A bicycle odometer (which measures ) s;u2caizgsf. xb8+bdistance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle2afxi g +.b;)u z8cbss with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on 1ys 4nweyj-y ;6ctii toegmi-eh:4* * kxn4 f-the rim have radial and/or tangential acceleration? If the dij4-en--yi 6o :xk*yhifes41 ;*gc4etmyw ni t sk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described byn2zp*fmns (923 :cb6ttu xmb o a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger foxc5aeo/vidgy 83 t2 p3rce? 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 ;aur- 1o-ofus sit-up with your hands behind your head than when your arms are--1f osu;ua ro 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 and three at the pedhv;t kihqv48y :bx1-wal cranks. In which gear is it harder to peqxb;:v hvt 4ihy1-8 wkdal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fasy(w3 ofd4ohy2rb bld- ybm czvjk;0 ,2w9.zt;t have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this z r.dhbb;9(y2 bmyww0vf l-dt4,zck3ojo y ;2 distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beamq*2vh+ vjo r wd4a.y0/ dmjzyn6 v5l;z?

If the net force on a system is zero,b g 3dbt).0x:05ig elg7tp1pw9if dd f is the net torque also zero? If the net torque:w0xg.9dplif ptb0fbi3 g 57g)1dtde on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontal.7iq22(3irn3ftn k0,wgr ey rl The same steel ball is rolled down each incline. On which inclineft y(nk 0i3n2i3, r7 lg2qerwr will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) dow 3alo25r v:qnhlr7 )j)bx0snmn an incline. One sphere has twice the radius and twice the mass of the othq:2r)bns 7r)m l3a5vl jon0xher. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They stal: v+-3s ho- v2tf1ryrv jhm/qrt 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 totayhv r q2v3l:/vojhm1+r sf-- tl kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or wtht m jq4-7-irotating objects eventu4-i7ttmhjw q-ally slow down and stop. Explain.

If there were a great migration of people toward the Earth’su,rfxs x sx 5-lln/m*0 h;m4mo equator, how would t5f/x,u *rh; xxm4lssn0 lm-o mhis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial ra g7oev62n-iiotation when she leaves the 62-n oai7vegi board?

The moment of inertia of a rotating solid disk aboz .2mzx mpmr280y7tygut an axis through its center m7yrz8z2x mp .2 0tgymof 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 holdiwmny ;sh:w4dv3r n m. *8eczz;ng a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velo*nvscyrnz;e;zmhm w3dw :.48 city increase, decrease, or stay the same? Explain.

Two spheres look identical a:igg2od 2- gmuoy8ob9nd have the same mass. However, one is hollow and the o dm2-89ogogiguo 2: ybther is solid. Describe an experiment to determine which is which.

The angular velocity of a wheelc8++92 intbsn)ro/ +3 de t6:mm )ijpfkbjjzb 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 this2obz+/nitr+mnb m)jt ji3e9 bkdjscf+6p:)8 point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing 4jyl sek 64dfh6:e1zcon the edge of a large freely rotating turntable. What happens if you 1 hfles j46y6 cdke:z4walk toward the center?

A shortstop may leap into the air to catch a ball and )jh ppar +s)x4143pu:7cx/.ecnis ;nr vujsmthrow it quickly. As he throws the ball, the upper part of his body rotates. If you loo4xn1r4upp3smn :+cuj.s;xai/)h )se rpv7jc k quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the ,tiihy :0pbuu 2jul +ui2 c+gq3n4k. flaw of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelleun3yc uf:2g k2iul i4+p,q+ ujbh0i.tr can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3g0w ,izx;1at11z isce0 $^{\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 coincidence. Calculate, j 0k2fx(fo.ia using the ix (k. fof0ja2information inside the Front Cover, the angular 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 Earth. T.y(cetkzdq - m*:kq hx5w: d.dhe beam diverges at an anglekhdq-:* q5t.xzd.y (w k: mdce $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned o k)pc, *).bnio5 nzvn -l.vcleff during operation, the b)l-e*.v l . ninpknc)z5, vcoblades 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 flo7nh lux 79)pa ) p6+ zmlk:z:gq) lo+zuz7cxuwor 3.5 m to another child. If the ball makes 15.0 7 pplkq z)ulzw)z9a6:h: m l7g+7czxuuxno )+revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter tt ;t 4s/, f( juggggddxrwz9(3+p9qfnravels 8.0 km. How many revolutions do the wheels make ;/9t4t( q, s9f3zpnjdfgg+xdw(gu rg ?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcm6-o1fn a3egoulate its angulaogn- a 36mofe1r velocity 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 revoluz2(nnl6u kz0ition in 4.0 s (Fig. 8–38). (a) What is zl2z60n ku( nithe 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 i ax f c7o6emwb,rn-9b8ts orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a p5 tn 8a ,u+qp9b3/x0xjcgmejxoint
(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 ifnrwk)ulhikve--j39r fv 0b0qi0 gf 68 a particle 7.0 cm from the axis of rotation is to experience ani)jfvivnb-glr0 qkf k36- 0we 0u9h8r acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel i y ,mp/*6cncnaccelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determi,m c*y/pn cn6ine
(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 radiusxo67fc7y flq.:kq;q e $R_1$ 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 spacebe p*10;5y;k q.uw:)f cjedijn xr.gpcraft 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 ev rqxc;nwbuypeg;* .1.j0jipefd:)k 5 ery 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 f6espn8 3a3p. h ftihk3rom rest to 15,000 rpm in 220 s. Through how many revolutions didhpf3pt s3ke6 i3.han8 it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 4q 5;zgur 5cjo;khw3k1200 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 fq7t b.w33uyxxor the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 27qxy 3ub.t w3x0 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;pk e3siac*)y accelerates 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 thisasy3*;)kiepc time?    m

  A cooling fan is turned off whenm.dkw6m w94jarsq-o8 it is running at 850rev/min It turns 1500 revolutions b6m94r8jo w. daqmw -skefore 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 ca p lpc:w5t*+ftr reduces its speed uniformly from 95km/h to 45km/h T+cl *w5p:t ftphe tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uni j typ0o h5vx1*(k6ybsformly from 95km/h to 45km/h The tires have a dj(b15 ksyp ty0 v6xh*oiameter 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 7it 3l9(eok; ex w7t:9bhfojhher weight on each pedal when climbing a hill. The pefwe(ejt9x7 ;ti ookhl 9h:73bdals 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 thbx8v7o.0 g kgce magnitude of the torqu08.c bk7g xgove if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the mf bd6gbo;vc(v 3)m+ adpcn;,wheel shown in Fig. 8–39. Assume that a friction torque of 0.b6dcc);fmd3 bm+gn(va , opv;4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to tpx2onja 8 47uche ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calcxpnjua4o7 2 8culate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tighteni r0/li2pvlv *hv* ,efong to a torque of 38vh2 v*rv o ll0i/,*fpe $m \cdot N$ 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 of3o ie/qy ao5(kdi p*q8 a 10.8-kg sphere of radius 0.648 m when the axis / i*8p3yodo5ea (qqkiof rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The n h ;a0 sc5y-nh0kgv /pv68jzgrim ;phvch vs- 5yka0 0nn6jgg8z/ and tire have a combined 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 oz ;4*ddb;ag) sl( bkeff a thin, light rod is rotated in a horizontal circle of radds)4 zfk ba;;*(bgeldius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on aj v*to6;gi8e*giz -mlatd-m 7 potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction 8*a-zmlmvdt*6-ggj 7 e i;iotforce 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 show)h8v9qb*m x7 vr6ejgen in Fig. 8–43exqe7vr mh)8* b6g 9jv about
(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 consistr0am( pzlhpx/4; -/kqlr:t*ghbos- bs of two oxygen 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 p s.jx )h-(t jb*qanx-cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the - *n- j q)s.bhja(pxxtsatellite 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 ayfb t,.zz*q8 q uniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg.. y,qbt8f*zq z Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swing +go( .wq9t*aiwyzw2 xs 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 tangentially on a sgqngoc14 p*,,3 *lnn pza+7hd7ls rdjoyxd)9 mall hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 ozd7dycg,7n*ro) n+lnp*, gp 1h9ljda4 q 3sx 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 10,300 rpm is shut off and is a)i *t e;t ar1mf dc*yxc.8/azeventually brought uniformly to rest by a friction f8t xim/ca)*e1r*;t cya.daz al 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 at2f7i lq+y *ugq 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 s*oyrrvuo2b 0 1au9x* action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. T0o oy 9b*vuarr2*xs u1he 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 )r *ebir/j,*ryq qojx7 /xrt-shown in Fig. 8–46 -*iexy, qbt)/ xjr/rr joq7*r.
(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 twe4 mmm ful)1lq ro04.eo 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 pauwb1* gk6b .:g vj)cwithin four full turns (revolutions) gpb1a 6. cgv j:wu)b*kand 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 m21 vpg ppt.icxnl8,djt7)kb: oment 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/q e:9/ cqwjut7lpc;q develops 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 in3e6m 95+; gaktagarwithout slipping down a lane at 3.3 aa69 i3tr5e;g+gk nam $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun ak;kbt*.gg.2/ vbscy ys the sum of two terms, /k.sg .bvc*ky;b t2yg
(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 vmkp r;j l)8.wfuk jyk+e9b*6ympmz9*1 n:yh of 1640 kg and a radius of 7.50 m. How much net work is requi6p1knjfmlrmh y98*kp*u:w9kmy);v j. + bye zred to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest andc( 3b;6f.)xd glxts ns rolls without sli x.)bsd3 g( lnfx6s;ctpping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on itwb 20xnhj* d,fs tip. It starts to fall and its lower end does not slip. What will be tdnjxh *2fb0,w he speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on tho b(n*x:w.ocm e end of a thin string in a circle oc.mw( bx on:*of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg unifolr1nj0;vv, l crm cylindrical grinding wheel of radius 18 cm when rota nj1rvl0,v;lcting 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, c4msxnexiw0 2ezp8t,m52lbg e:oq 8,on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speewx4:zxs88t0 52beq ng2 ,mpe o,lecim d 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. 8–29) can red+r0.rulm u ly7uce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1. 0 u+7.rlmuyrl5 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 :w c2 fgv/awtefq d tsf,/u*/5an initial rate of 1.0 tved:52wfqatgfs/ cfu ,*/ w/rev 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 through its center at*, e(u.zkdev6am 4npb ;:ehtz 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 center of the rotating wheel. What is the frequency of the wheel ue an6(m ze:ke,ptd4h.zv; b*after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at;3(jkwd afb 9 :nl1 u/zelty6d 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 angulaa flliu+-::gr+ 1lbk jr momentum of 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 inertia I 23.k6t c jmgncis dropped onto an identical disk rotating at angular ccnjkm23g.6 t speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2h 7 bdhj:c:5u3)e u6 ojc)5rtj.w tugc.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 a- j* wx6 ws.tkd7l;ddxt the center of a rotating merry-go-round platform of radi jtdk.-6 d*xslwd ;xw7us 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 ang tg.b f;g+yyq)ular velocity of 0.8 yq +byf;g t.)g$rad/s$ 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 white dwarf, losing about half its m rl4w-ue.ws11:k ad rfas1asww re1 r 4l:.dfku-s 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 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 winkn;bj0 chm2/ nds in excess 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 /qril,((urp6xhh 2mz$ 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 platfoydi/e9 .b9hb- ltw2mk.y qe3lrm, initially at rest, that can rotate freely without frictb- i mhe d/bw.yq9 kt2yel39l.ion. The moment 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 t2+s85l89 nkqyqvr xijhe edge of a 6.5-m diameter merry-go-round turntable that is mounted onxqs j +8qn2ilr985yvk 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 ropeh-+ qvamyff- da.. bej7 v;l1u rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does theama ld ybf.h.-vqu7v-+;j1ef spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the 2zd2qq7,;b jm 7m-nre sg z*bp)dh(sfEarth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbita qrgzmn z,s 2d*;pebj 7mdb- )h2sfq7(l angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

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

  A 1.4-kg grindstone in the shape of a uniform cylinder of radiusi5ngl9z )oon2 0.20 m acquires a rotational rate of fi 9oo5g )znn2lrom 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 d:y, kqrd*e9 agisks, 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,d:grq 9a e*ky. 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 szhhnfa te/5:1kam6s1 lnq 6k0peed 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 ma24 6+ceq fbkjuj(0f ouss 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is e 260fj uof4q+(ubck ja 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 it to use energy st:mhzq(,i/h1o2k jy 7blns vs 6ored in a heavy rotating flywhee/kjh 2h,nvsyl6 o m:zq(7i 1bsl. 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 my zf.+(ri8:0 zsgvm g$H_2O$ 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 (h7mk1wu 3,(t;ym )mpz .yyvsmboop) 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 cj1c (l2dl-zenan pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rdlj(2ez1lc - nod 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 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 vertime +/ui g*//o6/iidx:ufoewx cally on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step aga6/u/ g* xf/xew/+i:eiiodmuo inst 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 iv)7 . rzvqd6e20e3pm zi6dqqps making a turn with a radius The forces acting on the cyclist and cycle arezv6z 6m2dd7r q.e)p 0eivp 3qq 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 rock into a xnvgxr* *xep+; 1wv0csling of length 1.5 m and begins whirling the rock in vvexxc;n*wp x r0+g*1a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylindeod-p liig -4vi k1zse-z1 xr):r and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the rai-4)gik z1 -zpeid1 lso-:rvxtio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assemg , fmpk;ye1t s.qo*(mbly which consists of two cylindrical plates, of mgey.o m(qps*m,f t;k 1ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 tr hw/m/ly)c -7px vii8back of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is )i/p-ichmvyxl8/7wb 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 j /cx.sfj -oagws,q ,-26ar.*zeobd kassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the ctq 31 hwc wtzf1u5pj h(syi m2,;7+rpgar reduces its speed uniformly from 90kq(z +csfp75m3gwt1; uw2 hr1,iyht jp m/h to 60km/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