A bicycle odometer (which meaws2ulb2c.ylqa5i r+ gh67 3lqsures distance traveled) is attached near the wheel hub and is design2.6gl qbri7w25u ay+hq clsl3 ed for 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 a point ojl6- 5mh fa:gtbr at-8n the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential accelltfh-5jta: 6- rga8 bmeration? 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 ang-ho,/ k*:0 oe tcncpvzum sd/(ular velocity $\omega$ Explain.

Can a small force ever exert alzgt6: d8s lkm4*f f*k greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sij8c:m. x m*gyat-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help yomygcmj a8x:* .u to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three atjc5.u35 he uocckd706j 4plgm the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprockeg p3jcdhkcj5u. 6u eo70 cm54lt? 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 faskcuc9u l;y 4:,2 fzmpet have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the bay, empc4fuk2c;:zl9 u sis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) crvvc0 hd4m9b1yz 3ji4arry a long, narrow beam?

If the net force on a system is zero, is the net torque also zerelz r)yr)bj, -/(9fymidlf 0ho? If the net torque on a system is zero, is the nel) 9j-bf,eh(i/yz)0 rmrfdly t force zero?

Two inclines have the same height but make different angl k.qwp ( f2e1mtoyb5w*es with the horizontal. The same steel ball is ro5 ytoq1pw* (febmw2. klled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) dfmk+1/rvxq + zown an incline. One sphere has twice the radius axqk1rmv +f/z+ nd 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 themd4tgn3pd +nic6qdy6*1h w , c same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which3+,dqdhcg6 c dt1m n4* inwy6p has the greater rotational KE?

We claim that momentum and anqw;+czb4gl4m ljui 1;gular momentum are conserved. Yet most moving or rotating objects eventually slow down anj+wm gc44 ;qubzl1i l;d stop. Explain.

If there were a great migration of people toward the Earth’s equator, how woulea cco+mp ueea6o3q;*uf:/6ng00tz id this affect the length ofp g;tm:cee0*f6qiou/36 anz c0uo+a e the day?

Can the diver of Fig. 8–29 do a someil+ee) py 7 (tiaowf+)rsault without having any initial rotation when she leavesw +ol(ei7f)te)+piy a the board?

The moment of inertia of a rotating solid disk about an axis through its8i61e x+csdd0va zww9+pkc 4b center of mevw8 6+9cd4k0xwszi1+ cbp daass 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 holdigwlepphjg4t0p ..q 8lrp40m1ng a 2-kg mass in each outstretchedwq84rmp 4p.1.pt0pe jghl 0l g 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, odd(5u /zt0dc 3i q6kgyne is hollow and the other is solid. Describe an experiment to determine which isgik d50t6(cu3yq zdd/ which.

The angular velocity of a wheel rotating on a horizontal axle poiam14b,lcu oh ,h:;f ivnts 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 at the top of the wheel.l1ivh:a,f;o , hu4bcm Is the angular speed increasing or decreasing?

Suppose you are standing on the edge oflcm(/ync9tv;9iy-+odk zqqz5( d7dz a large freely rotating turntable. What happens if you walk toward the cm i(+7 5ztovddyk;- zqc/9 yq9cn zd(lenter?

A shortstop may leap into t y*qtt )a-ex3khe air to catch a ball and throw it quickly. As he throws the ball, the* aq)3y et-kxt 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). Explain.

On the basis of the law of conservation of angular momentum, discuss why a hel ifq5(5)jtl vjicopter must have more than one rotor (or propeifj 5)5(tq jvlller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radzv42t,gg q9h k:kl bm;req6o/ians: (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, uzm.kygg2a4 aa ,c5fb)9wf1ve 1ax z6 1uhac4 zsing the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on yb19 6hfkefg4 a z.z1 5am, xa4ca)az21cgvwuEarth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. hkb/dsw-*z/pc3+h jy9q3iy9f gt+ks The beam diverges at an anglegs s-c3kt 3 p j++/9ih9wb/ *dkqyhyzf $\theta$ (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**reczcb 5v *j the motor is turned off duringe5v z*b *r*jcc 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 mc- +e;8ozh bnw.:mbs3 t fw3qj to another child. If the ball makes 15.0 revolutions, wha -3nmb z8e.wqhco tj:3bw;+ fst is its diameter?    m

  A bicycle with tires 68 cm in diamet,w/ sgfy * fw0wno)j/v7-hjc jer travels 8.0 km. How many revolutions do thyj7f s )jgnwvw0c/*,-h/j ow fe wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rtabc2p/:r/tlf kl6xm h5vs35otates at 2500 rpm. Calculate its angular velfvsbk5l6//2l:ctp xth53rm a ocity 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-roukz;ekqro:5 df (ssc9- nd makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the centesdorz: (ec;9f k -s5qkr?    $m/s$
(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 arh4l xfyxru.mgo3/ :;2sn /gubound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a r6sp59vcf uwjaf)/ x*8tllbs4c: hd1 .nkth 8point
(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 apzre1j ,1us0y centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,000 ps1zej 10ur,y$g’s$?    $rpm$

  A 70-cm-diameter wheel ac8xh ul2d. wc9hcelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determi ld2c89wh.xuh ne
(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 ns;-4y rzc0m0z;jjign dee7y8* n+ d s$R_1$ 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, astra4tf */ plds6 :ye-,0nvedmm 6ph h2xjonauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated fromm /d :axv6he,eh4 td2j6py0 -*fl npms 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 ur g7 0(;ggscvpjm9dj2* 6hyc2,dvez. Through how many revolutions 9(z 2e*7m6gj ,gjpvsydvu0 r ghcc;2ddid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm 7m0 .v) fc (gcnzyu9kqon(9cl 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 sbb3 -2n e- 8qi;9 mp9q)4m8huek q* mgtmijomxtresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.iqn8 eoqkm; -mbpb j- t93eu4mm)9xih8 mgq2*0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diam 3nmj* our- 3ayawa5s,eter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a pos o3 y,aa53mr- jau*nwint on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns ca:5jg q6e4vt1500 revolutions before it coc5 gj :6eq4tvames 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 redj *v9 u3qxm,gguces its speed uniformly from 95km/h to 45km/h The tires have a m *9qux,jgvg3diameter 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 mak4 s yils 6u0/3wymlc)o+yqzmmi- 3ek9e 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km3q64 ks0 yecw3l)sz9-ymmuo+i i /ly m/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts a-tx+g6d l/u qqll her weight on each pedal when climbing a hill. The pedals rotate in a circu x+-g6q /qtdlle 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 fov xjss(jxhx2+2i c1/6s r8eqmrce of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque e86q( 1x j srimcxsx2h+/svj2if 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 ax7c:)xkn7 s.4t(prjao l8e tkfle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.a:f8)p(k7l o k e.jxc7sttnr44 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of ig5 s1gcztqkja2d9 j88 mqf-fb4kt-4 a massless rod which pivots as shown in Fig. f qtk-m14c25k89tjgi da-fj4sg 8bz q 8–40. Initially 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 require ti7pen4 t 28x oy bmkhi09o,c)agghtening to a torque of 38 bgmn kci)4928atoyex 7h0,op $m \cdot N$ 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 mg,f/(5a 6irbflefzy6i s 8x 68n.idwm when the axis of rot6f5iiae,6(b .yrflfw8xdi mz 8ng/6 sation is through its center.    $kg \cdot m^2$

  Calculate the moment ov 44fnhr (dq3ff inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of f4qnv3f4(drh1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of ndf-3p nxb, t:r 93smn4oap5ra thin, light rod is rotated in a horizontal circle of radius 1.2 m.ndmarxort 4pp3 b 5f, :9n3s-n 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 xhym jo(.o8stx-bf(9on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and t.9s -jt m xyohx8b((ofhe 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 arr3mn85xd/ady lqu/5vh r,+bkw ay of point objects shown in Fig. 8–43 aboutd vm5 y/ulr/xd n +3,hqa8wk5b
(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 to68 bwd0 tn1txatal 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 correct rateg-aj+p nic60 ,*cz qdd, 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 snpzdcd60 c+q -aij g*,teady 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 unz/ (v iavv(qokkl y8+6iform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculatez/ l yov8vk(iaq+k6v(
(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 frdimtm;ifnq28*q5 r6 excw7; aom 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 m:(t/f*b kxvr0 ;huqszerry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume thbxr: z(v fh;k tsu0q*/e 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 rotating at 10,300 rpm is shut off and is eventuallyt; ccz9b p/we bm8 rd77y;dkj7 brought uniformly to rest d j8mdwke rz;c7b pc7;y/tb79by 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. 8–4gz)p0vc 80-mi8wxa ratf2qx 05 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 solelyr32( t).t 1chyqp;n ij)qzxws 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 unifo ;pcirj .qq2)st(1zwxn)ht 3y rmly 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 thin rod)ue2e tui,m5y , as shown in Fig. 8–46.),ee uu2ymti 5
(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 4 lgnp:w:+ 0muhsy1zkpd *3guof two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turbe q9j4h1b q(hml/x( vns (revolutions) and releases it at a spl xhb 1q (bhvq(49/jemeed 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 r (ff5 m+xdm :tti1nbfyl/9,einertia 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 sdg k0 /ab-lfk:.ncd8x. *33 cwb hyaor6b1tcdevelops 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:0 lumu ui)ymm+5 jceln9iz*)- ;h ayp and radius 9.0 cm rolls without slipping down a lanel 0+ 9uy-izhy;*eumc min:5a)ulj)pm at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sunzc)mx b0gd9jg7: (; jxdb4t sllz:.b z)tpdv6 as the sum of two terms6bsd(:xmj07)j z9vttg l) ;4 pzd g.xbz cbld:,
(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 khs1/uu(qhn mq*d: n- 9xeqx 8 zqia8by8y/d4ag and a radius of 7.50 m. How much net work is required to accelery1 /:mn8*nu-/xhuq eh z dqa qasqxy(dbi4988ate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest) 82 u6p) ulf3yfm8x35xc9nmgnrvcb y and rolls without slippinn 5g6cncmu 2b3lf3m)ux9rvyx f8y 8p)g down a 30.0 $^{\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 it.lcz3+k)szs ds tip. It starts to fall and its lower end does not slip. What will be the spes.3dzzl+ sk)ced 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 0.210o 3l+ 0qvb21i /wfdenz-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speez0 bwqen+/ fld23iov1d of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uni-)vt8wsrf in pq-)* uz2omf yxtrp :-+form cylindrical grinding wheel of radius 18 cm when rotatimrffr+)- -):u2vn s- pyoxt8zqw*p itng 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,0a7zogibz8 s*a 2k-ug on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal bk807 2gs gz*iouza-aposition, 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)rd)p1 : kyvl)d can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when yvd lp kdr)1):in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can in 0hjumpee j.08 dx4u-pcrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final eu4pmhpde. j8 uxj0-0 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 fnh9xt j7 yb,2i 2aoq*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 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radiuaiy9n*qbf22h7ox j,ts 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figlr03 m* a./xpnzmzt*oure 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 -3ore nrsns p0e o e*tzq1b )x.2f24az-frbz9momentum 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 mo/(r3u8i5;tbyojtc * 9jam rt.:pbpm kment of inertia I is dropped onto an identica bt pko9r:/ tj85;rcaju3 .it pyb(mm*l disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2jea2t,c2: violcmf mot)n )p96xvu58 .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 merry-goud8-o7 hrrx3 b-round platform of radius 3.0 m and momentho3rxu-8r bd 7 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-gb +s6mxfg11 butzk/q.o-round is rotating freely with an angular velocity of 0.8 11 m.6/+bt zskgqfx bu$rad/s$ 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 comug (4sa6v bz*llapses 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 the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the neare sz64abu (gmv*st 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 12(8bwfghs u0,hgb; )hh0 $km/h$ 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 /ujxd0 7yg:tnxa0v2m $ 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 rj,) ws,a jh13ix36 wnyp,tl nwest, that can rotate freely without fsjp36x aw,)wjtw,i n3y nh1l,riction. 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 vyy z;h90)u6vkbt w x)at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a mom9 )bhzv ;x kyvw60uyt)ent 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 endbkg dj no-:8e* of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks8 g:jo*n bdk-e a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side altkyo ; kgi ms m(mb5x/*c6.mk8* v:eujways faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle 5s mkx;bom:ckuy/e8gmt 6 *iv.m*( kjorbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from respj .nqf+un1o / 1l7iust 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 cylindcaw+bqwk 8 40 eh:kf1ger 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 motor. fww+: 8gk e1ba4hqck0   $m \cdot N$

  (a) A yo-yo is made of two wp 8 xz07ff7hcsolid 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 diameter 0.010 m. Use conservation of energy to calcupc80h7 fzw7 xflate 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 tcq r9 v:0j7nzshe 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 mass 8.0 kko0/: weoxi nbtj )-va; (8yycjj 0*ztimes as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star iz /c 0-ek (w*tk0ovno8jabjyy);:xij s 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-pollutizpau89 8 ykqm4qf(vs ;4ed gk* a -ovqxbi3w)0on automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diamuw0o)8v* dmskgy4fe8-ai(za q3;kvq4qp 9x beter 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 illustratezoko i-cf3q / 17-r(c:zgxyabs an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a hor/)op ev2fysr/)l doc,izontal 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 leng5 arr fijmye( /2h:8oejp5s.mth L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shri2h /j:f jspmmo.a5 y(r8 ee5own. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing v 2 p7s6tu1uyblertically on the floor, and we want to exert a horizontal force F at its axle so that il7pu6t2 suy b1t will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s onr+c* zduoesrb n1)-:w a flat road is making a turn with a radius The forces acting on the cyclist and cycle are n+d- 1sz):r rweu*boc 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 beginsc+y8 k i:ncm;efj6 js, whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after8:f 6cek+ys,i c jjm;n 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 cylin :)(9osidusb(6sk dn tder and her arms as thin rods, making reasonable estimates for the dimensions. Then casut96s)( oikn: db(dslculate 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 assemb 9avqd*3z5m zp4lt)ialy which consists of two cylindrical plates, of mas mdiq53* p zz4a)9lavts $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radi.+zwg+8be n9yi ne rk3us r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of ew8 +rniybnzge.+ 3k9the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, b,2c0* g /jd+s onx5z vj3kmsequt do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as th,/z1kq b: jnate car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What w qbk:1 a,jtn/zas 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