A bicycle odometer (which measures distance t qu6i r 9qhd)vk:o/wd72 kyfj0raveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it ih)7r2qyj0f9d/u kq vd o6:kw on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular veloakwuc3/g+vufuee2 ;)lng69j city. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tal c k ;92jw6neeuugf+3/ u)gvangential 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 anh rng1svw f8)d9 ,+fkrgular velocity $\omega$ Explain.

Can a small force ever exert a greater t17x687ovcj)vl y z rf1cihv o:orque 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 hands behind your he kfgf.v0gq nyy5zj /sk-g3lf::1vxy 3ad than when your arms are stretched out in front of you? 5ffqxlvzyy3gkg jy0g: 3/:fnvs.1 k - A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three ati+mb5hzbav +/a 0 vur3 the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why+3 vr0m 5zabbvauhi+/? 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 leagcw 57dajew 7:+y jg)gs with flesh anda 5 c7)7jewg jdw+:agy muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow*hgjcgfw pi a68)atj (cd,/n yd-u; t) beam?

If the net force on a system is zero, is the ne 1gsx mh:)ys2nt torque also zero? If the net torqn)s2mshy xg:1 ue on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with..a*(c kkjy ox the horizontal. The same steel ball is rollx kk..a*o(jy ced down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultalqwqsu 1o)/4 rneously 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 glos q q/14w)urreater total kinetic energy at the bottom?

A sphere and a cylinder have the same radrtr1:. iqoed*rr xc9.p 3y0xi-heqb3 ius and the same mass. They start from rest at the top of an incline. Which reaches the botir3-r9re*h.y x.1e3xrp c: 0 idb oqqttom first? Which has the 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 angulige.g xh8;94w dwp f*v7t n+xzar momentum are conserved. Yet most moving or rotating of8 x+g ewg 4dxwvhi p.;9*nzt7bjects eventually slow down and stop. Explain.

If there were a great migration of people toz 3j;.e rroghl/f-2rj ward the Earth’s equator, how would this affect the le-g 3jl/efror2 ; .rhjzngth of the day?

Can the diver of Fig. 8–29 do a somersault without ha*lu 3 ksl2m6fme1qaw-ving any initial rotation when she leaves thal63 e fm-qswm2lk1*ue board?

The moment of inertia of a rotating solid disk about an axis through i7dcgo; wl3 d3dts center ogl 3dodc7;d3 wf 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 a1t wrnh, kl1k;v,rwdc.;ky2 on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will yo,,1vy 2r;wth dwn.k l c1rk;kaur angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is ho)co2l5 9 -sj2yzbp nczllow and the other is solid. Describe an experiment to determine which is whichso2)l592p yb- c zzcjn.

The angular velocity of a wheel rotating on j-kf 3t *lo2qajm;n (/btv 9: k*d)js9mplkoma horizontal axle points west. In what di;*m j2/ok- *j f ) ll j9m9q(:btknoasmtpv3kdrection 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. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a 9+ maloucnr-3n y d,;wlarge freely rotating turntable. What happens if you walk toward the ce,ul 3rwn+;n mcd-9a yonter?

A shortstop may leap into the air to catch a ball and throw -.uh-h e0ocucoo/g: +d pkj6hit quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite :+c0.oh ughuoe-6 -hojkp/ dc direction (Fig. 8–36). Explain.

On the basis of the law of conservation zb8/9aun n09m ai6gwlk0mqv*.ogr b(of angular momentum, discuss why a helicopter must have more than one rotormn9oabub0/w6i g(9 k0rql am.8zvg* n (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angludht2 m8qvakviv 5c1z5.zln so 96 /e2es in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coinciuf8 t62/ebpax cyt (qo*a (+gddence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, a q( c8xu/p(2 +batgy*e 6ofdtas seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 4;l;*h7p:jjq9zmbsux w.q -8d eoony380,000 km from Earth. The beam diverges at an angle -su:8q oxlywq one h7.4z* 9;d p;bjjm$\theta$ (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 ad)hh swz:n a2js*5 qhpxzr()7 rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acw5hs)7 xdashzr) j2 z:pnh q*(celeration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chm q 5bv.j::04xnhju+d*vvzdry 9pr;,ackm 7 cild. If the ball makes 15.05rqd4 v7 0c z9u:dn jv h caprx.,mb+:;*jvkmy revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions o, *obw ed dpkber075+1v+ucfdo the whe*1v+r0kco+bebwu f,e7 dd5 poels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter ro0a k3nxu, nwvt2 kpc89gu h4n1tates at 2500 rpm. Calculate its angular velocity ct2vknka uunpg 4w,n018 h93 xin $rad/s$ $\omega$ =    $rad/sec$
(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 ret 2eu,),mwhwrvolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m fruh )tww,2m, erom the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velh)f g5ie8)(z.lom zuwocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of y0j/1ufgfltu,1 d7x c a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm.-m5 p3j mtujq from the axis of rotation is to experience an acceleratpuq tm jm35.-jion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to ( uh6;jteri.y280 rpm in 4yhti6.ju(e ;r .0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius vwrj)iwr;2d z8.l4:5rvx 0dlgy9cm z $R_1$ 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 g umig9 :0c0 arnpa+mee4cmt;s )1 er*Moon, astronauts 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 from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft cacg)msce ri9ae:t ;r a04 upm*0m+g1en n 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 acceleraydwlc00dl y;-tes uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions ddw0c ld-yyl ;0id it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculae ,kimau :c-:hkj.(z-pys h n0te
(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 n rl o;8f.ee-(*gyaz.1fdcfg stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn th g*zf f-cd le81 fygor;.e(.anrough 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 diameter accelerates uniformly from 240 rpm to 360 rpm in eao:+1 frrewb+ q/ /qs((m wzs6.5 s. How far will a poirw req+/o(+ (q/wa 1 :sebsmzfnt on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it isu d +f7;zcbu,c running at 850rev/min It turns 1500 revolutions u,c; b+7cfzudbefore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces itsol7z-g r5q9e+ctevg 9 speed uniformly from 95k5re - v97e+ozcqgglt 9m/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 revolutions as the car reduces its speed uniformly,u(s+sj5h1i a hnho3xd.j0b r from 95km/h to 45km/h The tires have a diametx .bo i j ar1u(shhjh,d3ns5+0er 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:v5tz 2h+nci3 f kz-km puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle -n25htc +i mz :fvk3zkof 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 th2a shns0 2+4dk7 tktide end of a door 74 cm wide. What is the magnitude of the torque ttds4+2d02 nhiaks 7kif 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 k 2lh9blq4obngd (/-9 c(0ezme to3beshown in Fig. 8–39. Assume that a fricecet9 k-oble0g4m( b/ 39zdbqhl (o n2tion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a mass3uv dfp*f6k0ogv9n , z,4wyzh less 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 direction of the net torque o d*zz vg,403,pw6vn9fyuhkf on this system.

  The bolts on the cylinder head of an engine require tightening to a top;y fgm 5no/s)rque of 38)so gy/5m ;npf $m \cdot N$ 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 spc zg,*aht evo,ofe4:4here of radius 0.648 m when the axis of rotation is t4oo:,,cathz e *evg f4hrough its center.    $kg \cdot m^2$

  Calculate the moment of8ef4g)kum tm+ inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be)+ umf8gk 4emt ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontxt6r k/:f7 5cj4rideny 2er.lal4 re72 ei 5yrrdj 6clx/f.n:tk circle of 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 w( izn hga8(80yv.q wgpotter’s wheel rotating at constant angular speed (Fig. 8–42). The frictioh0(.qga(viw8wyn gz 8n 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 a-bt 6mnx f+i3ah3 mws0rray of point objects shown in Fig. 8–43 ab6f+mh03 xab-niwm3st out
(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 massjtuzed)r (b ,hjp:lx/ltybr*5 c/z6- 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 sat00sqaensw(z f1+ -q4fc+s yzmellite spinning at the correct rate, engineers fire four tangential rockets as shown in F1c s-a+0 f s wmzze+0qyq(4nsfig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.ie*b:s*c mtg/ lm;r 7v50 cm and a mass of 0.580 km brsm *:7c*it gv;el/g. 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, acceleratc)b5oo tz4i cztc3b) :ing 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 :. og6bl:7hu4 sqjmky 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 tukhs.:7o 6b:lj4mqgyo 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 eax1d *k vkw+,:gi5o52 ctugg/fh cpp;ventually brought uniformly to rest by a frictional t5p* p5x w+ o,ukiatk fggdccg/h:12;vorque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball g2dvve4 g5a7 dat 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-kwod2q qok ;+h8g ball is thrown solely 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 frd o+hqwk2q8; oom 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 bladets qms 89ml1m6 can be considered a long thin rod, as shown in Fig. 8–48t s mls1m96mq6.
(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 consh:rxjzpl x4 )1ists of 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 accelerahk6+5 vona. ly6k-osktes the hammer from rest within four full turns (revolutions) and releases it at ak as-kv6yolo 6h5nk .+ speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a m6g+y63euuf lhvtcfy*0 r -;s xoment 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 of 282buh1:pfso5(m ic; rf,sp wea/se + +j0 $m \cdot N$ 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 c8nx )6oo x -m lj3zb2k-j5xh2ve .uakvm rolls without slipping down a lane at 3.8x xk-o5h kz2n bu23e6 j.) oxjl-avmv3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eqxue d+ xl()m;d(sye1arth with respect to the Sun as the sum of two tx;dd1emu(l sx)( yq+ eerms,
(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 ;-8ejtu*rpx tmass of 1640 kg and a radius of 7.50 m. How much net work is required t ;te*8xtrjp-uo accelerate 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*ko2winw(c8zn04yx b and mass 1.80 kg starts from rest and rolls without slipybo2*8nw n w(0 kcix4zping 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 its tip. It starts to fall an4ps;3 .d kusdixxq+u. fl4gav h m;,woidb95)d its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground?b,au 9d.4ius )xp hv.g;dmk4l w;fqo5is3+ xd [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.2 qio)6ns9) cu m87f7s:d muqion ec(j210-kg ball rotating on the end of a thin st(uoqeqdn8i67usc2jis:9 mom c)n)f 7 ring in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wbl1wj ih97b4 m0r4xq e2crc s6heel of radius 18 cm when roth49 2bmrjiswx6b rl 7c041q ecating 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, om*ue zg) +d :eyvej3n.o0hat 7n a platform that is rotating at a rate of 1.3rev/s If he raises his arms totue+e.a ye*jg0oh3 z)n v7: dm a horizontal position, 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 F.56dps4 ; pjcnn :l x9lc n,tl:l)mohjig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck positml x:n9psp)c dnlo ,5ll4:6jntjh c.;ion. 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, a/c9soqb,oz her spin rotation rate from an initial rate of 1.0 rev every 2.0 bcq/9oz,, as os 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 around a vertical axis through ia+*i mehq/gi- ts center at a frequency of 1.5rev/s The wheel can be considem*h+ai-ig q/e red a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3;bh0vvyct6 2q3uru o;.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 E*6kn7+ 0ctsi e3ff,hwj u- bvaarth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertmwj*7 v ne3y ha7d-ew*ia I is dropped onto an identical disk rota-mwhyn j3 v 7ed7awe**ting at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns j umd)(bbrpkj1-7 35o2h z0nhvy0opaat 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 m: r .v6lfwz)heerry-go-round platform of radius 3.0 m and moment of r6ew.fzv)lh :inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is afz*p. -: x9.udul dowrotating freely with an angular velocity of 0auo-wd. d lfx9uz:*p..8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually coll. op *9ev;p *h;ssa l pqi*przzzr49(dapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. s4qid9.h; rp(zv lp*or;z*p*spe z 9aAssuming 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 excesyjn w9ohvj) dykbl 2z2lah:m5/,h0 2ds 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 b2j7.uxke2u etj+1s i $ 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 freely b ;eok hza:hic nj;5u6c 8/ux)without friction. The moment of inertia of the person plusnchi5 a6o u8zhjk:;;ueb )x/c 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 merrg dyn(zq2 kdpxjmy,jo-o ce,: e/: a/1y-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1700d-ze :/q1ox2ejympog a /cy(,ndkj:, $kg \cdot m^2$ 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 bo +v* s4me/ftthe end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move*+sfm /4vbeo t?

  The Moon orbits the Earth such that the same side always ( f,kz:q:xeocch8f0 i faces the Earth. Determine the ratio of the Moon’s0,k co:fe(fx zq :hi8c spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rat*pol5 oked -;q1b*wjae of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder ofpus4-5 mmg3vy/ry/d x radius 0.20 m acquires a rotational rate of from rest over a 6.0-s ivsymy4/prgmdx u5 3-/nterval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each oxc(l /o)bx5vedhb.t2: t4vwi f mass 0.050 kg and diameter 0.075 m, joined by a (co(:2v otw i4bx)hltecvb xd./5ncentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 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 anguluilm .wgh81k5e 5 pe crz:)m6rar speed of 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 mass 8.0 times as great, were rota:ygg: mi/qko ;km rph ple*019: fa0gcting 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 :k*:m0f ;go rqkep mhgl1p9a/y:g0 cibe? 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 automobile5c , vrep.wj7tvf be:4 is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass,5:bejv74v ewtp fcr. of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrateso.0+ 6mgx ktfu 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 8ukd-r2 tsx-b8lilf1aff0 d: /a ,/6 nwkudyya 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 Mo 7q1b k9n(./gwf9yj:1eok arcv z*oy and length 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 qy rg 1a99 wv. bzk/eynok:cf1*oj7(oof the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and (-hk1tj+alo4s2emz ra t(y- m we want to exert a horizontal fz+rh 2kttom-y(e ( l1s 4-aajmorce F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with 5qnbs-l.s bkx )5yuybe;52mn speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist uqs y b)e bl-ks.5n5mx5;by2 nand 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 rocjm:b 6*ijb+vd 6: scmok 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 to achieve this feat, and where does the torque come from6cjsm+:: *bjb vid6om?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin * 46/p4q4iu vygxe kxmrods, making reasonable estimu4x4pik*x 6yv/4m eg qates 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.   

  You are designing a clutch assembly which consists of 3exi7 6mup(tzi b:ji4two cylindrical plates, of mapitjx e76 bm4(3i: izuss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rollsd)li t/yowro*b31t z2-gtci 8 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 the loop yto)tic8rli-g1*tw2o b3 z /dwithout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not aygimklu ;2k ;vun0-z5 ssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as th q iy.vzgftv:-cu, 5n)e car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter o)zuiyc f-tvn,g:5 .q vf 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