A bicycle odometer (which measures distance traveled) is attached neacq;x)0 ,6skbl pudp a1r the wheel hub and is designed fk pp)0u;q6sx,cl da1bor 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does as.+,0e3popobg yd ro231uml dtq 2j( r point 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 would the m0+g b2yr3pd r(.,uqso1 t2o jp3moldeagnitude of either component of linear acceleration change?

Could a nonrigid body be described by a sini xp6f:j24f n zienw4/gle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forc3db ii3 k e-ur/l8j(4ditv)loe? 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 qu w+wq94uz;33.g 7liwe vjooa sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answeu.4qw9vz3e lijq + o3;g ow7wur this.

A 21-speed bicycle has seven sprockets ath/i(vnb c:q/u8mco6 t 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? 8/vm onbqciut6c/: h(In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with 1s-,xfwxr q 2,dbz 0grflesh and muscle conf,12drz s qwxbr -,0gxcentrated 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 walkers (Fig. 8–35) carry a long, narro/9hgys lupj-) w beam?

If the net force on a system is nc qot6a3m 2l g.gpw2:zero, is the net torque also zero? If the net torque on a system is zero, is the net forqw:g2c 2m3 g.panto6l ce zero?

Two inclines have the same height but make different angles with the horizontal. mkd tg/aq30ixy( ddltc9y)78 The same steel ball is rolled down each incline. On which incline will the speed of the dt(a)y k m/8 xc0i97ltq3dd gyball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollingkb 5,-;l xfkwa:tgx0b (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the0g ,kxb;:wblfx-atk5 greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They 1(,p (vwnlb;tlj1 dr zstart from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottorpl1ld( ,w ;b jvzn1(tm? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or roiv g77h 75tezatating objects evha g7tz 7vie57entually slow down and stop. Explain.

If there were a great migratxhcw:+d 8c bo7 sz12:en9 oxldion of people toward the Earth’s equator, how would this affect the length of the day?cc o7bez+:x:hx12ds8l n dw9o

Can the diver of Fig. 8–29 do a somersault without having76acf9bj z: td any initial rotation when she leaves the boj79fz6b a:cdt ard?

The moment of inertia of a rotating solid disk ab+w)x 1hbkc fkak3*ik5 0c3c ekqxu26f out an axis through its center of mass f 0cxkf a*uk)k1c26w 3e qk+h5 3xicbkis $\frac{1}{2}WR^2$ (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 sittinqxi) / p nil1roq.x7,eg on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly e r.n)ix iq,7qpo l1/xdrop 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 hollow s n:ocoa 1x5-zwkpn*8 and the other is solid. Describe an experiment to determine which iswokx:na-5s8zc no * 1p which.

The angular velocity of a wheel cvh3*14g g) s yxkdovvm2 28f)((rdgq pdh6bmrotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at46)m1k3ydvdx*hf)(rhg(qs2 2 vb vm gdpo8 gc the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating k2nw:: u2*r(uov xy tfturntable. What happens if you walk toward the cenkwx: nt* 2uvy2r: (ofuter?

A shortstop may leap into the air to catch a ball and throw it quickly. As he q1fm6 mv pyr qvy8j:7 2;jw;mcthrows 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 p68:fqr 2mjvqm;c7 y;1wjyvm(Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentumse*5km*+ abng1urhyh2un9f:, discuss why a helicopter must have more than one rotgsr9h:k nuybamuf*215e h n+ *or (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles ink; /5v7kl8uvr ui ox7y.i/ jyw 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. Calculate, us6bo vl5 :c.aaqing the information inside the Front Cover, the angular diameters (in radians) of the Sun andq .o6a 5c:vbal the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 st 2i:w4soy6d(.mik6 zvib n) km from Earth. The beam diverges at an anglwd oiv)6z ( 2kbst.im 6s:nyi4e $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the moto-k(4bcglhn l75 d/1 z zgu n)rndz7 iu0/pok9rr is turned off dnnhz)lgdu7ld zokn( 9cz b0u5/1 -p4rgi/r7k uring operation, 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 mm w6(me31 rewy to another child. If the ball makes 15.0 revolutions, whatwr(me ey31 m6w is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many k0a q m+orshs-:7i:idhvw.9y revolutions do the wheels m iah079khq- :v oiwrd+ms:.syake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotm7f1hmqdj0 7- ua;gi qates at 2500 rpm. Calculate its angula;1qij70q-g7 mfm dhuar velocity 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 complecqt c4a4p)hoytv x +0*te revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 +oht04pt4ccx *vq) yam 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 etk3 nyi a s88fu0bp7-of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear ssx*m *o *t+8( q7ieii+ku0si lmzhs, apeed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a z8ym:-3gkcr,yoh 1xua8 t6q xu ;f* ntparticle 7.0 cm from the axis of rotation is to experience an acceleration of 100,0u83o -6hr,:z8 1 yfnttx*gacqk mux y;00 $g’s$?    $rpm$

  A 70-cm-diameter wheel accele)dlc/0ofi3mce wsi-6rates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determine mdlco6c-i ie)0f3/ws
(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 :tes7-l8 gfbs$R_1$ 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.cu4d k6bnf* b put themselves into a slow rotation to distribute the Sun’s energy eve.6 *dub4ncb kfnly. 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 uniformly from rest to 15,000 rpm in 220 s. T- 9or3icvg8zi;2 zsdahrough how many revolution-igvca2r;89oz iz3 s ds did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcuxmhrf/cdzai/z8b l0 g+igb 1u :pf5 o jw778x2late
(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 highspee y-l;w2pobrr )d jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching it)or;wyb pl2 -rs 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 rpm9 ls*y0 (sc d3okpoj*a to 360 rpm in 6.5 s. How far w so0d (a*9*kslojy3 cpill a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/minhg)auzim08,ky(p ;mz It turns 1500 revolutions before it comes to m mi0yz;azph,g) u8( ka 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 cafhz vc3g49o:;9vdhs er reduces its speed uniformly from 95km/h 9c sf4d9;hov:gz3v ehto 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly fr j,p3uc)gk )hkom 95km/h to 45km/h The )ghk3 up), kjctires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each cfi7oq nrtov:7 hll3(9/. rsnpedal when climbing a hill. The pedalchvl7qrs 3o olt9/n 7:n.fr i(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. What is thk:a ee) nxn5;0,lrw jre magnitude of ta ; rwe5: n)el0nkjx,rhe 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 t i7f ijk +4rklg:k*:uhhe wheel shown in Fig. 8–39. Assume that gkf*ul:i: 47ir+j kkha 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 attached to the ends of a massless ru oc:w3ec8 l,bod which pivots as shown in Fig. 8–40. Initially the rod is ,o3ceu:bc 8l wheld 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 require tightening to a torque of ). 0p*gvw.iyzsc38kj2 d qcov38* 3cciqj2) p vod zw08k.yv.sg $m \cdot N$ 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 ra 4 ohla*fsav60 u818 an*iyrvpdius 0.648 m when the axis of rotation is t *a a0s 18iy6vulnov8f p4r*hahrough its center.    $kg \cdot m^2$

  Calculate the moment of b 4yrx9u+ zwemfxn +6 vj6mso0,+7kzrinertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (w 0x4 kw6omny+6xvjbe,7s+rzmzu9f+ rhy?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a hosrhywo7t 0;v + -evn3zrizontal circle of radius 1.2 m. Calcthvn+zy s r07-;eovw 3ulate
(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 wmbe) f5a*k xue)sx; h8heel rotating at constant angular speed (Fe)xh;8*s5xk ) ufmbaeig. 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. 8–48a8z3d rg- rqyn mi..+ vex.vy3 aboute-.r.+d yg8 yaz8 v.ri3vxmnq
(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 oytme b+5gt/ 9two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correctq.yg,k pibwv/ 64ho( j rate, engineers fire four tangential rockets as bwg.,o qi/ 6(jpk4 yvhshown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and gu m9m3.*ekc qa mass of 0.580 kg. Cal *.mqge uc93kmculate
(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, aczb06(ps29s ehfq(ml r. 9bdatcelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-dx0 +uoowg(wut* 8qpq 9riven 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. Calculategq to uuw*px8o(9wq+ 0 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 r4 p;vx,. oq(4bog .uue3vj)jaqw*hdvotating at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional to vo*hovd.3)u.g qj4q;uaw (pxjv,e4b rque 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 /iewiq3nm2kvb2e :c0 ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action ot2 q( sne:.)u2aobwk,z mo9qhf the forearm, which rotates about the elbow joint under the action of the trm.kn2q ),o qw(o uhzbat 92:esiceps 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 be considered a long thin5 qruudo)be-(n)1 e qcr;.c by rod, as shown in Fig. 8–465uq1r;e qc)no eub)c- r y(db..
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two mah4lrejqwq4 0.) - 1vetpky4(d,kmq s usses, $m_1$ 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 ha:g :j5wy 5h25 hth5d;syglmnummer from rest within four full turns (revolutions) and releases i:jyndw2muh55h ;gs y t lg5:h5t 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 inertia of m )mlt (pdjg;epeu2 4:$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops aj vk-(l aw7b tqktr )2gsm33.5ibk.la 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 r4 ph13;momexz e9/e;b*cy;g1x v wlfdolls without slipping down a lane at 3.34xheofc zl ev ;g3b /w19;me y1;pm*xd $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic 3bxr3ur8 ii b,energy of the Earth with respect to the Sun as the sum of two tir ubx3r3 ib,8erms,
(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*up lqzlt t+mcy*( 6e4eo 1 m66rkmsq6.50 m. How much net work is required to accelerate it from rest tos*m 1mcq4 66p+ok lryzeq66*tue tlm( a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 1fjquuj/4d5-5,zp ljx3ep zm j(/somcm and mass 1.80 kg starts from rest and rolls without slipping down a 3mudfjm /,pul1j-sj3o5x/5z(q p zje40.0 $^{\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 bala 9*-, vgyzhcwtnced vertically on its tip. It starts to fall and its lower end does not slip. Wh wyt-*,cgzhv 9at will be the speed of 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 0.210-kg b bfru.hgfp,o4) p:+iball rotating on the end of a thin string in a circle obf4 pi:r)obp gh.+f ,uf radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of j qcg n.we2.8ca 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? c j cn82geq..w   $kg \cdot m^2$
(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 a ra. :t;rvkmppxog* gf 6r us2q d2+9-pxkte of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotationp s t+qu:vr g;k2m .pr*g9x 6xp-do2kf decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her momay2rub3dv h5**c6fakent of inertia by a factor of about 3.5 when changing from t6y2r kv3a5chf *d u*bahe straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from xsao 8ep)+7xxb+4 8o7jlmay dan initial rate of 1.0 rev every 2.0 s to a final l+xed a7o7 4)xp+8smb jx 8yaorate 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 id xv lw)5dnot yz8*ug5dgqv*(w 9 g.-fts center at a frequency of 1.5rev/s The wheel can be considered a uniform disk.l *y(dug8o95tn)vfv*w-ggd5q zxd w of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum ogb.xl l(dn-ucu+1n/xf 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 6pra8dwgtz ..yh;h e.nay : t0momentum 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 of t 2h(()k iwi5toe0dvnto an identical disk rotating at angular sp)t th fe(v (0dk2oiiw5eed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 nx +zv 9 sea8;u0-mraj$rev/s$ 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 k*w8(d,gjm) p/m+eh rc hsxd u-g stands at the center of a rotating merry-go-round platform of radius 3me(8) hr,gmjcp/ -hxwd us*+d.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 vsl8)h8c hg,crotating freely with an angular velocity of 0,hl8g8hvc sc) .8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half -ftny)-l ebp/u3 : ws3ip(,qp(zmnt22 xtxvw its mass in the process, and winding up with a ralf-2z pptp(u3ix/2xbv e(m y:w,- t 3nnw )stqdius 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 s 8 +eb zsdd:5:1fkhsj120 $km/h$ 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 :2ee5zmd)uet5z kiw2pg:l7 m cs pnmtfe,8 85$ 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, that can rotate)-30c (dw*tp hzqnp50 wkqjd kvy cg40 freely without ndwc00k jk5)zdgc-v(*wq3h 4 yt0ppq friction. 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 stands at the edgel(b(.67k oijsj x/l.sp 1obthk8ulkdmin2: . of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of on /1s2i7jsb kklxm(:kp(t.d.6oj.lb hl8iu 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 with wm7g bo0 ac:5wne,n q2the 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 unwinds from the spool? How far dg e0a 2,q7o:mn wbcn5woes the spool’s center of mass move?

  The Moon orbits the Earth such that the same smn.,y4tfqe x ,1cc: (ogcit9wide always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own o.c,gtntyfc ex(q4:9 c,mi1waxis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1e)6fc af,9rccb 3fv9 j 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 7djhp4s6e8 ,k0yt o ldcylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the moto4dd6e hlp,jy7 s0k 8tor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrica- vw kgvu2nr/y8/bz-ol disks, 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 cal2b-g-wru/nk vv zo/ y8culate 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 whfxg z v9wj.-,)/qo;adww8vcgeel ($\omega_R$) 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 8.0 times as great, were rotat;gi6 x37guz7tm 4ro miing at a speed of 1.0 revolution every 12 days. If it were to undergo gravitatizoim7t mg 6x;4g3ur7ional 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 automobile is for it to use ,6(9 aupi +uy2kvhgpu ;yifl;energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg,l,u6hg uvk(;2ap uiyyi 9+p;f 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 ww*(yz3i y sg84hz2bman $H_2O$ 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 onsdjx, )a0z -g* cjkyq1 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 a7 0bn 4ipzg6a,m )hfionp*0i friction) about a hinge attached to a wall, as in F0 7na *b,p0if4z)iami6h pog nig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It isls kk*;bmj.-zbmti /b p .r:;u 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.r/pk;bts. ; bmm j blki-*:zu h

  A bicyclist traveling with speed v=4.2m/s on a flat road i2k5h,9b h,bhxve6+rdhenk .n s making a turn with a radius .n+k9 ,h,k2dvbe 5rh6bexh nhThe 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 nymozgo 24g8z1 y( oo8begins whirling the rock in a nearly horizontal circle above 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 g2g48yy 8no1ozo(mzo does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her2 -nr9lz*pxu 1mtd9wed 48pqw arms as thin rods, making reasonable estimates for the dime9 pnxd*dw8we1zu-2lpm9r 4 tq nsions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists ofnc d 0ir hy0e:dbx)e7 8l,9t rb+h3asj two cylindrical plates, of ma0b ey3j,8ie07dd:hr l acxr s9tn)b+hss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fi.n.rx+yc9/br du. x)cs 3g nsdg. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highestscn/d)ncb.r.gr+yd93xu xs . point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not ass e*;00 3ty-+dqvvzsy8k efp cmume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed un8oxmz(y4e2;(st is/u euyz5b iformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular eb4zy(is e(soxtu2; m 8/yu5zacceleration 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