A bicycle odometer (ws mrr 6(l6 h,zf+p,gw)fliln2hich measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What h+(p,)6 ln 6,rrilm zlhswfgf2appens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a pocf.q-yawlzs 7jk7s.:mk . sq9 int on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases wo.qs-7.9a s.f:jlwsymkz 7q c kuld the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular ve7jyo0iqni7)jusx a62 c 6y 9eglocity $\omega$ Explain.

Can a small force ever exert a greater torque than a s0t8f fr0mpn- 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 head than wyqbdc1ollx1p5w : s ,.hen your arms are stretched out in front of you:ospl51xc,y1ql.b w d? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at* jrdm;x v- unr 1sde9c:rh9o6 the rear wheel and three at the pedal cranks. In which gear is it harder to ped:ru; o edxrd9mn9r6csvhj- 1*al, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on beinxrk,vcbfq10;i7 8jg n g able to run fast have slender lower legs with flesh and muscleq0v1c8i7,kf jrbg nx; concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkersjasvk:: +g-n q (Fig. 8–35) carry a long, narrow beam?

If the net force on a system i lba itv0 7;9a85iqllts zero, is the net torque also zero? If the net torque on 5b a98ltl7t 0iil;va qa system is zero, is the net force zero?

Two inclines have the same height but make different m yn**mw +xjee5*)rm lkc5;pe angles with the horizontal. The same steel ball is rolled down each )ye5*m wn ;p+lm *ck*re5jemxincline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) o t y ee 4i.b9clpvy1eiz2+8i:down an incline. One sphere has twice the radiue4 9i1tvl+ eyoi82 :ezciy.pbs and twice the mass of the other. Which 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 and the sameaf 5djcgw8(z0 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 kin0cad w(z8gf5j etic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momenth h;o04ugo noj xluk+(k+58mn um are conserved. Yet most moving or rotating objects eventually slow down and stop. 0n5o8;o uk+ nloh khj4xu(+g mExplain.

If there were a great migration of people toward (pps vl8 zc6c ,rh-k7mthe Earth’s equator, how would this ,-smp7 cch vp(rk6z8l affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotation wp) ank4e.bo 4.*kuiappmf: t2hen:.bmao epip2f u)t.k*npa4k 4 she leaves the board?

The moment of inertia of a rotating solid disk about anpq8eo hkqn98mx *ct9 :p,2b lbler-q- axis through its center of mass kqpn8mx 2be9q*qr- llcbt :eo8h,p -9 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 holp c h(ya4h*eu,ding a 2-kg mass in each outstretche*hp h4ecuay, (d 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 is hos/dw.vfc7/osc( t/ h be/:;bnbbph; u llow and the other is solid. Describe an experiment to determine which is whichw ; tu;.fnb vshdbc/cbsh 7:e/(pob //.

The angular velocity of a wheel rotating on a ho bg) fk+c*+zoirizontal axle points west. In what direction is the linear velocity of a point obo *)i +zgf+kcn the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotat6gau, ex pz(k1ing turntable. What happens if you xpz(, ua e6k1gwalk toward the center?

A shortstop may leap into the air to catch a ball and throw it quic;)f xeh4ro d-skly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explai-o ;he rx)fs4dn.

On the basis of the law of conservatrnib g2 2zmkw,h m)x*1ion of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep b* n,2gz)mk1h m wxri2the helicopter stable.

  Express the followingz 3e5zqd y+m2k angles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calcedd 51k91jp4b -rvf zrulate, using the informatd r9bj4kz1-erf1dvp5ion inside the Front Cover, the angular diameters (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. The beam dr1 5)d a+ntdcmiverges andr1+t dmc5)at 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 rota8db5qbq7 qg /up5ochjt9who g8+r 1;vte at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is5d1q r9t7h ;+ vq /ob8bhjgpco8q5wgu the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level flox5i3gyerj1 f3 o r*b.por 3.5 m to another child. If the ball makes 15.0 revolutions, whai *.3rpgj1fo brxye53t is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. H1h s2q jtq+ +b:ldpxs./y ;jrsow many revolutions do the wheels makepb:q; qy/ 1x r+ lshsd.js+jt2?    $rev$

  (a) A grinding wheel 0.35 m in diameterwux 8qo2 k0l.n rotates at 2500 rpm. Calculate its angular velocit wlku2 0oq8nx.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 revolution in -mac.d+q3tjldg /9m w4.0 s (Fig. 8–38). (a) What is t tm3cw.-dm +dgq/9 aljhe linear speed 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 its orbimzy h59+m 3 5,w2wc.z iygugsut around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a q)0)t9 *.qnm ld+rt hqcr.)tr /ku wanpoint
(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 rota *qu:fria 1gf,z ,4qtkte if a particle 7.0 cm from the axis of rotati4a1gqzft ir:k, ,u*q fon is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 ris, yyl7:wulz* 9dj )b m8d 5f+x;cndjpm to 28,z5yyj7; 9c :lnd*d l si8uxmdwbjf +)0 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 radiusv 49g(+rd rkwz $R_1$ 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 themselvee:vx))3kc7d zrh bch11t1l j ts 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 inl3v k c)dh1x1 ztc )bt:hr17jeterval. 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 228w/d (lm dr5dd0 s. Through how many revolutions did it turn in (dddl8w5 /mdr this time?    $rev$

  An automobile engine slowspm/) kyfn/5p-m 7c(hm j,zf xa down from 4500 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 fyki 5 n*.n jj ei-s,tifm*a1/highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolunesjtm1jik/i**i5,a y .ff-n tions 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 36p;(.ktra ri.i0 rpm in 6.5 s. Hair(. ki;p tr.ow far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runni5gfk/ oyn2nfny )zy:7 ng at 850rev/min It turns 1500 revolutions befor 7y/ ynzk)yno2f:fn 5ge 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 its2ieces,w d.c: speed uniformly from 95km/h to 45km/h Thee2cc e ,di.:ws 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 6zj3mp2 9k fz qbl;ys7speed uniformly from 95km/h to 45km/h The tires have a dia26 y3kfq9s7jpzb l;zmmeter 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 when climbing a he2l3u nft(hf) ill. The pedals rotate in a circle of radfehu3 l2n ()ftius 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 t8zc (vmhh) i474 cm wide. What is the magnitude of the torquh chi4 vmtz)(8e if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39.-(biyp s4+vk-i gx rp6ou-dj7 Assume tpikrpjbv-y7ox( 6- 4uds+ -g ihat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attacfw l*emj1283 p3yj bnohed to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal w*y8jj31nb flm o2e3p position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tigkm qy/* )oe) +cs. b/6j+lqmaez0dklchtening to a torque of 38 / / .l)aceql smed+z0qbk)ko6yj+*m c$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m whiegj v70p-b- hen the axis of rota-g jbv-ehp07ition is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. T myr*,ml;mqmp )aq 2z 82;gqpzhe rim and tire have a combined mass of 1.25 kl pmrz ;mg2mq yzm,)pq2 ;qa8*g. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball onyf:u+jyd( 27 urfs8ni the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. 7dy :r 82u+njyuisff( 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 boyi93nnrl9e 4qwl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 9rle94 n3 qniy1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inerl x99gyzy+k (o nc(w:btia of the array of point objects shown in Fig. 8–43 aboutyzgw n9: b(okyc9x +(l
(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 oxe rhj-7bj-adv*h4:/ xw kkm ,oygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylinli+m: vu(l 6 ualo4jp, a.6-tkd s)iradrical 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 steaddjpuik6oala4(+: tu6r a l -mls)i,.vy 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 xysoc:eg.v v8j-a31 m a uniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calcoev. cyjmxsv3 :1 a-g8ulate
(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 tqz5qmhj a x9p-.:mis 1o 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand fdl0fkd.b57 p-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) 7lb50d.ffk pdsit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is evend j0axu:1u*7k )ynly jtually brought uniformly to rest by y y jajxunld1 u:*k)70a 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 7 vm2ba.skoyu ;dp3 1i3 $m/s^2$ 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 of tl+ga 6 q(vhjr4d 2bar(x(d9 l8ivx oj(he forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 ox rarj q2ig68alvvd4(h ((b +d(ljx9$m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. oi+x1fkys2w 0 8–41 oyfxsk0i2 +w6.
(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 t.9q;jm: u oql n1ido(gwo masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from p ihm0mdphvh7) 3mjj.* l 7sj.rest within four full turns (revolutions) and releases it at jijs3)0p h.lmp dv m* .mh77jha 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 aj 5ore6.0kpia 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 vh 0owndnl0z* afg 58wp/4m+edevelops 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 7.3 kg and radius 9.0 cm rolls witho+ o+qypvu4gdxyth94v ctlvc k1/ m43.ut slipping down a lane at 3.3 9 +yx+4c.1cud4vvmvhg3kt pl4qto /y $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum pvc6, 7k2olxa of two pa 2vok7c l6,xterms,
(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. Ho8i)cnbsgkt9 -e(kvv fxeewu 55 n 6fa/z;)m+aw much net 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 cylineka9kf-gb a6v(ns5inu5fct/m e)v 8x w z+e;)der.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest andgl2gl1k ekw(ph;v7ck g :(7jurcx8 k bd+:5xf rolls without slipping down a 30 (ef1v2 7gjg w kupgkd :h7rk(x+ x;bc8llk5c:.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall azj7a z :)x6p1ym oj.fpjubz w)5w8lv qd(e)c9nd its lower end does not slip. What will be the speed opjom yaww5e zj dx :.pu8bq)c97)j z(1l6) vfzf the 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 0.21j2afjd x4:k 7g0-kg ball rotating on the end of a thin stri4d:jgxjaf2 k 7ng 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 momentmtu/:oom4 jeme67kg3yc82qoum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rot2m:gt7o m c3/ qeo68uyokj4e mating 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 his side, on a platform that is rotating at abec0-aiz iz., rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48z .-ibz0eaci ,, 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 re 37uiwyz *hs8mduce 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 when in the3yzw* 8mh7sui tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation lbk tal4,e d*.rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3 e4l,t dk.bal* $rev/s$ 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 verowr9h- i,gq/v r nkt6 0e*5dmjtical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-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 gv- i0rr65,*/mhod9t jekn qw of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momen6d,a;wy vlgg6 tum of a 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 moment8z-s2 4n denc 5.rwy6ygh zojn/l vv-0um 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 inertia I is dropped onto an id0ml891vurgm24 zzc pdh l/ux4entical disk rotatz04z u/lv84gpmh 2xumcrl 1d9ing 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-qj /itp8 0nei6q4eh3 vk lnb8 $rev/s$ 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 th +y).wg q 721tftbji .cik,tewe center of a rotating merry-go-round platform of radius 3.0 m aj7i1) .t gtqicfw2kb.yt+ e,w nd moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freel5npnk5f/wm . 1lyumdo rgl.7a) p15; gw 7mplvy with an angular velocity of 0.my gmwgln).1.p7 p;7rl dufowkn av5l5/51mp8 $rad/s$ 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)u dc 5bb*nqb2c-mks+ into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming kbq+dc s25bc)nb* -u mthe 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 exc4 koy :s1mrd;wess 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 gh)y2f8 qul zjm/v7 o4$ 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, initi-v4w 5jg4xbog bdm5 3cally at rest, that can rotate freely without friction. The mo cg44 5b3vwmo5j-dxbgment 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 stands at the edge7l 9i 5k.isl7,hr rswf of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and hasl.wi,ik59sr l r77h fs 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 theknz8h/ 5reb. d/cdcs2 a6dd)p ground with 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 persodd. d)k znsce6rdcbp2 //h5a 8n 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 same0ekms yy98.6 otc++7 h fpkc,e0ksl vr side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum k 0remv7t f6sk9co.k,+ c8+yply0ehs(about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at// z.zarv.r,0so jv fb8gjb s( 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 cylinder of radius 0.b9pxa343vz ods j5dpi2 5ei1c20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motox bc4i 3dpojp93d2vea 55z1si r.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kgdz9,b:n1 nbtw.yipu 7rnx q)1 and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. itn:)npw1d.7 n ,qu9rz1 ybxbUse 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 rem k4c /v*b6wypxq:)ju ar 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 Sun, but withp*byj)z,ek6 p iq x3q9 mass 8.0 times as great, were rotating aqpxkpq3bj *ey6 9 iz),t 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 carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobil5qb3(,4a rjzi 0hg jwge is for it to use energy stored in a heavy rotating flywheel. Supgjw4 i(jba5gqh0 3r,z pose 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 an 8m; mmb) ddhz7$H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface4:xbof/, dd)k3 yobgss e ,5ts 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 itstodt- w.+g.,ia qmx 2vi6(j gnore 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 s (t+v,jaxt.62wdmt -qi.io gof 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 h)t:hz2q w- bq0 u8)pc1gyeqaR. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where hcbq2)pquw08hzytae:q - 1 gh )

  A bicyclist travelingbb27xvm qlsot*5es1;s 0( lmi with speed v=4.2m/s on a flat road is making a turn with a radius 2l xt0vibs;l57oe1s*bmms (q 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 0.50-kg rock into a sling of length 1.5 m and begtlas(n:wm xz)+z9-poins whirling the rock in a nearly horizontal circle above his head, accelerating it frop z)tx:( mw9naoz+-l sm rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder +*27 c ;0wdviqqvxe( wky2xo:ctw-nw and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio o 0q+ xotkqnewdivywv(2;:- cxcw 2*w7 f 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 cokn v.h3e3kd* gpl i2q v4x*z;bam3-pc nsists of two cylindrical plates, of max2v g;dp*l4.3m bka - *qez3nip 3hcvkss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 8rc6*j59t q 0qkwdgx aradius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h qt wgcjr0 8x 965*dkaqthat 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 jly n uy3: pvk6e/qc0yuc5c03not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speedx7rl.j2b48 ru)mqmb0wyq nj ) uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each wjr xymq lm)748bn 2bqurj.)0 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