A bicycle odometer (which ik 0u*;z f5 z0lc(znwwmeasures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bi z*wnwicul0zf5z ;0k( cycle with 24-inch wheels?

Suppose a disk rotates at c4*mv lkavw,ysi m j0i5sk)0oq (ks9v1onstant angular velocity. Does a point on the rim have radias,mow ak*0vi 95l0k4 y1)s m(vjvkisql 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 magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular veloci fc1 /ttoe,mtq7lrx.8ty $\omega$ Explain.

Can a small force ever exert aj04.ei kq d/ia 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 sit-up with your handhh,;m: 4f2 55fj h/oifd celsg3e o5qps behind your head than when your arms are stretched out pi3ffhdh/ m,fh55 eoo5q lj2es4;:gcin front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockegv1.hov4vt+h- by( qo ts 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 sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front (v-h ov v1obg4+.thyqsprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with f)u zh qw itw4yfb 682d8tuvz;k(xr *(plesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageyv(r8 *pfw84u6;2xbtz( ukztdhi) w qous.

Why do tightrope walkers (Fig. 8–35) carry a long, nar /uhsyfc1b4dw9y yr,- row beam?

If the net force on a system is zero, is the net9dx c51z;9r7 nnm:l4nwlcmz k torque also zero? If the net torque on a syxmkc nl 7r4z 5m :l;ncd9n9zw1stem is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontaiv*rr 5yt:0wdbk2-dm4b -k 6sr8 ovejl. The same steel ball is rolled down each incline.em 4ydk kvdrb:r 8s*6v0b-rto 2-5iw j On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously xd pgk- xfv s;bgzn*6;tj 14e-start rolling (from rest) down an incline. One sphere has twice the 6g;s-dt ze ;xn-kpxg fb 1v4j*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 the bottom?

A sphere and a cylinder have the same bhpxdo+ (bm k*8 xv:d5zvl *p0radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater*m0z vk:b*v p( x5lh d+p8oxdb 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 angular momentum are conserved. Yet mod;17rye*1we3s x:tgz zat4h 5p nwfk3st moving or rotating objects eventually slow down and st53sx gzw*red17tpkta hn 4 :e1w3y;zfop. Explain.

If there were a great migration of people toward the Earth’s equator, hohx u c1kb;6a.u yc*t.ifa7m rm vo),d4w would this affect the length of thdcf; cayrok7,)uv *mi ma6bu.14.t xhe day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotation eu +aprs:(c xjg+,o:a9kh,k kwsxk:p (go ku: +,c+9ke,ah jrahen she leaves the board?

The moment of inertia of a rotating soli8t l*vo xby6/ )x8b:d;-yo )udphw uttd disk about an axis through its center of* b) wpt-d)/oubt6:8ud8l txoyhvxy; mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding aibz2 9v 5olzx 1ecjk(- 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, orzb i v-k25oxz9(1el cj stay the same? Explain.

Two spheres look identical and have the same mass.; bg gxr6jew )7va-q4q However, one is hollow and the other is solid. Describe an experiment to gvq 46 xwj-be qgar;7)determine which is which.

The angular velocity of a we72 r9e nc)dnnhj 45rbheel rotating on a horizontal axle points west. In what direction is the linear velocity of a po n)n7 9brerj25ne4dch int 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. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a la )lfb:i;an(0tx g0q ikrge freely rotating turntable. What happens if gin0 x iktlf(0 q:ab;)you walk toward the center?

A shortstop may leap into the air to catch a ball and thrve8 iv yan0k2:sa har0z:f6mps +3ge)ow it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and lefzkm rny2a:8e h )a0 +6:3 vse0vagispgs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of cox 7 mvqmeqpr (wm6;ddsw- wudry6u5 t+(55o4tnservation of angular momentum, discuss why a helicopteo r m wt4mpw5uytmxrs-5+7uwd ( qe(d6vdq;56r must have more than 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: (a) 30 xicap a7 fi hbjpma- 2t/02y:4$^{\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 Earth1 -1genjyh7r;vfoh+iy* l mm h :j4w+u because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (hho fiy1w gujj-y:+nr he1vl7 *m;+4m in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km fo34wmvet(uzl9b6 q2v rom Earth. The beam diverges at 2uvbm63 9(qovzl4wetan angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When thftkw.zxun/ ) q v(zzcl2.yj28e motor is turned off during operation, the blades slow to res )(vq/x z2f2ln.uc k.zyjt8 wzt in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makes c0qg2z;ky qd2d /- haxw.v q:r15.0 revolutions, what is its diaqr;qxy hkqc2:dv. /zgd-0w a2meter?    m

  A bicycle with tires 68 cm in diameteren r-7-hhncig tl/j5/ travels 8.0 km. How many revolutions do the wheelj- h7rh- i/g5/tclnne s make?    $rev$

  (a) A grinding wheel 0.35 m in diameter r+c mnh8e2 (nzx) 3wzicotates at 2500 rpm. Calculate its angular velocitycexhnnc8 (+i2z)wzm 3 in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig.7oe 7t k(z.twf 8–38). (a) What is the linear speed of a child seat( fwktotz7.7e ed 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 sg m2v 8tpr20urqu5l13)dfr n its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a p7f.i-ubzo)yv fz cp2(e 7gle2 oint
(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 7.0 cm from thwdw,2 kg8 s5p9 u-jwkue axis of rotation is to experk9,w25 w8us kgp djwu-ience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly 3xys 2knflo(1 about its center from 130 rpm to 280 rpm in 4.0 s3(yk sfxnl o21. 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 radiucft(2 cha5i a3sqt85c v t96vhs $R_1$ 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 Apoldf5yn(js, h: znh ,2gdlo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from noyh dd2jfn:,(s nz5h ,g 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 1k)4 rn26rzgyt 5,000 rpm in 220 s. Through how many revolutir4z2 gkt6y r)nons did it turn in this time?    $rev$

  An automobile engine slows down from 4507g1 igt6 5kp x1pjv0kt0 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresueqyvd 7 px01j*0r+jjses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its+jx0u qv rj10*ej7dyp 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 49si201 il ,tdorlhozrpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in iois0l r1,9td42 lzohthis time?    m

  A cooling fan is turned off when it is running at 850rev/min It 5n igif6c0s7a turns 1500 revolutions before it ca6c f07si5n igomes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces it) s*(iz3) c t muvezd;pt*io. 3bvfah.s speed uniformly fr ii3.3o t; uvbmdc ha)*z.)t* pvf(szeom 95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutiote)9 fig/dg5n ns as the car reduces its speed uniformly from 95km/h to 45km/h i)9 /d5efngtg 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 all her weight on each peskp 66gc 8w hkjsp*8x6q s-4ctdal when climbing a hill. The peda8 gw -*ps4sh8qtkx6jk6ps cc6ls 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. Wha3c5i lu oadz8 (xaps3 z.;5l6l( vvqqjt is the magnitu35v ( sod5az836aluj;qz lpil. cxqv(de 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 wheel shown in Fig. 8–39. Assu-n(w me: bgq:qme that a friction torque ofe b qq-w:n(gm: 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m,n5o.-+-wzrdrjxak6 : 1gg8bl qzu:ej are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and dirxjl-e6-8aznk 5+o dw:b gu j:grzrq1 .ection of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torqueotcn., l;sx ;eiw jy94 of 38 c ,iyn wt;j9.xels4o;$m \cdot N$ 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 ofnfi54ja 0i/bgio hk+69 r/inx a 10.8-kg sphere of radius 0.648 m when the axis of rotationn i /5 h x9b/jki4n6iargof0i+ is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a aikdir0wc:02 s5 r7mnbicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass7rand mi:5w 020cskir of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light 4pz-8r,b9rv b ykatg5f3+wa arod is rotated in a horizontal circle of radius 1.2 m. Calcu 48r z+rapwbfb3 -g,ty aak5v9late
(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 constbg6 :5(bwhi g- ttv ;oda+fom8ant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 vfh( a tg6 5m-t ;w+obogb:id8N 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 t+le 4ykd clba-dra.;9he array of point objects shown in Fig. 8–43 +alcak.l -;dy9 be4rdabout
(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 ato04fet-mx bje.ms 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 saten1fnb ;db be zzo/)*l0llite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has bf1 nnl0zzo d/ebb);* 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 iusqyj p on48d3 u u*(cudde7lo/2p 35a uniform cylinder with a radius of 8.50 cm and a mass of 0.2 ju5qo oiu4ndle38/pspud (3uyd*7 c580 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accel3605fcxhymu a erating 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 on6z2xdf wp4 6q 7 j+qv2iogwzad w)4eo: a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting 6wdodp2oe )6 fqjz+g:q7 i4z4a wxv2wfrictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpqj1c 0pr 6h mu6el jv-8ycd(o,m is shut off and is eventually brought uniformly to rest by a frictional torquermv pe 1yhq (l-juj 6o6d8cc,0 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 accel(a:v (caas0aysg,8f h erates 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 solely by the ak45nyqq6 tyj5a-y-w9y - ue-wirxd66clv n m8ction of the forearm, which rotates about t6l- k-6eq-6t uanywix4yq9jwdrv8 5m-y5c n yhe elbow joint under the action of the triceps 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 thin rod*,8mmc* dg ,yp0g* vg0bxkgoo, as shown in Fig. 8–46.* *xk, 8 dvggbg0,co*pmog0my
(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(yk0y md3vx eyy7)dn;, $m_1$ 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 thed:2qhrx(ihjh+9 0b xk hammer from rest within four full turns (revolutions) and releases it at a speehd:+0xh(r b9qi2k xj hd 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 o-woc d(b w2dmi3.dhdx8 50qmvs *s,mnf $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a eqw,e4;ii y.(,p ae+ pklmvd1 torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipp qv9a(pl7g+s lh/+z abing down a lane at7a/apgl9lzvb(q s+ +h 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth rz ajlh:9 ek9sd3z73l /(cubywith respect to the Sun as the sum of two t da9s: z rllc(ek7j39z3buyh/erms,
(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 .rgh4(tjmpeg /ko 3kkki )vej.d2 /6y of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.0kekk3h.rvtg2 (d ge4/. /6j jypk)iom0 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.808k3*w5 oi3zyo m- xk/tkzl0a+ltg5kf kg starts from rest and rolls without slipping down ayog 8-k5/k iaklt+ mzklf05z x*3tw3o 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 ontqvb;-z 1 mk9:y o/amw its tip. It starts to fall and its lower end does not s- kyv;/9qo :abtwzm 1mlip. What 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 ball rotating on ti3vm.8 qu5 g*rdol4z ihe end of a thin string in a circle of radius 1.10.izi g4358*udv mqlor m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheelf7ox i ,0x3fpq of radius 18 cm when rotatingoq0if,7 xp3fx at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a,mr(h xbo4 kxq;fzu1+ytdr4757v *pqkqfn+x rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the mk+u 5pvq qd*4qf7z x(xo;4 r,7kbynfr+ tx1hspeed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the9wbxgu*dcl7 (-cw8gz one shown in Fig. 8–29) 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 in the tu cl-g* wz8cwu9d(xbg 7ck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotazpqc l8;g8m,k ycst ,.tion rate from an initial rate of 1.0 rev every 2.0 s to a final ratezkctl,,8 cy;.p8 mg sq 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 ve8rjlxx75n: :az0nb lbmwv 9 n6rtical 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 chua5nmbwzb j::7nx80 nvlrl 96 xnk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of ao3-+ os qdxuov c-1 keichm+;( 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 ond,rwjtfh l7p9 mqg///ks a64f 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 dil xh2x n:4ng/g bej8jema-;77ry c)rosk of moment of inertia I is dropped onto an identical disk rotating at angular speed r lha:b)joxj8rn/x ;yeecm-7gn47g 2$\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 29g z*/jy9 nchdcaqo 4:.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 st ci72. bg4q0.ejexyqqands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inert2.qx ye0q .47beq cigjia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an ang+n l6.qwtkw it p6i+unp9,0glular velocity of 0.8,+uw tp. 6it kiwpg+n9nll6 0q $rad/s$ 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 collapsesv-t14tq)s ; pg2i bhsu into a white dwarf, losing about half its mass in the process, and winding up withipb;s-qu)t ht v12 gs4 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 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 excesscgnpgn.l:gdbw.5*yd /-w5 8 y nosxy( 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 8l+ udd e(sw,o$ 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, j un0eu490hbh initially at rest, that can rotate freely without friction. The moment of inertia of the 49hn0u0 ejubhperson 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 edge of a 6.5-m diameter merry-go-round tuw:/a9 s selb6qrntable that is mounted on frictib9w e /:s6salqonless 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 grounm8 6;sp7a p3o2 a1axtnthiud 3d with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 1236 hnd;7a8su atm3xap iot p8–50. 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 ck0falvwprws)660 x w8h ip7*k5tc 4p side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) 6pap*0tc0 f)pci hxw7r l8kw 54v6k swto 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 .k4p3h* 3wzu4m dciburate 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 cylindh jxb,;h:,t4vl4jwxp.m jxwp)o os (.er of radius 0.20 m acquires a rotational rate of from re,4mh,:jp)xp;to wl v. sx.o(4jhbwx j st over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two soli r )2mggsr+3dud 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 calculate thesrrm +)ud3g2g 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 theeu l2b vmx5t68 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 xn ),e) t;3dezu*yfqm 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momenm) f *duq,n;yzt )3eextum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to u8oa4f org :(rqse energy stored 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 8:argqo(fo4 rable 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 a,:ne3 yynu6xy ri; lu-n $H_2O$ 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 hyx)6 4 x z+mzdx *eolfp-)lsi)orizontal 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 fr-jt4 i7js. a) 6qeguwweely (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 aqj-s47.ateg)ww i6 u jcts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standine2efq cw1z*9g g vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a wefc1z*92e qg step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with spybq2te f0h4-kqa2lov:8ob-iwq *w .l eed v=4.2m/s on a flat road is making a turn with a radiusq bq2:vwa2yib0hf olo*-- .t8w eklq4 The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0. )y afm1ciu8.jod01d2q8myji50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required iy2. myj0ao muq dc1f i8d1)8jto achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods:rbsx/;-k uqe, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body./:;q-rksbx ue   

  You are designing a clutch assembly which consists of two cylindrical plates, /ryxym4r8d t /of mast/8/ rym4xryd s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 an0i wbm,-y r,cgd radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble mwr-0, by,mg ciust drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumrn+ -iq02uqij4 (qzh7*os phb e $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car re*8oeop c8jb7tduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0ep*to8 jc o87b.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