A bicycle odometer (which measures distance traveled) is attached ncri8:k4nq1 4 ,./evaxnfmvmeear the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle win rmq,fv4ie1ca: m.8e/xn vk4th 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on (v13f,squhpdl(g* eju d ee.,the rim have radial and/or tangential acceleration? If the disk’segd, vslq1u , efe 3ujdh(p(*. angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular veldwv4*xy1 fgc,f5 4 omgocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger fowg -u81s agr9k9khf, drce? 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-upnat7 )3mf/(q h mbp j2vhzob97 with your hands behind your head than when your arms are stretched out in front of you? A2 hhb(7 3b/)7 znj mqpf9ovmat diagram may help you to answer this.

A 21-speed bicycle hasx2nk6cm6e -k ci/ ;u nfm4ax0z seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sproc2u6mf 4m x;ek- nik/c0 nxaz6cket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower leg)x9k jq rz:mzfv c108t/6g bh y6ba9aqs with flesh and muscle concentrated highy9kar8/qq 6)zf mbt0j619:v agzhc xb, 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 arf04x -tcgk 4t long, narrow beam?

If the net force on a system is zero, is thef2 px bpe;un*dav3 d14(96o r0u cvnob net torque also zero? If the net torque on a system isue c pna 3; d4*60(fx1bdbruop9n2o vv zero, is the net force zero?

Two inclines have the q( xw8j8qg d)j8otb.rsame height but make different angles with the horizontal. The same steel ball is rolled down ed88 gj o.rt)b(xqq8wjach incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultanq8b/b9 aq tupu1 pxv. y+x.c/beously start rolling (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 the greater speed there? Which has the greater total kinetic energy at qxcyp 8b.ax1./v +tpb/qb9uu the bottom?

A sphere and a cylinder have the sa 6blpub fta)0jj1o*6fme radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the)b1bp0fl6* tj o6f jua greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angul/8pwymj/y hmf;da r t17w8l,v ar momentum are conserved. Yet most moving or rotating objects eventually slow down and s/m/ wdw 881, ;ayhr7f mtyvjlptop. Explain.

If there were a great migration of people toward the Earth’s equacbkbym4tg / k;moz8 ()ds+s-ztor, how would thim) zokbm+/ t8(gkcs;ybs4 z- ds affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotati,hjf0,z:a3gy b )imbxoc8 ah:on when she leaves thiofzc8:a,y3:b ),hjgamx hb 0e board?

The moment of inertia of a rotating solid disk about a-b fq/i35ic v kv/htz+n axis through its center of mass hcb/q5k+i v z3/ -tfviis $\frac{1}{2}WR^2$ (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 rotatb /l9hzx/lv :jfh.qi .ing stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stai: //xfjzbhh .9.q lvly the same? Explain.

Two spheres look identical and have the same mass. However, one is hoh6 a s 1/4aem 5z*tly;(kdaaewllow and the other is solid. Describe aaldaa1shwzteky;4 5(/m e *6an experiment to determine which is which.

The angular velocity of a wheel rotating5; 8rnf6sazz q 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 thrqzf5 z;68ansis 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 rotac:p +eqza yc.j k5xfu(v1vm72 ting turntable. What happens if you walk toward the center?vp( qc:.kf2a+vu1j m5exz 7cy

A shortstop may leap into the air to catch a ball andcfdk jbs1k;; 2 throw it quickly. As he throws the ball, the upkkf ; cbs21;djper 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). Explain.

On the basis of the law of conservation of angu xda8q)0mupk -i. wwn1lar momentum, discuss why a helicopter must have more thanwp8u dika)qn 1wm0.-x one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (k,i 5x; rqktg2a) 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. Cs7m5e 8wswenu) 33tyaalculate, using the information inside the Front Cover, the angular diameters (in radians) of the ta w)me537 3wnsus8ey Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at x5vi:2eor;wm the Moon, 380,000 km from Earth. The beam diverges at an ari2w x:m5 ;eovngle $\theta$ (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 m- l*i 8a.uuagaotor is turned o* aa-.lu8 iguaff during 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 levelo ak y8:fe67 nrq*d5tx floor 3.5 m to another child. If the ball makes 15.0 revolution:*oqder7xfa6ty 5nk 8s, what is its diameter?    m

  A bicycle with tires 68 cm in diameter trav(lvm94i we(kj els 8.0 km. How many revolutions do thew(jml(e 9ki4 v wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotatrex+c:2izjz *es at 2500 rpm. Calculate its angular veloci*:crz +2ejizx ty 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-r1 c62f3 nzw+ e1:awswq+lqmwqound makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seasq c1qqm+w wen:l wwz1af32+6 ted 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 orbit around the)8ptp r)8t lw:tc/ puv Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a f+z,b y7zfs9e 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 particle.. 1i nyfcili gb7.-fe 7.0 cm from the axis of rotation is to experience an accelgi.fe .iyinfc7.b 1 -leration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly 8 1np wg*rrn(iabout its center from 130 rpm to 280 rpm in 4.0 pwr(nr 1 n*gi8s. 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 radiu.y 5 lfm/trfdd9)1hpm2rpm/os $R_1$ 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 Mojs5nln9h( x: pon, astronauts aboard the Apollo spacecraft put themselves into(nj:s5h9nx l p a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 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 5vk+y;he3kh 8p,e wf8tnf bb w.(mn9k uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did iteh+.p(9 k ,e tn5bfn8y b kw38m;khvfw turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcul.0e9kfnrh jb zt49 zkx5.s6a dflq 2l:ate
(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 hipm q7r7 oor wl,3sl6.xghspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its fxr orlq6o3 w7s7.ml p,inal 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 b/dey3get 6 bt6,w/mouniformly from 240 rpm to 360 rpm in 6.5 s. How f6/o 6/d3g,bwbt mtyeear will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when i tak nsq66bxff,6 tysh5 s4q::t is running at 850rev/min It turns 1500 revolutions before it comes to a stoq as:b: 64yt,f5xss 6t6qhkfnp.
(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 auyqs gbrp*pd.) gu7* 2s the car reduces its speed uniformly from 95km/h to 45km/h The tires havg)ppb*2u qugy s7r.d*e 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 m(:)od juc -ann (dzgw(ake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The (odjngd -)n(auwc :z( tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all h3 (w4yonps1kq er weight on each pedal when climbing a hill. The p4kp q(y3o1nsw edals 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 ty,(n 1vvt d7 0uyw( )dbgd6rgdhe end of a door 74 cm wide. What is the magni76r (g nb0y1u,)d wdgvvdyd(ttude of 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 wheeliq 8r2ztisdo;:*s y p*h)tr. gru6,pa shown in Fig. 8–39. Assume that a friction torque of 0.4 urdoh);aytt8isgr .s2 6*rq *i,:pzp$m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod whihe.ie:o plj r+:;uk pmfq 0,-cch pivots as shown in Fig. 8–40. ujcprmef+ .:e0h; opl k,-: iqInitially the rod is held 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 reqm39ltzvxk; zqz0h nj *z3 jx:-uire tightening to a torque of 38 zj:zmk- 0qn3*tzjhx3 ; l vz9x$m \cdot N$ 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 when the aazi8 so 2t(/ab7dl4q8j lnb4exis of rotation is thrnd qt84izbb 2l7/o 4jle8as(a ough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 a9 . gfw-eghd-cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of- hf. ae-gd9gw the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, liz*5opfqgf o0b k *bm;/ght rod is rotated in a horizontal circle ;o5p ogq/f*mbf z*k0bof radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angula lrfe1-9 u4fdg;unsfj8 * p7jj6f2zjz r speed (Fig. 8–42)-uf 4jjgj8lsj6e1z *r fu2ffdp97z;n. 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 ig)y3va f7ur9zrbl1d0jjxa 2* j4c sh1n Fig. 8–43 aboutyhbag)ljxr 72 d3 c1 f41zujrv*js09a
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total masov9uf7gqw n s:qi cxs0-9j.f5s 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 cylindrifbj ;6tz1y rd* y:/tkfcal 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 steady force of each rocket if the satellite is to t b d *f:fky6rj/;yz1treach 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 wg1hdd 4 87zhiand a mass of 0.580 kg. iwghzh8d4d1 7 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 ba gztew-j9t lm 4+5cw3gt, accelerating 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-driven merry-gp*b69s1ro 3hkcl lco6 o-round and is able to accc9o3k6bolch p1l rs* 6elerate 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 produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatingoysy7+ l6p qa-xtuuk 693af(w at 10,300 rpm is shut off and is eventually brought u6a 3uqkt+y wu- yo6lps9a7(f xniformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8 z hc7*ri2aeuy ;o83 +gs7lu4lmpu a:n–45 accelerates 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 sj n a)x9cbsuf2queg;2 egpq2xn0o ,58olely 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 accelerated uniformly fr5 fe2qegn2u9 g0cxjq su2p;xnao b)8 ,om 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 ;a*vdm47 gz hir+xwy. can be considered a long thin rod, as shown in Fig. 8–46.vg+x7 m d4i*h;ra. yzw
(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 masses, yn*y(j,;5 lappwkfj )62jv ql$m_1$ 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 1-os:8n fw1m9cnurk g hammer from rest within four full turns (revolutions) and releases it at a spe1mu8n-gsk 9o r1n :wcfed 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 mom kc onxnsr88;z2(q a2eent of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque ofyf8fme0t4hkbp v9pqol4+-x +u qt-u 9 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and.9d i7mf1 akjv radius 9.0 cm rolls without slipping down a lane9vkdia1. 7 jmf at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eart e6i9wve hkae- (d*ri0h with respect to the Sun as the sum of two t9e(a*ew riiev0 -k h6derms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How mut,h6g2lx 2*glm7 m larch 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 llar ,t2x mml 6g72*ghsolid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from resto.yypi):1ep ;8 jp1eot* jyln and rolls without slipping down a 30.081y e j)jty:*ip;.1plepoyno $^{\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 balak7ru9amslb 76v.y cx*nced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the g97r v usbayc* .k67lxmround? [Hint: Use conservation of energy.]    $m/s$

  What is the angular my5hfaj j vt.co367oq0(ka4o tomentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angjyq ta 36k(fa4 0j7 c5.vohootular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cy r3*ud6g3hc ollindrical grinding wheel of radius 18 cm when rotating at 1500 rpm?g63 dulr3ho*c    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on nkz: u fq hh,9soz+r,t8r*se2a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal po2e*:t,uqh,h9 z8+k nz frros ssition, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her mogb* +jdawz*xcib*: -r.w 1lxa ment of inertia by a factor of about 3.5 when changing from the straight position tojww+:lc *gb xi- a1*b r*ax.zd 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 l1.qwjnco / :xeaynx 6z 5m7;ther spin rotation rate from an initial rate of 1.0 on/ :a6jxnw5 e1y q ;mztl.7cxrev every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating 5lakob j9 wt3.around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.9aj.l 3ow t5bk40 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 momen3l(mm)gl - c/iatj *o;esd 5kftum 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 momentum of the re+f77pq9cg e u -nb7wEarth
(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 mom5,kfd /llvoqvxq42 +rent of inertia I is dropped onto an identical disk v/r kd xlfl24q,5o+v qrotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsh+ h xl2 sh;a2 kc8)/8wws*a4lxfh2qud-d fww at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merrh0 tpho -0 ixjj0rqn n*kl1 s,uu kqv,5dde4;/y-go-round platform of radius 3. id0q,luh;-p,ut0 no*x5 4jsv k/qrn0e j 1kdh0 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-roie/ dyt3fxe,- und is rotating freely with an angular velocity of 0.8 e d,3it/eyf-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 into a white dwarf, *8+mzpa*v91gapwqm5 -p*ik gcqc :shlosing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(roa*vcgp 5p wcm m+- *gp*8:z9a1 iqhqksund 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 , b37b bi*ujqewinds in 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 dhy4, i1 uqgh3$ 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 fru mccc 4 p-v;o3sde po3a;b2,ueely without friction. The moment of inertia of the perso3;2peo3;- c bodcu, uc4mspavn 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 8q) zaif5/da ustands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frict uia/fz)5d8q aionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on noxt(7 wx l/s.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. Wh l.( ntxw7sox/at length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such tu 1p:zqe:vdvh 6y.:vk hat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In t k yv::6vv.eu d1qhzp:he latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from resb y pid3hng8kwp3:j/h a lcd0r2(:3lnt at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylin9dq(t8 g9lno ffklmru + j )/wyg-at:8der of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular agmdf uft gn+ty8 -q98j/:lrl(a9kwo)cceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made o3tn,zzw(,l qxsz 78 xcf two solid cylindrical 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 diameten(cz,3 zzs,xx8 l qw7tr 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of tbs:kohdsi*xp6s 1, u: w)zc4kx79gg 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 of our Sun, but with j4 9 3dm :fi0n7ttla: xxj;yjtmass 8.0 times as great, were rotating at a speed of 1.0 9:itdyjlmj 0t3 tf;xn4 x:a7 jrevolution 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 automobile is for it to use energy stored2thz a4k5fx 5y in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheh 4fakzy 2t5x5el “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 2t75f.d*l ycfa r20i+ho fkhd0bct+i$H_2O$ 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 (hoopeds45l5q0qd e j8s ni9) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (v:z.h :se;h4oekbm ;i i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held hor;izb.4hv;e :hes ko:m izontally 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 ; 8(thu fyk.rqu4lt t;R. 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). l8f;.ukr tu hq tt(y;4The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road igkonz2f) 1: axs making a turn with a radius The forces acting on the:axf 1 z)2gnko 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 s n 3ax74l8px5fcas hz6w5m(fnling of length 1.5 m and begins 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 does t6sp7mxxnancf43z w5la8( 5 fhhe torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder lg.so59q*6v t9kgupfand her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratigq* so g995tukfvp.l 6o of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutk/1 yzr1yyvg0 ch assembly which consists of two cylindrical plates, of mass yrzyk 1 /01ygv$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rouf4l*) +d:2bifwa u qipgh 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? Assu +ifqui: da2b lfw*)4pme $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not ddk ) .8w,ubnjs/ xd7r;8k .ywz1wugpassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unbo ls9ez d,w+;iformly from 90km/h to 60km/h The tires have a diab9s l;+zedw o,meter 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