A bicycle odometer (which measures distance traveled) is attached near 65zlf7r kkq3txgz1 qhv yoam319-pf(iev 4k *the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle kzt3olg(3p v a-*16hk 4ifkmze9 yf5 rx71qqvwith 24-inch wheels?

Suppose a disk rotates at constant angular velocity.5cg )2pmf tqarew4ra vn/:. +r 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 tangential acceleration? For which case/g) vcrr frp n.q:e4 wa25t+ams would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by i+, q4acarw 5 vg-myp,4kv:-+hke yisa single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a grea7q59 e2jiphu0) sekwater 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 oy.(u;1lh x;oub**uma /bx /ib;aqzi to do a sit-up with your hands behind your head than wheh/*1a ; ;q*.xyu(ubioxzm a/b o;iblu n your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel 0 *su j5fnch38uugf/tand three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprognu cs /uuj8 3t*ffh50cket? 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 3tbm 1t v6pidiulrm /k9m8 86cto run fast have slender lower legs with flesh and muscle concentrated high, close to the bo/6mmv mt18dl u93bp8itrik6 c dy (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) cmkmt hj): h1 fprz5) 9mdboc ;qyl n5-157lqxlarry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? Im3ppu2zuqc 6* xow/ pgh l(+m x:f3-unf the net torque on a system is zero, is the p2uu x x(o c3/+m-:p3 z*6 qhmngwflpunet force zero?

Two inclines have the same height but make differental w +90lu::a. kcijce angles with the horizontal. The same steel ball is rolled down each inkc0clja9+ ulewia.:: cline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres sim)4uyb91kjq. n li1vqn ultaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reac ).u qjnikn19lqyb14v hes 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 salxh plt(:.x 5l j(z(gjj7/i hlme radius and the 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 g j7.lhjxx(il:t( zgl lph/j (5reater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum44 rs epo94r dc8t +cqrnm+i6d are conserved. Yet most moving or rotating t mrc +4npr6sc+qo8ei44ddr 9 objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how xg u;xplxo47 )would this affect the leng;x g4uo)lpxx7th of the day?

Can the diver of Fig. 8–29 do h0*z(0y1y cfsvs itw7 a somersault without having any initial rotation whenss(fi v10*h0 tyyczw7 she leaves the board?

The moment of inertia of a rota hz49k ibx9nb2,o .jjiting solid disk about an axis through its center ohj.ozbb 49x ij9 i2kn,f 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 a 2-ksvupg 7kgzdi71y 21f/ g mass in each outstretched /s yz7p d12i7u1vfggkhand. 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, one is h. )+/fmgq ygc2zb b,jiollow and the other is solid.mi2c,f gyz .q+b )j/bg Describe an experiment to determine which is which.

The angular velocity of a wheel ro3g 9ihpj.:t ye 9exv6gtating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential e6.he39v jpggity: x 9linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are stan3 -4zmjs ou)kha0w9owding on the edge of a large freely rotating turntable. What happens if you walk toward us 4wojmkz-oa 0)9w 3hthe center?

A shortstop may leap intymca)qs( ljc)4 8ote; o the air to catch a ball and throw 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 legs rotate in the opposite direction (Fig. )cmc ley4 8ot(qsaj); 8–36). Explain.

On the basis of the law of conservation of angular momentum, discu1sza0v e:, lwhss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to zhv1a lew,0s :keep the helicopter stable.

  Express the following angles in akjdgf 5vkgm djf8+/3n/;mr;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 amazinggh x132i5 fgwc coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, g fg51hxci2w3 as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direcp jj49ezmsj, 2ammg3+ted at the Moon, 380,000 km from Earth. The beam diverges at an ang3smgm 9jzj ,mj42a+e ple $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotatj:rme , *g zj(xhgwu;5e at a rate of 6500 rpm. When the motor is turned off during operation,gj w ej(:mxzr ,h*gu5; 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 m to another child. If the ball es *)ang8 oo)kmakes 15.0 revoluti)oe k*sa)ogn 8ons, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How mt: pcarbn( (j7any revolutions do the wheels makn(: pt ja7rb(ce?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its 8 +w y+q*h *ryjof/. eam-snroangular velocity iy++ar *of s nyq*er 8jho/m.-wn $rad/s$ $\omega$ =    $rad/sec$
(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 41dgvg)m b. +x9yyp7b/os; pwu.0 s (Fig. 8–38). (a) What is the linear spee b/+ ms;1p )o yv7gxguw.dby9pd of a child seated 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 veloci74n*u 2g fnbsubmhp(0ty 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 a o* 89:gy g,w.n4qmsi :c 0xka/thng eapoint
(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 cenh;9kmg *lx 0agtrifuge rotate if a particle 7.0 cm from the axis of rotation is to experienc;90*g kghmla xe an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm tqsbkz x91ta8ve2y za86w3 kvg0*5w mgo 280 r gx zm2 w6te0va1*sb8 a vkg93wz5qk8ypm in 4.0 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 w0x(i ore/-1 +(ymm3j jzhh jleg8eo;$R_1$ 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 Apol6x80agemfjw6, 4fq . +fgs lpnlo 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 can be thought of as a cylinder with a diameter ofg. afn,m8fg+f w6ej0s q6px4 l 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 r 0o yob)k +:.8jybomhgyyb+bib05v7s. Through how many revolutions did it ty)o yg bk mry78b.50b0: hovoi+ybjb+ urn in this time?    $rev$

  An automobile engine slows down from/x f hweqyn4o aq7;9flma518 o 4500 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 stresses of flying highspeed jets in a whirliba4(va4rj n9p:imx 9oz+lg;t ng “human centrifuge,” which takes 1.0 min to turn through 20 complete revol9+l(n;i tj 4mb9ov r:z4apax gutions 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 rpv1d s2l sf6l:rq d(cs,m in 6.5 s. How fdf1 sv:,r 2s qld(ls6car will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revolizqy;g / u(sm2utioqg/zs(;mi u 2yns before 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 it 3 j.f 4x.czqe8a;gdajs speed uniformly from 95km/h to axj q;f .3ac84egjzd. 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 revoluti;0;g,miu j/x. ligw otons as the car reduces its speed uniformly from 95km/h to 45k wlx; gt.i,jigom0 /;um/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 all her weight on each pbo.h 5fztuu3y 50 ;khfedal when climbing a hill. The pedals rotate in a circle of radius 17 cm. ht3.k;0zf5o uyu fbh5
(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 m hom01-lvbh( the end of a door 74 cm wide. What is the magnitude of the torque if the force is e (mh1h-l0vbom xerted
(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 axl2 a(5 x7 nl*qtbjfuw18rsztl/e of the wheel shown in Fig. 8–39. Assume that a friction torque of a*7b/sj8t l uxl(5f21rqwz nt0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends o,ep: wgl8zud tl6 ihcm;h(1y 5f 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 deh;5gyzu:, 6wcml8 l( h 1tpdiirection of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torquezs2, .5 ll(zvhr-oi 36hkfpyn of 38 yp2. zl ivlz35on6 s(r,f-hhk$m \cdot N$ 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 spherew( 0t8grkek.l of radius 0.648 m when the axis of rotge rkwl.k 80(tation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The ri(nbgo2 : *sdb elmyn4 pi8pl42m and tire have a combined op4 n2bmpndylbg(* i42l8s :e mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod i2g;a8mp ymaq6:2 yresm9 +kjjs rotated in a horizontal circle of radius 1.2 m. Calculat;kjm2aj qr8my: a+ 2mpy9esg6e
(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*.51cpsj + ib(ftnuuf wheel rotating at constant angular speed (Fig. 8–42). The bp jufcnt*.(5fi s1u+friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inerti*om o, 1f-nj(u9aoban+fz r )qa of the array of point objects shown in Fig. 8–43 abo9o r-b jq*)+fzn a1o,aof (nmuut
(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 oxyq*bj4e7haaarxy q )31gen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at tk 2qxvz4brb6+- wr;f/jti 9w phe correct rate, engineers fire four tangen2bp +fx iv6wrr9-q wzb4k;tj/tial rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to 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-:yvyg 1e*i8kxpj0g r ab 52gr..n)1 pecdbnu.50 cm and a mass of 0.580 kg. Calculatay02) r i5 enurgen vpg-kp :1b1cb*8y..gjdxe
(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 ib)lgyyg( js:o ksnacx-3k ;/8t 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-duqge4 c*;. xmck+ ogx6riven 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*c;kqg emu4 xg6c.+ xo 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 10,300lm 85m:y ydw2t rpm is shut off and is eventually brought uniformly to rest by a frictional tor my 2mwl85yt:dque 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. 2av,j eic * c2rqh0zfh83)cq g8–45 accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, wzw9x*-bvxv -hhich rotates about the elbow joint under the action of the triceps muscle, Fig. 8–4vx-bw -v9 xzh*5. 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 lai58qae4d udn s*oo: 2e)/9szz ul2 fkong thin rod, as shown in Fig. 8–46. sdd2l8useouo4:2i nqaz fe/ 9* a)5kz
(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 masz 39ifyt gvcno 265v)mses, $m_1$ 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 acceleratqy+( oth4qv 4oes the hammer from rest within four full turns (revolutioq+t( 4o hoyvq4ns) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of o;v:8;bb+z3geia p7fxy s( nx 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 de;js.msxcd59sbqr c vh-t 10x3 velops 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 and radius 9.0 cm rolls without o nluzo9imlag4ch2+ -/ xbz 0es6x:5t slipping down a lane at 3.3 nei694 altshgbz2u-x5x /l o: +mo0zc$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun ash5s0 8pfxxbhbd6 kw9 m0uwhs-us)ss)j . 18zt the sum of two 6shb jdbf.)59pzu kwh8-)t0s1u0 8x mh swxssterms,
(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:zacnds*s9q4t3o h p(bwp8l0 radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? os3hn pp 8qb (0:t4sda9clw*zAssume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1kkphiy l6bq1q/h8pe d d9 )-c(.80 kg starts from rest and rolls without slipping down a 3q)-6q l b8k 19h/ppeicky( dhd0.0 $^{\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 txyu 6wz7bt (/vip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservatiot/yv z 6u(7wxbn of energy.]    $m/s$

  What is the angular mh dw. 2edvt*bq4 wffh2,3xkb 3omentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an an4k q,3ew*hdtv2ff bw2hx3. dbgular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of od ,8xbf6nqnk6c5urq93ps djd + * l-pa 2.8-kg uniform cylindrical grinding wheel of radius 18 cm b9n du6s lnod+kc 65rqf jq8x,-dp3 *pwhen rotating 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 platformff7 ggr/lidoa uyc2p1 -;:x5z that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of gfu2cydx5r-; lpiaz7 / :o1gf rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can redi85s tzwfbsa -e c:v1+uce her moment of inertia by a factor of about 3.5 when -: tafsv 1sb5w ce8+izchanging from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initialn*z9unc02 t lbv-w x8u rate of 1.0 rev every 2.0 s to a final rate n8 n-t xbv9u2cz*l uw0of 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 ver8 t li6xddjwd( *q,:zxtical 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 radius 8.0 cm, onto the cdqz*xx:6 d,t diw(l j8enter 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 figk r5ywlksy+ 4(i1s5ha ure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Ea1a yz)koxx5 qojt :50 e*o:awqrth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped ont a4c-7+hkwji 5,a)x+ cxmoih(vhe rb,o an identical dis+a,x45h) - oeb7a ji,rimx wc(h hk+cvk 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 2y5hw) v wvu.b2.4 $rev/s$ 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-go-rouo,y5o-(5dz4qj8q z 9uka jhj qnd platform of radius 3.0 m and moment of inertia 925 zjjqk45,(-ju8qqyzoa9 o dh0 $kg \cdot m^2$ 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 angular v1a +ku2w (7v;z(ip grdyau yu)elocity of 0.8 z ;w1+(ukyv(y7a rdgp) au2iu $rad/s$ 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 eventually21 ogvs/yrgd/ collapses 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 roto y/g/d1sr vg2ation 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 7a,k76udpv:d 4s vq*sbj op5aexcess 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 : 8rzlupb6rf/yy(kny vc4 p .6$ 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 fre3wnuvyyf a137ely without friction. The moaw3 1nvy3 u7yfment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diamet chdv2;tcx zkh*xp+ 6)er merry-go-round turntable that c 2xx*v)czt+kh; 6pd his mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope5r;;5/fk83jk tlqky i /axpbm 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 roll;ykp/b5r fm / iajt8 ;3xklkq5s 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 always facb .c/ ,6dmmjp7zx tn8des the Earth. Determine the ratio of the Moonjmx8 t d,p/dc.n6zb7m’s 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 /tm,4aq8 z gwq c1)dctrate 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 cylggy/+ 0g6g,ikspo /wj) :jup dinder of radius 0.20 m acquires a rotational rate oiy0s+ jdo)k wj/gu ggp6/g:p ,f from rest 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 solid cylindrical disksl 7u n1sj.aei2, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of msaj el.1n7iu 2ass 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 hjhvxt(kg r3oxv/u7;+ 2uhi:is the angular 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 greatv57you hds g*4, were rotating at a speed of 1.0 revolution every 12 days.huog4d5 ys* v7 If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for ,- :l of4rtfxui* x8lldd7d* git 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 diameter 1.50 m and maiu4d l:7l l*do f rf8,xt*x-dgss 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 illustrateswja8 qh1pb8* qc4ev/q 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 horizontal surfasitls3 i0*ct/ce 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 pivq1uxc2l waoel(n: 0 -iot 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,2lo a1wcnl0 :uie-x (q determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and48iev-o ;ydecsfj 2m.x*)+3oqa at ih we want to exert a horizontaio aty)-.ecvf h2 ix8*3j; doa+q4mes l force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s 6knmb/nbdc h3i3;/fr on a flat road is making a turn with a radius The forces act36kinb;mrb /d f /nhc3ing on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rodbbsk **+:edi ck 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 5.0ded:* bs+ ki*b 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 cylinder and her arms as thin l+)n7c 5ynyscrods, 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. 5cyl7+nc) y ns  

  You are designing a clutch assembly which 9xmj3b*u nrx-* l xwd:lqn- k:consists of two cylindrical plates, of masmb9nnxdurw -kjqxl : * 3*x:l-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 and radius r rolls along the looped rougn2/vl0+ k1eopa h6gs94fw s rwh track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to al2nvp6/049ess frw+hkg ow1reach 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 assumft:ke-m a o7780:roo jekefd9 e $r\ll R$ h =    (R-r)

  The tires of a car make 85 lvz0lk b6 ;mm;revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The 6kv bmzlm0;l; tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s