A bicycle odometer (which measure//nv7w nr umvoqt 9q37s distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happeq7r7 noq/ v3mwvtnu 9/ns if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a d /8akx3 uyx3 li3nl:zpoint on the rim have radial and/or tangential acceleration? If the disk’s angular velocity inclyni3 /ukz:xl8adx 33 reases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by al4e rf.3 h4a4;ohdc5 enu zjx4 single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater q*,sk.mi1lhutorque 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 u1. ibbhz7eemw v2i3 *with your hands behind your head than when your arms are stretched out in front of you? A diagraib3e1. zve uh72w* ibmm may help you to answer this.

A 21-speed bicycle has seven sproo, ymwz:-rkan gi9s-( ckets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Wm(9k:w- o-,a yrz igsnhy? 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 hu+:i+ *aj/+evahhrc dave slender lower legs with flesh and muscle concentrated high, close to the bohaev :jhi+au+rc/d+ *dy (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. hdp1f/ fw m.6z/ p5ms))aqz jn8–35) carry a long, narrow beam?

If the net force on a sysqfs+x / 7 im7+;oioygctem is zero, is the net torque also zero? If the net torquc ;+ qi+oy77xom/ifgse on a system is zero, is the net force zero?

Two inclines have the sb3vg2ed d v+u9ame height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed o39+bv dev gu2df the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolliwcu(by/x:i y aa r7i80ng (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 hira(0 8:cay ib7wyx/u as the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start fromh*o hql1aev)e 7 1cw9d rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater roce1v ldw*9h e)q o1h7atational KE?

We claim that momentum and angular momentum are consedc )rdpqx5rkew9 2-w, rved. Yet most moving or rotating objects eventually slow down and stop. p xd 2wd,kwq95e)-rcrExplain.

If there were a great migration of people towars y( )bvxvzy q/t *mxd:yma950d the Earth’s equator, how would this affev 9yt)0 5 mzyyxqm/xadv*:b(s ct the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any in f-tjd.(d+y liitial rotation when she leaves the boarfj ( yt.-+dlidd?

The moment of inertia of a rotating solid disk about an axis th +rdyqiqtw,*p021m t6 pfrdv.rough its center of mass isy,0r ir tw*62p+qdpd .qmvf1t $\frac{1}{2}WR^2$ (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 maxr ei(x p zu7)ce ,;:gigsh4c1ss in each outstretched hand. If you suddenly drop the 47u hee,: igxcirczp ;gs1()xmasses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and t:6 /xcb v) a8d*axav pya-y8fyg9)o hdhe other is solid. Describe an experiment to determine which is whivp o8 g*x/ d a6)axbd-9:hvacfyay)8ych.

The angular velocity of aw-mh-a3lzsqqo )o;s,y wkafg 6 q): j1 wheel rotating 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 linear acceleration of this point at the top lw-q)3j wfqao1ms-6 g ,oh ay:);szk qof the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating )h*2ro r q+ nz5nzs3wsturntable. What )*wzz ss n3rqrhno5 +2happens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he th3(zcyoxxkq. ,rows the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and lekco y 3q.(x,zxgs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why t/v1vyy mkg,4;xnwq2x 6(4ubl miit,a helicopter must have more than one rotor (or propeller). Discuss one lkbq;2146i/ u,i4y vmv m,ytg(wxnt xor more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians:33ajq-*d/ka gwd 6oxp (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 coincidx xzcb ex7wad/ q:(t,6ence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun anb,xzwx(tc xa ed:7q /6d the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earud5w-a+r6*x m+92nvrnhk kq hth. The beam diverges at a nmkx9 r hqd-+2k+*vh 5wu6nran angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a m0mg1ayq,ru+ pzr e** rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What 0+ grmm* *zup,y1rqae is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m tdng6d)pd;7j p a0.9ocg5klt uo another child. If the ball makes 15.0 jddo)g96p5k cpl.a 7;tgdn0u revolutions, what is its diameter?    m

  A bicycle with tires 68 cm i82t5v6tw 7v-f ucp0enst 1sed n diameter travels 8.0 km. How many revolutions do the whee07 vfesc n8 5-tvt ptw1edus26ls make?    $rev$

  (a) A grinding wheel 0.35 m in diameteai9 en ,wh mn cj7l74o+lf0(yxr rotates at 2500 rpm. Calculate its angular velocity ine9o am7 iylh+4,f wcn0 xnl7(j $rad/s$ $\omega$ =    $rad/sec$
(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 o -r je.5trzf;vne complete revolution in 4.0 s (Fig. 8–38). (a) What5efrzj ;. tvr- is the linear speed 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 velocity of the Earth (a) in its wkpdu6r-8 hiwac,3i/ orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed z(x8 d0 fs) gqs8iluk2of 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 particc9mp0b t,,;sk7zjr 9 7w/2/rriu hgtfxa-twble 7.0 cm from the axis of rotation is to experience an accelbk0cgf jr b,;tr9/x2ir9/t7t7wa ws mp ,z -uheration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cenkrkzta :48:5.:ct+oh ollb b8njc fg:ter from 130 rpm to 280 rpm in 4.0+8abc84tb ntc:ohfl: gk :z.:o5kl jr 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 radiu4u7vw+ ejm3(gy 0gyzgo y)9y cs $R_1$ 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, astronautsat82z; tlbqck 1n/ gf+ w(gqs7 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 minuk1gb q tq7g ;w+s(na2/8ltfczte during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Trbbpg v2o1 w58y)ws-qhrough how many revolutions did it turn in this timeo rqvg8 y-b)ps 5bww12?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcj)gluy qqsq+3 gy0,z +ulate
(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 ii98or5 x *n h xml et/jug18ycqe:7j1for the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions xge i8y*lj h: 58j1qx9e1muotnc/r7i 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 y.z)*fz ,z4u; q klhzbrpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this t4*;bz)f hk ,ylzu .zzqime?    m

  A cooling fan is turned ofl57+ n;s, :nbzwbo f y0ew.otnf when it is running at 850rev/min It turns 1500 revolutions before it como ,5t ;.n70lzbn :osywebfw+ nes 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 its speed unif;rwceevn lj2 .6 gpm5 jx/8v.dormly from 95km/h to 45km/h The tires have a diamnjv w26 d/ ;lx8 vce5mrjge.p.eter 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 iq3zjj .rm4 (lgr+vf(x ts speed uniformly from 95km/h to 45km/h The tires gm .+((3 vj4jqlrxrzf 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 pu,xt4;cw4o p xuts all her weight on each pedal when climbing a hill. Th ,;t4x4oc xpuwe 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 oqn)1ul5c maqh3/ido 5f a door 74 cm wide. What is the magnitude of the torque if q )ai5oul13d/mh5cnq 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 k29g,,cyy5h9 g)w(ugxypx j n about the axle of the wheel shown in Fig. 8–39. Assume ,yj hn5g9(c uxy wgxp 9kg2)y,that a friction 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 end14,5 qgua jhm+ix n.f.mxwyw4s of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and th.u f5q. m +,yw m4xg1ani4hwjxen released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a0,oqgy,empq 0 torque of 38gp0ye,q0m , oq $m \cdot N$ 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.v nwt j;,4owgl(2*h os8-kg sphere of radius 0.648 m when the axis of rotation is through itsto2w j( ;vlsn,h g4ow* center.    $kg \cdot m^2$

  Calculate the moment of inert;uyww9n 6*ukw ia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1 w9nw* 6wu;yku.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end ofy2n4ibzi0 r16.o+mp kdeg t. a a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calce4rnp .+d6zm iky t.i21ogb0a ulate
(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 dmqo /-; h7qtka potter’s wheel rotating at constant angular speed/q; -to 7mhqkd (Fig. 8–42). The 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 inertia of the array of point objects y 2/wuda+e: lzshown in Fig. 8–43 about+dzuaew: y 2l/
(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 y-iif 4k.gzh 1oxygen 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 the correct rate, engiefb gd6r *prk mu5z)e2-1xtu2 neers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocke z1u )ee 2p-f6krgumt5xd* 2brt 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 8.50 cm and a ma ;qt fuo4toi+ke*6 boa8id)q:ss of 0.580 kg. Califota:;8tqoo ueq*d+4bi 6k)culate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest to 3 cvjewfn *xe1 */q4tuh24o7jv $rev/s$ 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 merry-gok/8urf l+;qon-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the accelerati/rlfoq k;+nu8on, 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 w a-l ahcxt 67, b+mk9n03 q-lcchdb/,rwoj8m is eventually brought uniformly to rest by a frictionc cd ,xojh+ 7n m/llqwk-,b-t mab680w9rach3al 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-kgirbp ,v+da 6hb88jv* b 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 solelnl5d( xfqbhlye4i ev0d v*kj j,3.t 25y by the action of the forearm, which rotates about the elbow joint under the action of the tricfhbiv.* en5yl4x l, ej5 k(0vtdjq3d2eps 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 rodp nu +8- wze/6umzulg), as shown in Fig. 8–46 +e-/mpzunuul)g z86w .
(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 mazn*q4b q-w8ucg x xp1r qt(o5m9 l3t-hsses, $m_1$ 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 hammejz 6b6 felr,t:hjy.;o r from rest within four full turns (revolutions) and releases it ajt;,jzhy .oerfl b 66:t 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 ha92)wt,l ahlp)ovug /x y jww);s a moment 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 280 ). vp- tyq-sy)ohze j0 g5j*cd$m \cdot N$ 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 slipping down ro.4rh/h b cpi/a-4x ;u1ocae a lanh/4o p-harxau; c1/i reb oc4.e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the/ mns;nibn4*fl1-;.exat 0bo4 vzg jw Earth with respect to the Sun as the sum of two terms, v fe.4n xsbnnj;g0/41 bm-toaiw;z*l
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much +zjbq vrd 1wi;,q g2 ed0+ddz*net work is required to accelerate it from rest q+*d0zzrgj, w; d2dbe+vdqi1to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts c6b:z hwhbmdgs( z )zp7o:(n+from rest and rolls without slipping down a npzg 7)zh+hmd6wb b(:c sz:o(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 balanpf*p:z-1e 4nkxi. ytu ced vertically on its tip. It starts to fall and its lower end does not slip. W :zp4tn*e kxp-1.uyfihat will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ba 7t- t58oalsqcll rotating on the end of a thin string in a circle of radius 1.10 m at an angular spea8t 5scl-t7q oed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum,uu-: l4wr,r* kzeaom of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm w-au ,u wrmel*,4zo :krhen 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 platjv jq.tbj9 9x1form 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 rot9jxjtvq .b9 j1ation 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 ejnqh(0t vyl q0uf0(3. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If s( n0yqhl00ejqt(u3 vf he 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 initial rate of 1.0 -cd;8*hhefj:odq h.rt3;fx ulpdt .:rejdrd.xt hu;;qo:p3hl- *edcf: 8htf .v every 2.0 s 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 through4;0:acyia n/lwq lzf0 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 8.04/n yz qwiflal0;ca :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 figgnhz/. t/9 xf84f l6kil5ccnwure 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 Ear(wgsg-ylk:hq ur unl4 *.v3*a th
(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 diyh/ ly,y 894(p nyhbvysk of moment of inertia I is dropped onto an identical disk rotating at angula,yy h y8vhy/n 4lb(p9yr speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a5zvmmu ege)-f96ro3p t 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 merry-go-round platfov75n.0bjek6m3t5dbc h cvn50h0fmd sog76 uarm of ramdfjd6hbctv3 05oh 75nmcenb 7k05 6g v.u0s adius 3.0 m and moment 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-round is rotating freely with an angular velocity of q2xgodaa6.z 5 a9d y hbqi-/h;0.a56 ;dhgyox /.b-qaai zqh9 2d8 $rad/s$ 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 collapses into a whi8u.hcu:m9xk-i 30law ar 1 smnte 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 an931a kl8 :um0umhixsna-. cr wgular 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 exa-w ns6/wb5j1mepzeo2 d1*sd cess 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 n4eik amst 0u8ha 9.a,3wxes*$ 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, thatmm b:2pbcxk3 6o8l2nv2;h xna can rotate freely without friction. The moment of inertia of the person plus the platf :h262ln 3mcva8;bbk x x2omnporm 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 stacbds9 +(/b gosq8.ll qnds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment +blq9gdsq(8c os/l b.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 rope lyiow)6/gxys)cpq k3/ .sers ;skng on the top edge of the spool. A person grabs the end of the rope and walks a distance /)6y;skcpssqos k3 w)r/ xge.L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces t 0g14mi5jpib mqlfo9ihk94 /e he Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum.gj4b kefi h4m51 /iim0l9pqo9 (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate ose (2 x*l/rve hevars*jje389f 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 oz,raewus1c.is8 :e7 zgf 5h( bf a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s intere 8:s( af,rw.1ube75czzig s hval 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 of mass 0.0t6t4-,aubm v ix) uau150 kg and diameter 0.075 m, joined by a (concentric) thin solid cy tv-mx,atu1 4)iuub a6lindrical 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 angular speeuzh j;eo3emo1 f,sxji//(n o8 qe e5+ed 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 rotaht * f )y.ai88qkcv5upting 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 i 8qcv.if yk 8t5a*up)hts 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 *i (y;. :dwnmb w8ju5cu rqwwi,0f;ri automobile is for it to use energy stored in a heavy r wf(*8wq idic;. m,0j :wrywr;uu i5nbotating 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 illustrates an) umcmgyvb441 $H_2O$ 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 horizontf yiy 17d27k)cbnx+lg al 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 massd- 7z8vxu)i/hjlfwyd*.e c7 t M 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 hlexv7 cf)ywud dj7-8i/*t.z 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 ths88jicqxfd2 2b38wy m*mt i2fe floor, and we want to exert a horizontal force F at itsb *282qmdix3 8j8y tifmfsc2w 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 spr)e -sj9co(7xqnbdlpj z9; zs6i9 ls+eed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are t9qsrcel +x; djjil(snzs)o-9zb976phe normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m a2q we,yz0w/r)zmh- dpnd 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 required02my/w heqr-z),zd pw to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder anf;4xrx fzk-(h d her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinningfz(x -x r4kf;h skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consi,:m24n .ig pbu)hjp d4kki+ wysts of two cylindrical plates, of makminb:2+dwph)j. ui y,44pg kss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 tq+x2rgti r7c)c x,eq0rack of Fig. 8–58. What is the minimum value of the vertical height h,+ qgciq7r)c xe20t xr 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 dod(jz(brx)(d j d:.vh f not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 rei3q d9o+q spa/volutions as the car reduces its speed uniformly from 90km/h to 60q d+s9aopiq/ 3km/h The 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