A bicycle odometer (which measures distance traveled) is attachi/9ns rqhj x0(k7g87kc( k2eglli yj4ed near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle(9exg7qgknijyrhk 47l ( sk8j /ilc 20 with 24-inch wheels?

Suppose a disk rotates at co4qwdyo )+bvfjv9y9 x8 np+g-znstant angular velocity. 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 taf+v)wp 99+ qy8b4 n o-gzxdvyjngential 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 thed*ib(px44f e w angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forcf7(fn b2 .mhos xv4jj2e? 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 han )2a 9n.sr)xckle5gyo zg+ oq:ds behind your head than when your arms are stretched out in front of ynogx2) zgr.e 9y5l) :os cak+qou? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at th4y 9-or* wtnm2csgk9c)o; gc re 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 pgcr 4mo 2ny)9cw-r c*;ot g9ksedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowk d9sqwp;7:c9+no,f0pl 4 igwgn 9rw fer legs with fleshgw dop sg4kq wrp099nlf cifw+:7, 9n; and 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. 8–3z y;uvow7t j-s,e i0i35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? fgj3i)sg*2f -g 6uew mIf the net torque on a system is zsm 3ig jf)egf *g62-wuero, is the net force zero?

Two inclines have the same 5iczxg ;02ilo height but make different angles with the horizontal. The same steel ball is rolled down each;5 c i2l0gxzoi incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (frg6 f znlc8ab f to3-6p.gpi2+kom rest) down an incline. One sphere has twice the radius and twi8 6i-b3pkop gal6c f.2z ft+gnce 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 thep - )z2 g wq1xqsf(l(w3 :yhmj;nrom*i same 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 greater total kinetic enejil(hf;2 gy(n -qm p*1wrw moqz:)s3xrgy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or tq)1q 2mn lx8urotating objects eventually slow down nt)xuq2lmq18 and stop. Explain.

If there were a great migration of people toward the Earth’s equaypga 2 g cc 2m(aam)q-;sp*gq+tor, how would this affect they);q2pga* macg2s(+-mcagq p length of the day?

Can the diver of Fig. 8–29 do a sobp66 f12j ) ayjkdmpz.yp83eon)h3 dqmersault without having any initial rotation when she leaves the boyzb 6f j jqdmopdyp)).phk86ea 13 2n3ard?

The moment of inertia of a rotating solid disk about an axis through its center/ca/2o q2 xqrpoihad:in0o69 flg bed -*..tm o:cio.d2ieq tpd hox a b*2 g-ml069/onf ./qraf 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-kg mass e1k/w(u; h f7g3ja5eqt j ,jnnin each outstretched hand. If you suddenly drop the masses,un;jaf, ej wk7(1qh5jng3/te will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one isf*l* a /j4jr b2dem4dbt0ocj + hollow and the other is solid. De0ao lc*2j*jfbm4 t/4 d der+bjscribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontyu-j852p hhepal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points -eh u2hpp5y 8jeast, 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 osr0(dx:x lsg hw256c large freely rotating turntable. What happens if youldrsx wco 6h:x(250gs walk toward the center?

A shortstop may leap into the air to catch a ,k sfsi5n1kqq;3 bxl;oq01g qball and throw it quickly. As he throws the ball, the upper part of his body rotats;fq1goq50k; ,x1 q bkl sni3qes. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of con o1jz 4*68upjlgg tyuj-iv/,lm+g *ppservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss onejt-4l/ zouj * p pgpvyg+gj68mil*,u1 or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in rrj2:y1sg qr ;upaecj:w8,3t sk)v)jk adians: (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 anon2kik9x nzw;- as (6a amazing coincidence. Calculate, using the information inside the Front Cover, the ang n-; sxnkk9iz6oa(2awular diameters (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 from Eartasrb :n-:u 9xvibxoyea* ,r/ 8h. The beam diverges at an anglebxvyoea: s:xu/ b *r,rn9i 8-a $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender sb5;k ygoz l51rotate at a 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 acceleration as the blades slow down? yzkl;5 51o bsg   $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anu,* bkswj f/g(9v6rf 5qza4heother child. If the ball makes 15.0 revo4fs ,hze/a uf(5brgw*qjkv9 6lutions, what is its diameter?    m

  A bicycle with tires 68 cm inla ,vh5wve1z q4.fj3vp5wg-k diameter travels 8.0 km. How many revolutions do the fh ewk31v,v-wg 4av ql. j5pz5wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2 ff hwv849a0ra500 rpm. Calculate its angular velo9a8f4f0 aw hrvcity 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. 8w*tr vj.d cq**–38). (a) What is the linear speed of a child seated 1.2 m from the vdwcq*r . *j*tcenter?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angulapg+ r)fm i(*l r,kevi3r velocity 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 o co* mgt1.*5*yisqhfef 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 j,h9s5-uco avn bjp8:q0rkv) 7.0 cm from the axis of rotation is to expbru,:-o ajkn vh p8s)9qjcv05 erience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm w pl9cv --a:8muu,iixto 280 rpm in 4.0 s. Decu:iuw,m -l-p9via 8xtermine
(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 radiuo rzjwe, )vc3-nau)f.s $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraftaxphafmwa w(.r-8+(wx,ip zpn9 hv hn38z6 z, 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 revop68 ma,9p vwxahr zwn(+3wiphx ,( z.f-8hnaz lution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 3yvw3 tjl7c1* ovfnk +s. Through how many revolutions did it turn+* yvc1n 7vk3ftlo3w j in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 12zw:kn+*y j94 xi 5jjfh00 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 wz)3/3mox-hl vtmprp ,a 0 vx1in a whirling “human centrifuge,”/1awl ,hmrv p zv-03p)ot x3xm which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter acceo 2i30yfdrxh*dqu8nu, s -c9elerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this 9qu-,rdo0cn 2 deui3y* hsx8f time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns hpp n74e:e4eep9* mdg 1500 revolutions before it comes toe* e4eh m:e4p pg9p7nd 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 its speed uniforx0r3 w8pitkpw ,rmz+*l9f2w5v6qfbz mly from 95km/h to 45km/h The tires have a diameter of z5wi 9rx6k 2bfptz* ,wvlq0+p8w mr3 f0.80 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 revolutionsjtx+wqfgkhv2xx9(- *.do4cql mv5i+ as the car reduces its speed uniformly from 95km/h to 45km/h The td*x.v 4o-2x q+(w9tl c ih+5fgjmvkqxires 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 pedal when climbing1a+b ls , .r 7zx73gwrodyype5 a hilo3adwg+b ryr zx,y e.p15s7 7ll. The pedals 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. What is the ma,q6ll ezll9su *h*0t ggnitude of the tq,eul *s zg96hl0 ll*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 ty+a16ockm2j5w 4 mgu fhe wheel shown in Fig. 8–39. Assume that a friction torq6g 2jo um5+14kmcayw fue 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 massless rod whiqtey 5as5*5c34ewk rz ch pivots as shown in Fig. 8–40. Initially ty*4 ec wsz a53q5trke5he rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requir:;x.dkz9qn a90vc z yxe tightening to a torque of 38z :n;9zvkqx a.dxy c09 $m \cdot N$ 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 4f fk9b tfwa335 9gt :wu:xwhc3e6wtk sphere of radius 0.648 m when the axis of rotation is through 3a6wh fb3t5kw:4fktugf9ww9t cx 3:eits center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyclegqabdy on433y1.j c20 /a1ji.xy yhh v 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 ignoj 3hhi4.0j 2a .xygbyvyyq1a /cond31red (why?).    $kg \cdot m^2$

  A small 650-gram ball oklsiq3i 1hm 7fg(w m/-i9o-uf n the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calc l/-1hu73w(ikfi-f sim9 qmgoulate
(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 .bg:,jtmhq g/j 6da6u rotating at constant angular speed (Fig. 8–42). The friction forc:6ghm/jq, 6adtj u bg.e 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 arrayb a p,szw m1o;+/bet(o of point objects shown in Fig. 8–43 abo atm;p z,+(wbsoeb1/ 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 to+iiv x0lp2rx7tal 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, uniform9 zcornej a 6*wx+ji,0f6n o9u cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fiin0x6o6w*9o n ,cj + uzreafj9g. 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 witbs* e/ ou.t1zuh a radius of 8.50 cm and a mass of 0.580 kg. Calculatouze t *us/1.be
(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 swingw+l6 xvf7ie r/s a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentiall0obu1c. ;qra27 kznfakg+ j g/z8y.wyy on 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 bf. un rkca/y+ 1qz0jg 8yw.2oga7zk; 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10, .btioa tig ;-qm4(q 5:liany7300 rpm is shut off and is eventually brought uniformly to rest by a o.-ygm t(biq ili5a: nt7;a4q frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at 7t(j,m4)dn byr $m/s^2$ 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 bal ga9glh*bu4 5zl is thrown solely by the action of the forearm, which rotateu g 495hzagbl*s about the 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, as shown in Fig. (m4lr4jzk/n+ xouje, 8–44m+, (rjx /4ujozn lek6.
(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 1rvcvb on;.w) oct*r7 / w,bzltwo masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest withinkljz;q.fqad8 h-ooeb(+ 8lm, iy85 eh four full turns (revolutions) and releases it at a dajiqe5.8 +lqm ; l o(h-yze8ok,8hfbspeed 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*9kpnw tl 9gwk; l)5go 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 torj9 2o1s pg. e2vx/sjwique 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 rozq-z e2gauy, +lls without slipping down a lane ata2qz ez+,guy- 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eart qb 3:g0nywqc4h with respect to the Sun as the sum of two termgyn0 b 34cqqw:s,
(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 ru4-( 4mtkockl6( evle adius 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?u-c4(kkltlmve6 o( 4e Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg startjmxuu* c,k:4ls from rest and rolls without slipping down a :ml u,*cj4ukx30.0 $^{\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 f-yd4i rp y72 v0aczy(*vu ae;and its lower end does not slip. What will be the speeda4;z fyed*-r c 0i7uy2vpvay( 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 qq7 6ni6y(yijwn ( wy;rotating on the end of a thin string in a circle of radij(nq; iiwy(qw67 y 6nyus 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*n .s3x pjq/p/3zwadg.8-kg uniform cylindrical grinding wheel of radius 18 cm aq3zpw/./3sd n xjpg*when 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 platfct+f9c 8po c52wu hx(torm that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–4xfctc85owc9pt 2(h u+ 8, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. c0vkwvf6o bfv42 0isea.xnh0ia-n 9 68–29) can reduce her moment of inertia by a fknvo-20ax n0i9a 6ew sfv4vbh.fc6i0 actor 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 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 iniozfc6o i;9g k:4ux.im tial rate of 1.0 rev every 2.0 s to a final rate of 3 4oz.fg 69iux:mkc;oi$rev/s$ 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 aroun/wfyb/bh)m4gs1 aw i4d a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of )sbbmfyiww/4 1 g/ah4mass 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 moment7oan n+tph i*qqa8k )3um of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of9*ybonl,g .r 7hct f+:xo)vhx the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inernes sxbk0t4ol+is+)xu-8 0x b tia I is dropped onto an identical disk rotating at angular se80os0- nxkixbs) s xtl4u +b+peed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 :ef.npg d y- rj0f1kv5 e7rcv3$rev/s$ 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 atz ;g9rmt:,b:v olyk(s the center of a rotating merry-go-round platform of radius 3.0 m and moy :t,ovm:lbg(rk 9sz ;ment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-rouny26zlaqp) sd,3+eni w d is rotating freely with an angular velocity of 0.8 6 pdl+ 3as,i zy2wq)en$rad/s$ 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 event,5kchj.q gyq1vt/t 9 f6 hu+ihve3)g*jwv py0 ually 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 ro6/pv 1u qyqh 3,ygf59hjv jhit *0t.)ve+kwcg tation 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 excess o(ejeqg fxmnm 29 )c5b5-ac x.aw;:efpf 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 ec0p5 ri()kbz u)qm7 b$ 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, initialm8+gwol.mle, eh(z7ifv/qr)p n r+gy2sz v88 ly at rest, that can rotate freely without friction. The moment of inertia of the person plus +8 e)gqr .vz 2mnzs(8r8,vy+ opewg fl/i7ml hthe 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 5(o sonm +81rg7biaek of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a 8e+ b( 17sg5aokmorin 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 vtijc. o uo,8vqv)m++ 8r7dtv 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 l md)v.87 rt+i8vqocto j,v+v uength 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 faces the Earth. Deter+1b9kvapu3, ts *c5x9klytni mine the ratio of the Moon’s spin angular momentum (about its own axis) tyx 5* ul19 ksp,t v3b+nat9ckio its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest a- :t-wlo vsc4kxc(4)mg jmhf,t a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinderhl6 ef1o;d qp: of radius 0.20 m acquires a rotational:he1;fdq 6opl rate of 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 disks,de98n - ss7dzo 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 conserva7zsde -9s8ond tion of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear whrtq. ggcmv3i s*03p+c eel ($\omega_R$) 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 ouro5d2;kdsabi5 4lq2ns Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to uq4na5s kd22oidsb5; l ndergo 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-pollutios06yr- , ydoqun automobile is for it to use energy stored in a heavy q0yu ,so-y6dr rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a 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 illustratee b ei6cybxxw9l, 6l03s 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 (hoopba2hs dw*gf ty*n-1j 3) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., og:tf jj/zxq -v(29l cx/hh9b 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 at jxvg 2f9/-x/(: b9ohz jlchqcts 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,ps 14h*kob/ aqjpy /.l qzw3pf+s;0ce and we want to /13pzq0ws. /f yh*;qpl eksjopa4c+b exert a horizontal 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 on a flat road i3 (mxilcb.r7g s making a turn with a radius The forces acting on the cyclist and cycle are the n br3x(g.7 milcormal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 t1l z:1tb -),wmqgm hpm 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 1qg thtw -mbzlm)p1,:where does the torque come from?    $m \cdot N$

  Model a figure skater’s bodyh*3y r;3*dmpdku. c3ngx oo7y as a solid cylinder and her arms as thin rods, making reasonable estimates for tryd pxnoh y*.o3 ku g;cm3d3*7he 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 two cylindrical pt1z :pwcicbn8 - vz-/blates, of81z c-:v/- nbic btzpw mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rough track of Fig. 8/4-(y4fok:wose iwry x th *u4–58. What is the minimum value of the ve44/-x4sh wtiy kr:y *efou o(wrtical height h that the marble must 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 asuav 7 a1y9nqdbk40t2crk:yv: sume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces itsh3 bkvup4 7w 0qi+g*jwl5a s2b speed uniformly from 90km/h to 60km/h The tirs 2kw 4puwa+q03*ljv 5 hgbib7es 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