A bicycle odometer (which measures distance,qr1kdphm7n 3 traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use itm q3kr,hn1p7d on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does.wsj3mg0uu9(jed l i3j g(om7ua 8eq- a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does tomdg9q 83a( je.-w ugjl7ej (uui3s 0mhe 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 a singl6 tb9e.):qse p7g s wduu3+squ hb/l0ne value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger foi) r:th(n8ir) a vcqd8rce? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your he8nxwa5kvl2o+l. c+ f mad than when your a m .ok+f8lwncavl 25+xrms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the re2vz qful, 8udb;i ,(maar wheel and three at the 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 pedal, a zf ,; qulb8au,imd (2vsmall front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs wi;4m5 znu9:rwle6xdyv b4bv;y th flesh and muscle concentrated highm;v4b rv4ylyzwd6exb 5n:u 9;, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lfl:n70 .hkzv. rv fjz,ong, narrow beam?

If the net force on a system is zero, is the net torque also zero? If theq a4v8af.h9y.fue:kx net torque on a system is zero, is the x8f a. 9yef:q ahv4uk.net force zero?

Two inclines have the same heig1k- qbm sogo87 of. ;g4lks4efht but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greogo-8 .1lfk 4fo b4sesqk7mg ;ater? Explain.

Two solid spheres simultaney.vvz8(3k 6 +lmifdiu ously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic en lvi(i+ .dyku6z 3vfm8ergy at the bottom?

A sphere and a cylinder have the same radius and the samqxf6yyc.0.9 i gdn2dpe 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 greateqgi.fyd29 x0. cn6p ydr total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet mosul1cwcfw 1 9(at moving or rotating objects eventually slow down anac9w1wf l 1(ucd stop. Explain.

If there were a great migra-,n x.rjou* kaqy4nt yka6p0w:vb6+o tion of people toward the Earth’s equator, how would th.+ru:*0w n-yjaoa po4,vt66y b kx kqnis affect the length of the day?

Can the diver of Fig. 8orpc(.-3). ca/itl 4ei s;mga )evskv7eqg8 k–29 do a somersault without having any initial rotation when she leavesscl(7 q.)eg; )s.eva/4- 3gmark pv o8t ikeci the board?

The moment of inertia of a . /3g+o,. 0cpygudqo 6ich7 vqpvzv 2yrotating solid disk about an axis through its center o.cd,pog7ho3 6q0v yi/.qz+gyv2 u pvcf 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:yu a-,cu8 a(ds z0*lhdul1t. wvt(cb stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.wuzhctstd a-du , ac10l(8 .ylb*:(vu

Two spheres look identical and have the same mass. However, one ru. as7f(t7w ouu.t vs6 s3ue;is hollow and the other is solid. Describe an experiment to determine which is ..ua(vs te6sf st7r7w;ou3uu which.

The angular velocity1f ra2p nq*i 3scgulre+9-o ;e of a 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 pape3iq2l u1-fr9 ;o gsre* c+noints east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on t 0kef pxu 9*wr*b4kse5he edge of a large freely rotating turntable. What happens if you walk toward the cenex**ksfe0 wu4b9p rk5ter?

A shortstop may leap into the air to catch a bal.4n hv-c6la whl and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Ficv6wlhh . 4-nag. 8–36). Explain.

On the basis of the law of conservation of angular momen oyp05iffu ild4j ) 9+2y;8t(crfgm pltum, discuss why a helicopter must have more tht0(lf2 4id8umy locrfp ipy);5jfg+ 9an one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3yfk0fxtg/zk xm1 0 (.x0 $^{\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,-a9p )-c wmglfdmiw 25 v(+wdg using the informamdwg25ic --wvampgw9+fd ( l)tion 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 Earthp3, m6 5 9irblk4sdeej. The beam diverges at ankr95ie b34jm6ed p,sl 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 rate of 6500 rpm. W+v pf srx+cl ,qkqko51.dna7/ hen the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelerati q,+vl.ops fqd7 r+ /5axk1cknon as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the bal mx1oktw.05-w *jwdna:cyj .e:h2ttal makes 15.0 revolutions, what is ith:xaj t52d 1e*ow.y0nka:t.j-wtcmw s diameter?    m

  A bicycle with tires 68 cm in diameter travelsvrj q:t,) kzw9 8.0 km. How many revolutions do t,)jwvk9q : tzrhe wheels make?    $rev$

  (a) A grinding wheel 0 5b4e8ara e(o wv:slz..35 m in diameter rotates at 2500 rpm. Calculate its angular velro(zw lba.:8e4s aev 5ocity 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 make(qf tcsbk 4y97s one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from t9f(y 74kb tqcshe 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 Earth1b;7 ky q skys .*w)g:8d-zakpfh m8ac (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spefq3 nst) 9s.v( y,setwed of 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 centrifug:lzol24 ph lz -9iyfsq0dfj:1e rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,000l f-l p:29j:lioz1 ydq h40sfz $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm t 6mzwb2v2ini x/)tp(po 280 rpm in 4.0 pxiz(i6)m w bn /2ptv2s. 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 radiuf5pp7b 60,;)+j9lnd e2uvv f klyuw fes $R_1$ 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 Ap -.b ovwm.g5:lc3i 5qvno.zma ollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip,.5lwvg : vnbamc -o5 .m.zqo3i they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter 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 accelerat ujw e1lxe/21- g2lm7oh0cv omes uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions 2ec02mwemv o1x h1 -/lj 7gulodid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. j7 qoo;.x rh4hp fxlgg8),e* fCalculate
(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 uhwvw-kiu7; 5a9 wj:a stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 cwvku i w h:a5aj-w9u;7omplete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 s h7rl d6s.5wyrpm to 360 rpm in 6.5 s.rys w5dhl.7s6 How far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev p8cnm8f-i3)g78xjczxb c e2y/min It turns 1500 revolutions before it comes to a stop.b c8ec28g nm xj)z-xci7ypf83
(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 thh/i7p:uqk g o:e car reduces its speed uniformly from 95km/h to 45km:kq /gi7:up ho/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unitop5 s9tv c0+cflr8dn h. 1(fiformly from 95km/h to 45km/h The tires have a diameter ofhcrfdscvp.9i8tl(nf t+ 0 5 o1 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 climbing a0i67e oekw,3j9e ht0 qnuym(g hill. The pedals re7o(9 3w,ukey0 hi6 qnmg e0jtotate 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 thg :p0w/ u.pdc( wne;tae magnitude of the torq /ew( 0dtwanc;pu:g.pue 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 3 ;leulg,(uw.9dz +wp)o yatethe axle of the wheel shown in Fig. 8–39. Assume that a friction torque owu.;a ,9de)e pt+u(gwlz3ol yf 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached m02m*t3lpag sto the 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. Calcua0*2 l3gsp mmtlate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder hp vnxyc6e/ --fm5wwi/h5x7ga ru;si+ead of an engine require tightening to a torque of 38smr6 +a7yfi x--we5cvx/5np h giuw/; $m \cdot N$ 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 w;+g l:5v(l tytzj7v asphere of radius 0.648 m when the axis of rotationyz 7tgalt:+ wl5jv(;v is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel m( qid.+m i r+iqt,na666.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of thd+ti qq+ir.,an 6mmi (e hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rr9eoty bb nl:gx /- dvd1v1//motated in a horizontal circle of radius 1.2 m.v/y 1r/n:dgbo9bvd ex m1/tl- Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant a /79hoikkc uuz91v,clngular speed (Fig. 8–4klo /7cuui9kch z 9v,12). 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 *f5bgm(s sg78vp)rhqthe array of point objects shown in Fig. 8–43 hg(m5s)rf vp*87gs bqabout
(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 consiswqf apd,* 0b,tic5.8bn u;rtsts 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 cylindrical satellite spinning at the correct vtjbn gl a0r.;l1 j7d.rate, engineers fire four tange.n l.jv rbat1; djl70gntial rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uqrar.2*5lc- grthq .bp92fa nniform cylinder with a radius of 8.50 cm and a mass of 0.58f22gr q*ra.9.acq r lbn-t5ph0 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bao.erugj)v2qm. z5i , yt, 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 small hand-driven merry-go-round and is ap- 4)kmg1okuj ble 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 thk j-kmp) 41goue acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 aun(y b7c 17fd ney-g)rpm is shut off and is eventually brought uniformly to rest by a frictional torque ofgn(ybefuna yd7 c1)-7 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. 8–8 2u5gkwq tezgnb i z04z*7b+c45 accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the actxso+ ,qqzu5z-ion of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unquoz xs,q-+ 5ziformly 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 beu7lbxx)m0,/ rwyzw2k)vj8v c considered a long thin rod, as shown in Fig. 8–46.,bj8kwzlx)mv rxw72 ) u0 /ycv
(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 o fpbul652 -wgf.vow c1f two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest withbj8wqnl ( 6tu o0)e8bx:hm1noin four full turns (revolutions) and releases it at a spee6mqhuljb( t 8o80x)no1n:bw ed 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 inertqs/:o,dlk+ vhf.. g vovug1e0ia 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 torque14k mhc4y.hoglp8*kys-b . y d 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 an*,/p5(0ajj98 mhtoiibe zn scd radius 9.0 cm rolls without slipping down a lane at 3.3 (/ 5 azp8ct,nh* se0iob9ijmj$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy ofc6ou42d:rrsw the Earth with respect to the Sun as the sum of twwdu46cr2 : osro terms,
(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. ,- dp*h o,veeh9p+uvh50 m. How much net work is required to acceleratu*-ohh , pved9e,hvp+e 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 and rolls wi0l m9xabw,t k6thout slipping down a 30.0 b,mk9 al6w0tx$^{\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 fav rfts5)rt, kc/k-hgw *v 2zfud ox)h*;9/chkll and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.fkthzh,fh 5v /;rg*cwu /x)rvsk*t 2k 9co)d-]    $m/s$

  What is the angular momentum of a 0.210-kg ballgmv6;5/ aknehlg*l0 x rotating on the end of a thin string in a ciraelmg65n; *kh0x/vgl cle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cycd 6a+r:u z3 oal7)zf k 6gyz;bajq.*rlindrical grinding wheel of radius 18 cm when rotating at 1500 rpmzck7;ra+qa*oad6rjg: ).yl3fz ub 6z?    $kg \cdot m^2$
(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 platform that is rotating at a rate zz q 0 32ol5i(uq0mx;vovknfiax1;hqj4vo27 of 1.3rev/s If he 0z50n 7vi;o z h1fxvoi3 2a4;q2 j kmuqq(vlxoraises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of ine4 o f81 l)ha 4w)azaidb p4sk:vxkj,4lrtia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotati,zkb8pd:4xllj kso)h1) 4wviaf aa4 4ons 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 asi 6r k 75sf2zizid83on initial rate of 1.0 rev every 2.id86 32risfz7iozs5k0 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 vnxm60bya )zpk pae)c90f x s5(ertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg a) 0ypaf(0xkcm9epa6)sz xn5b nd diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater slv0u, /lhn9 8if8oyqapinning 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 moiz4bqc u/.zg*mentum 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 is dropped onto hag-6ocat8n2vb 68efo v ab.6 an identical disk rota v8nehf6b6o ova .2tcbg-68a ating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4m(gmf(oq2 1bfmu h wd6p- 3pu. $rev/s$ 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 p mr r(,5jy v5buhcvpcl0.g*u7latform of radius 3.0 m and moment ( bm7v ujgr0*pl.ur55y, chvc 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 anxxfxt b79+3hg angular velocity of 0.x ghx x3b9+7ft8 $rad/s$ 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, lofl0 oo**y5lql+ lxh/r sing 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 rotation rate be?(round to+h**xl/5l lolfrqo 0 y 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 wq)0hkmf 6cpg) inds 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 7qyvyt t6:qgzv(u z9 4$ 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, thatdzc, ,). ;d q;qxr:sf4ftm-m iwg*z pt can rotate freely without friction. The moment of inertia of thd,z m; .zfi)qx pw,f: mdtr*-ct q4gs;e person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edg-ipx8wkzlgy zccm 2 /j )8 18qyw(brs-e of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings a )1zbxly2kwc(8g jm p/-y- r8qwzi8csnd has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying(htyg33 g2vrm 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 ofv hry gt23g(3m 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 alwaysmbohd4o 8h i,tvmf /.) faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentidhf8m.mob )4,v oht /um. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates frombt0 wxyko/z:y8o,z(m rest at 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 ibshr) 0uqh-7r n the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from reh7b-0suqr rh)st 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, each of mass 0.1dl2srdf;2f71nso nm 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 conservation of energy to rf1lssod 7 fn;1nmd 22calculate 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 wheel(pkh rb(qjix;1awlnb0eru /(8o 9j k1 ($\omega_R$) 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 rotasg9+2ku/ qf5 s;h ogwl fp0ad(ting at a speed of 1.0 revl0w;qf/d(s ua2p+ ko f9ggsh5 olution 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 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 automobilwo 20v83ii/sy ikjw j+e is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindriisy 3w jwv20+i/8i jokcal 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 2)6*d , yyzpdwct lf0g$H_2O$ 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 ai .w )5enjw)a3; kbl/rdosj )g 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., we (mm7o +)xl4ai eeufau.m.7w rri6v :zignore 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) xiwauvr+f r.46mm z 7u.a:(7leoi) emthe angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on th54je ,s( o6exv7 :hv)r mdk zec-synq*e floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). Th4y szov*e:skvmq xe -nd 6hj )5(e,7cre step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road lldjy 4m+mbi0d-,z.y is making a turn with a radius The forces acting on the cyclist any+yl 0djl m4 zib,-.mdd cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg)+prd4iss1 n6h9fjm t(6 oqxm rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a(qsp9 hmo6+rf m41ixsdt)6 nj 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 sol.gscj( qp1imr7 -r d.lid cylinder and her arms as thin rods, making readrlg-r qi71m.(jpsc.sonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly w,b +omjkz *+-radj2 bby8j5pc hich consists of two cylindrical plates, of mass y5 8p rjd,kz ab+2m+oj*cj-bb$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rtnw-, )*xhffw7 3b yosadius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is)w3*xtb-w7fs foyn,h 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 qp;u;e j9y *n/7evax :.cd ekqqz;mth/q,cm: do not assume $r\ll R$ h =    (R-r)

  The tires of a car map glok82b.*w t.zn9yoke 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire?p.zw *2 gbyoo98 k.nlt $\approx$    $rad/s^2$(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