8.)ykep(mac3ed0 gt i4t constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point h+e jp 0-8d3ewgl)cituaagk.t (4myi; ave radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described b kavtz7k6,wq2hu:w4 fy a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greatc q:zccei:2 m5er 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 .abqiu8r)9hp6l) e- 8b(acp jku 9oqxyour hands behind your head than when your arms are stretched out in front of you? A diaop 8)aau8 hik -ub.x(l6r 9qjpb)eq9c gram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel an p*n kxy(n8d-(lxoc/l b4r4f/ lu 1almd three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? Iucpf/4nm*r 8o(ld4nkyb -laxx( l/1ln 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 fleskqo/--/aw sarh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why thisaa r//kw q--so distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long,9,6 ta1iv6d hyz4fslh*b. hrz9/vmac narrow beam?

If the net force on a system is zcu5jpjp0ft) :ero, is the net torque also zero? If the net torque o f)ju0pt:p5jcn a system is zero, is the net force zero?

Two inclines have the same height but make.vp7ehrv7ph 7q7 jr6wdook ,e8nt9y. different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of thep7veo8 .7y,ro6.k9nqph j7h vw 7tedr ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling qj 3rvboo.c 72.;hikc (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 cockq7o. rb hv;. 23ijfirst? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have xot*u p3ckt */ .ilcf45oc8eto7m4 gk the same radius 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? Wh *t3e of*kt8o544p/ .oc7ckcxil gm utich has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular mommi+0 q45 f+q4gmc lflgentum are conserved. Yet most moving or rotating objects eventua+lcgfqf+mm0q44l 5i glly slow down and stop. Explain.

If there were a great migration of people toward the Earth’s e obx* y 6l/fnck8f*sb qm pi0az3uro5(:(h st6quator, how would this affect the length of the dak(oifc sl3/y:6qsb85 far*mbn*z p 0uh6o (xty?

Can the diver of Fig. 8–29 do a somersault without having any initial rotq xjz3y +/ +ip1qfha92c9eekxation when she leavesh1f/ p + e3qk+a29qi xeyxcj9z the board?

The moment of inertia of a rotating solid disk about an axis through its cec ;h(shpw/l n:nter of ma n wl;pshc:h/(ss 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 holding a 2-kg mass in each outssis5 p6wyi-s, tretched ws5iy ,6ssip -hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one i: qwt5n snki2 cz8z;(leb,h6 spm9c .xs hollow and the othe;:9nct. 8 iq5ps6xn z2cwzl(,k b smher is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points wespc2 use1q0i v+t. 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 line +i1c 0squ2pevar 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 rotaelqcgk q5p : 2upp,08uting turntable. What gp8,clp 0uu 52:kqqpe happens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As hw/y hbv5z 5mg6l/:f yre throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in thewhz/m 5yg/ybvl:5 fr6 opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a7+/3 efwqb) u( qhuym-g ch:gv helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller cam3qbv -w7 :+ gfe)g hchquu/(yn operate to keep the helicopter stable.

  Express the following angles bo4z 3tr+ 4wzqin 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 becao;l;l1gm88 xti y8p djuse of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as ; 1gy t8;p88oilxmdjlseen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Mo6 kcd glu.g*(qon, 380,000 km from Earth. The beam diverges at an angu* (qgc6.lgk dle $\theta$ (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(rl.w 2ecpjh4g/vxyy w3n5 x4ate of 6500 rpm. When the motor is turned off during operation, the blades slo 42g4rv/cxpl3 hweyn ( j5.xwyw 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 avq*v, xo4n+ menother child. If the ball makes 15.0 revolutions, what is its diametex+qn4 *me,vv or?    m

  A bicycle with tires 68 cm in diameter travels 8.0 kmgg. 0son8tqkh z; 73q5b,w efc. How many revolutions do the wh8tc7hkge.fbg 5qowz 0s; qn,3eels make?    $rev$

  (a) A grinding wheel+m wsipa+d4wbs 4*h9y 4s+qgi 0.35 m in diameter rotates at 2500 rpm. Calculate its angular velocity igi+4 sdqhwp*b+ imaw94s+s y4n $rad/s$ $\omega$ =    $rad/sec$
(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 revolgkp/ugf+m136 kfuz 6b ution in 4.0 s (Fig. 8–38). (a) What is the linear speefgu3p6k1f/k z g6m+ubd of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in itqa: 0 df7e+a t(mb7jvps orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a (nnc:/ o0cb-drlz /wqpoint
(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 centrifug w0bwbigx 2pl ;c33,xwh l;df 9z3g rx/*w2wpge rotate if a particle 7.0 cm from the axis of rotation is to experience an accelwbl b3lwc xw2x3g,h0;pz9/ xpw *f32gi;wdgr eration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center bk8 ;qtx+**pb,ufonj from 130 rpm to 280 rb+ 8,txk opfqbj*;u n*pm 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 radiuo y zc(y(cm3x*x)fw, ms $R_1$ 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 Monp) cz7 5s;sjirsq n76on, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute s 6q7r pi s)s;c5njn7zthe Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 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 ,jyy;,c2m ir :e*ldg puniformly from rest to 15,000 rpm in 220 s. Through how many r* mdr 2,eyi, ;ygc:pljevolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4i8 e9 m(wk:owk500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying e2e5o dpeq5-o highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed 52pe edoeqo5-.
(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 my1+ v)lqwpe4t8x5vl n ;xe)o from 240 rpm to 360 rpm in 6.5 s. How far will a poinx+x4l1 )owemq5 vvye;p) nlt8t on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It kxhv4/5 e /rj jh+*ttbturns 1500 revolutions before it c 5jvhrt*tk bexj+/h/4omes 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 unf3vb 1g1fr vuv3 )h8pqiformly from 95km8 rff1 bhpv313gq)vuv /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 s h8e0i hxaj,h8f*es 299mldp ga11qqmpeed uniformly from 95km/h to 45k d2h 9e9a, *ehifj1q 08p1ahxq8mlmgs m/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 alxx.ar0xtw+a84m,k or zel7g. l her weight on each pedal when climbing a hill. The pedal r.,exa7+zlw4 0g8rtakmx.x o s 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. Wha 2dv kxh(zo7te/g6) jnt is the magnitude of/v7otgxndkh2 z j)e6( the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel showxq.yy in9 nr)(n in Fig. 8–39. Assume that a frictni)xq . (y9rnyion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a kkk )jnp.zx62 updfr; 41)kjl massless rod which pivots as shown in Fig. 8–40. Initially the rod is heldxdj f)zk .pr;n)kul 21pjk46k in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine req*(rww)h 6d et9wk4 i;mnpq)hoc;l; spuire tightening to a torque of 38*lw ;; cwdqs4ht)p ho(9)wi r;mnke6p $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 7ln:4dofk su /t9 ure:y h1yy,0.648 m when the axis of rotation is through its c u7fytryo1hn:del: k/su,94yenter.    $kg \cdot m^2$

  Calculate the moment of inertia of a + *kfc q+u hzb34l0arvbicycle wheel 66.7 cm in diameter. The rim and tirr kqbah04+lvcz3+* ufe have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lind(2g 76l zfinght rod is rotated in a horizontal circle of radiui6ldn(72 gfz ns 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 cw 69vytybg .siwp7v2,onstant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N to7wvts9b g6 v pywy.,2ital.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig.zkoc r729lbug cempp;eup: 6x m+0l7. 8–43 pmzc7 .l0e:meuxk+ p b;7 cl2ourg9p6 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 qugd qhxh68 kpyk:48 3atoms 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 sal+he.-qf gu;fcit) t3b5v/ 6/w 8gc rwxbmx(f tellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If thf/ ; .ff-qhuiblgx c twb)v3m85g(ec/wrt6+xe 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 cylinder h4ir*ib+q3 n7jya3 pe with a radius of 8.50 cm and a mass of 0.580 kg*7ei b+ qrinp j43yha3. 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 todx0inx(ldtx 5 2i,u7 o 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 tangentiokpd j(sbl. m/oio-g81d j9l8ally on a small 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 edge. Calculate the torque required to projdlo8do p1-8 ib9o. mglsj(k /duce 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 i-,1l;g teifm6a io0/bw unn .zs eventually brought uniformly to rest by a frictional torqu gtwi la1m /0,u- ezn6;nfbi.oe 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 xvw1 w uxt63 i*n(5pfgaccelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown sg5bg dy. xfj.3olely 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 acj.. 3ydg fgxb5celerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be consi ouz24l48prxgw,j new. )fo1 y9oe/dodered a long thin rod, as shown in Fig. 8–46.y4pu fgx zo/lr1e9e.jn)dow2 8oow,4
(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 tt19lnwkwi-y,phuj4/2ho:suxf ; v l:wo 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 hamme 4-p mcpj)l iw0yxol0,r from rest within four full turns (revolutions) and releases it at a speed 0low c-,ipp)y xm40 jlof 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 o1, p-ulgli o1q/5z;sbynbjg 6f 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 of8uuy 4mk:,ei u 14lzb nchx4q, 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls withouty qbcaz3yt98 .5 3lt*pd 2udgo slipping down a lane at 3qlt yb .u8d2g3 5ap*y9o c3dtz.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic efd;py 6+v 5amvnergy of the Earth with respect to the Sun as the sum of twoy+m6;df5 avvp 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 u*z 8(bgp6.lm 16m3qdlbxbd jkg and a radius of 7.50 m. How much net work is requir6 xlm13*lb6dzqdgjpmb8b(u. ed to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from r,a/ lng-:tn7 u y.snstndo *o8est and rolls without slipping down a 30.n, usdls -o. :y8gon/* t7annt0 $^{\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 oed8ch 7kc 6sj ;s8 l d+x+rj ;0gx+ax(+mzhwmqn its tip. It starts to fall and its lower end does not slip. What will be the speed of the upp(asx jmds ;hcx0j7z 8+r6; c ++qkhxl dwme+g8er end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentufw* sv5f+x;bt m of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.4tf+x5 f; s*wbv $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding 1bk+ broy2 w.ewheel of radius 18 cm when rotating at 1500 rb ewby.12kr o+pm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his sifyw7:il 0 wgo,icze:hq+z+ g(9,f jwhde, on a platform 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 rotation decreasg +w,jwg :0ezo,7f iyqih(w+c h:lz f9es 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 d,i*r im90 secinertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 ror,sii*0c em9d tations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate ofs. t4is fkqxz1s 0)ns* 1.0 rev every 2.0 s to a final ras zs1.k 04sti xfsq)*nte 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 at ikz8.v-bd.3e tzl ph x7, in,qa frequency of 1.5rev/s The wheel can be considered a uniform disk oi .zvt-l3 ,zibn78de , xh.qpkf 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 it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at ej) ry;fw 1lp0 ef3tk.z/oxhx c.60wp3.5 $rev/s$ 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 mo( vssevz2ucjxq-8y.n ;+ua2/* w 2wyo ,iatpdmentum 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 dihy wsb/+5cl6g o,w 0fisk of moment of inertia I is dropped onto an identical disk rotatingylwg 5s6i ,f+oc0bhw/ at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 . ,xgue 1wc5ij/otgy. $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating m3mm* 5a 9k) qg,n tjz-mwbgw*werry-go-round platform of radius 3.0 m and moment of inertia 9gtwkm,n *jw9 -mq*)3 zam5wbg20 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocit u;xr:ze8d w6cy of 0.8 6;d c 8urezw:x$rad/s$ 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 int;cu -cbma24buo 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, mac u4u -;b2bcwhat 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 iw zu+9;i/ blqxn 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 / j kjb7cg-:+qwq mr1g$ 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, e1e)kz- jb a:xthat can rotate freely without friction. The moment of zaexekb1j :) -inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at tg52in e2bkvj7egj*1i4pxr0 edid 9 o)he edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has4 ioejgkxin) 279*5 bipj r2eev g0d1d 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 grounuy b-q8c )g-zqd with the end of the rope lying on the topzq-g)q c8uyb- 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 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 Earth. De,itwf qh g0(9atermine the ratio of the Moon’s spin angular momentum (about its own axis) to its (a i,q0wtgfh9orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from restl s*jg3jwism67nj( o+ 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 tj 1z28(5* gwva6 vl5*bxzubkab ft0hshe shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s inte5u2v0sjgb (6ftk lxbahzzv* b a5 w8*1rval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disk m -n:+jdpr c ib9o-ss0l15ddhs, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it rems crd 1inj +5b:od-9-sdl0phaches 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 speedj6)zjm)wm-hoynfn: fi ;1gd: 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 on84l 0ri )dxsyf our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass ca)l id8rxn 4ys0rries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution a(d6i(.+)h bevu u,n2e nh8 ry7lqrs pautomobile is for 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 flil2haur(e(svyn b7 d 8hn ,p6.ru+q)e ywheel 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 illustratesm nrm )x(36 p.dgstz9c an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling otu2a7 s /jy7rsn 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 piv(dl/vm*rz3i2 b a64ofhqp /pcot 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 the rod, and (b) the linear acceleration of the tip of the rod. Assume that the bprh2l zod/6p qam (v4icf/* 3force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor,5fs4hk0cigf3cks yag(jy.f:w 3 d,q( and we want to exert a horizontal force F at its axle so that it will climb a step against which it wqh5. ic:03 f gskydf4fajg,yc3(sk( rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is:1bwq 7uom9tgielmwx( s o1: ( making a turn with a radius The forces acting on the cyclist and cycle are the normai7(:gel (sq w 1mot1wuxmbo:9l 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-kct0y / m /o50.f7maewv7puptm g rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to atvomemf75/w ptcy p70/mu0a. rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and he5es*kk:7wkn r r arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of r n5ek:kw*k7sthe 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 cyling8b hf o9cm l;.;3hxnzdrical plates, of 9hzhm3 ;; fl.8xgnobcmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 a2ou9xloe28c7q 2u gs r rolls along 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? Assume 2 x7aoqlu 298se 2guoc$r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do nokl*e z;fhh ws/9a v-6yt assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revoluta 1g1iy aj5jo7z,625u lkbcghions as the car reduces its speed uniformly from 90km/h to 60km/h The tires h 7ub6j,5 zy15la goahgk 2jc1iave 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