A bicycle odometer (which measures distav1que)f37 fcuc+ zz/bnce traveled) is attached near the wheel hub and is designed for 27-inch w b+ufcf/ze3v)uz cq71 heels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constan 18*bb xgld dug,c.agvfk 1f08h n5p4vt angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change8 d udgb*g014. , vgbva1pln fhkf5xc8?

Could a nonrigid body be described by a single value of t5 i0t/erly mg5x qsfjw(z( :68fte:jdhe angular velocity $\omega$ Explain.

Can a small force ever exert af53z;id-rj i o+0by(3b( nj css9 mcwa greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your h3a jeto52i/ygy,j59w2qea bw ands behind your head than when your arms are stretched out in front of you? A diagram may32 ebga iwto5/92y5jewy qa,j help you to answer this.

A 21-speed bicycle has seven sprockets at the rearp5p dt15o;k iecvcoa0s o9r*j65sw g9 wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprockp1csp06o ;j5 cova r9w9kts dge5*io5et? 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 fast have slender lower legs with fle)qhhnyr )noio67o j4v7gi*n9 sh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational o*h j77i nqnri69 )4hvooy)gndynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, nar m.c,pmmy6va qz9p0vkm: d-e:row beam?

If the net force on a system is zero, is the net torque also yjr:lbq-5s9/vuzl5 c zero? If the net torque lr5qculvyj9s/:bz5- on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the hpfrm,vbz 2yszj3e rt5xz+ x9srw06k c dh45;5orizontal. The same steel ball is rolled down each incline. 0tdr;2zmzfv+sxb4ck5e3 r sj y ,9wr655zh pxOn which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollh3*xu)k dspw 4s 3eqn1-2h lgxing (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Whichws14nkp )xd-3q2l 3 gxuhsh* e 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 m- 0 y6a/; gdqnyfa)micass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Whichncmqi -yf0a;y/)da6 g has the greater rotational KE?

We claim that momentum and angularx* mvmopt3w ./ momentum are conserved. Yet most moving or rotating object o *mptv/.wmx3s eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, hu 5+5rfxpb o vifa(sy,(rmy( 8ow would this affect the leng5ar((yp+ ixms(,f8uvry of5 bth of the day?

Can the diver of Fig. 8–29 do a somersault wr kzz ;7-nk.e pc0hq,lithout having any initial rotation w,rpknqhe-cz0.lz ;k7 hen she leaves the board?

The moment of inertia of a re(k65rvlmg: 7 vm.hurbd7 j:uotating solid disk about an axis through its center of mar:vr7(.khm dl: mv7 e6jguu5bss 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 rlh o;r-w7 3.q; ,dy6dzicn vyyotating stool holding a 2-kg mass in each outstretched hand. If you r, y37wdyz; vql;yncd.i o-6hsuddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one)*qlrp;eb gi + is hollow and the otherl+)e rg;i *pqb is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle itdguy8 -)lb, 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 tangentiat)gu8-, d lbiyl linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating n-2wxgjsmoh kouc0 6s6 6sncpe /y+cb43)q5p turntable. What happens if you walk towardc+ bnpn shk2o0 gep wuc6/65q)6y 4ossm-xj3c the center?

A shortstop may leap into the air to catch a bx+ oc1mhn -.h-ezn2brall 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 dmer2x+ h o-b.h- 1cnnzirection (Fig. 8–36). Explain.

On the basis of the law of co 0c-apm)sfo9i nservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one oso c) 0paf-9mir more ways the second propeller can operate to keep the helicopter stable.

  Express the following4a+mjq45x ww/c rho8v angles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth betb6z oxu:dx3 8cause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameo3t :b6u dx8xzters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direjue 125jrga4c +algg- 1sqi7g: 4fzx rcted at the Moon, 380,000 km from Earth. The beam diverges at an as:-2zxu gjgqg7gj451 1crr e+4iafa lngle $\theta$ (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/ms nl;ve hddfn;76a5 rate of 6500 rpm. When the motor is turned off duringdmf6;/e nvn7s al5dh; operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the bfg v: ooa3d3. :b(zzg9dmgrl(all makes 15.0 r. v: mfo3o3 9d(g:z(lrdggb azevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Hz5)o sp31 24wnbno)rhkx w9lyow many revolutions do the b35h o12 9nk)l zrn)wwx4pysowheels make?    $rev$

  (a) A grinding wheel 0.35 m in/a2f4fh p3 dwh diameter rotates at 2500 rpm. Calculate its angular velocd2hfh4f/3 w apity 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 o75)o j j+ffn:ob8yj ivne complete revolution in 4.0 s (Fig. 8–38). (a) What isf)j+nji5 y7o j8 ov:fb 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 (/gw,xq /d ejl- //tq.ozve7voa) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a v+n hyc7*e1gmpoint
(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 dcoy1acj*wrmy v5y f:;4s8rmc:f:u (rotate if a particle 7.0 cm from the axis of rotation is to experien*f;uc81 r yyrdf:c:yj:c4oas5vm(mw ce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center ghhgv*x6/ j.dieb8: r from 130 rpm to 280 rpm in 4.0 s. Determinedgb6 ./h: erh i8gvjx*
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius gz2e.26 jo*-ff3fjmdm 1 khlr$R_1$ 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 Apol,t-fnxoe; gb9s7 .5iyyb4 ad x2krs+t lo spacecraft put themselves into a sloxsd5 yn t;xby ag .sk t7f-bir,o924e+w rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter 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 +) v+4mk8rkrc;b obw+y auwp-rest to 15,000 rpm in 220 s. Through how many revoluti)kbu-+mr +vwa c4rpw o;8+ ykbons did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm:xrnp uham,c,01w8 fs to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying j*n( 4b)zho s sf4a5yuhighspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachinfah4 uj(5zoyb)4nss *g 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 accelera3ddh6-w w q j;bkx;j3o ufyf)9tes 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 thisdqfdjuo);ww 3 y j6-9hf;3xk b time?    m

  A cooling fan is turned off when it is running at:1*ig bu kl-kjkur,b9 850rev/min It turns 1500 revolutions before it comes to a jr k u-:9l,bui*1kgb kstop.
(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 r:oxiar,5ovcjr:lak( 7b,z84 rf9w( gv qj1d qeduces its speed uniformly from 95km/h to 4z175rdaq ,ri q:fjb woorjkc,(v9a :4 g x8v(l5km/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 revol lut ayr-b(wlc77pxyqs :6 /;sutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires ha7lx- y;wbu/rq:st y 7(6cp lsave a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbin,eu 4ri.-. ejtyy7 bawg a hill. The pedals rotate in a circy iuea4-..eybr,t7jwle 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 fot8 b. mrwz92um6f 4ymrrce of 55 N on the end of a door 74 cm wide. What is the magnw9umm6.zt 8 2rry f4bmitude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the whee8anp7xd( 9yrk4m u y8fr5a0xu l shown in Fig. 8–39. Assume thnpx05u9ryu x8 rk7 (dfa4yma8at 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 ends of a massl1:w;qy6jwfhfg5l cd1,a2a an5m(zw n 6la-m mess rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of th 5l 12- m;w nz:fgl5cfw6mnjaha(1w, 6ayd qmae net torque on this system.

  The bolts on the cylinder head of anf v 0u9mgm5 3bhx;-v x,z8aoai engine require tightening to a torque of 38 af;hx gu 8x503za , 9mbovm-vi$m \cdot N$ 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 q ml fcqdl eonvq2,h7 6:0-hqhu2*s8o sphere of radius 0.648 m when the axis of rotation is through its ce6f dns8q vhmho*q: 27lqq2-ch0e lou, nter.    $kg \cdot m^2$

  Calculate the moment of inertif kw5dcvb9 640:s2ahq kpiz.k a of a bicycle wheel 66.7 cm in diameter. The rim and t5k wpdbca0.s:kh k 2z6i v49qfire 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 of a thin, light s p0xu;-hxiw.k z -xv(rod is rotated in a horizontal cz w0x xp;k(xih--uvs.ircle of radius 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 a potte, r8l/wd9 omtp5tm )n5lvi tj5 z91sgfr’s wheel rotating at constant angular speed (Fig. 8–42). The frictt/9 5,w)m fstr8gzdmov55l 91ln it jpion 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 objectdvvz4r) ) cg;ss shown in Fig. 8–43 azdvvgc )s r)4;bout
(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 consist2)cos0 j dky0ns 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 satellrgp7fbywq.me 4yu7gu99,lr , ite spinning at the correct rate, engineers fire foyfluybp 97mw7 gu.9re 4,q ,rgur 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 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 unifor qwhh7u2(m wuwp7eu3k8y. 0 uym cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Cy3 uyhk0pq 7e wuuww.u8( hm27alculate
(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 fr er a u:)/;hlnch2hh1bom 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 t8t,o7, yv fxchand-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 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 frictiof y78t,c,tvx onal 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 eventually br/w (v(hqvb+py ought uniformly to rest by a frictional torque of 1.(py+w hvv (/bq2 $m \cdot N$ 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 a-z xi5uvx cm u-;vi:-hccelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forf6vj68p1t i ecearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest1 6pcj6vt eif8 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 consif(ifi,6 1pr ;tenby z)dered a long thin rod, as shown in Fig. 8–4f(p rty;,iinb1 z) f6e6.
(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 masses,f cc89ir5ue- s $m_1$ 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 within (ykg/d3p(crb four full turns (revolutions) and releases it at a s/bgky(3pr cd (peed 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 moy q)zhov0 ki1fwb *: ndjy 2dg*k:b-4oment 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 n- nxb+bovz0, $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg a (kj/+nheigw)1b ub5em+7 mxgnd radius 9.0 cm rolls without slipping down a langm +75gkxn em+j1/( bbwehui)e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth w5d g9 30:6a ax lsy6ir+g :4luufj1la lpm-vixith respect to the Sun as the sum of two terms, gaailmudfj3y0xl:v6 lg-il+aups 6: 514 xr9
(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 a jw cz)a7npn1kd,u3 .6mwlh+ hnd a radius of 7.50 m. How much net work is required to accelerate it from rest t3u,k6hwc+.m z1 nlnh7wj)ap do 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 starm 0tx; lt,o41k4vaz o15 nzluots from rest and rolls without slipping down0 l4 ,n ;vookz 1mlz5xa4uo1tt 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 isv68hbfu8s+f mavtb+- balanced vertically on its tip. It starts to fall and its lower end does b8s6vfh+vmtb+8u - f anot slip. What 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 ball rotating v; o;4hnni1dtw(77 dpqb.0- xyq ojfea28venon the end of a thin string in a circle of radius 1.10 m a ;toy07qdefn2no1dhab 8vqp ;vx7ein4(w-. jt an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cyliqsr )i64yxqa q 3x)86d6 qvvwbndrical grinding wheel of radius 18 cm when rotating at 1500 rvsviq6)6y)abx q46qw r3xq8d pm?    $kg \cdot m^2$
(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 s/8 lpx/9nbvs a rate of 1.3xn/s9/lv 8sbp rev/s If he raises 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) csxv iyxv.z u uv.2; )n4sj6rrj8k: w(jan reduce her moment of inertia by a factor of aboj .vx :inv(6ujsk rr8 wy.zuj) ;2sv4xut 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spuv (y-8mse2in;sq nb63.vbduin rotation rate from an initial rate of 1.0 rev ev-v; 2 6udsenub8sib nqy3vm.(ery 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 throlo yz*0c,lc(hugh its center at a frequency of 1.5rev/s The wheel can be consid(lcoh*y0czl ,ered 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 after the clay sticks to it?    $rev/s$

  (a) What is the angular m5 zgo3c dwaby:g /xc5jqn339vhh*j )x omentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of thekbcjrt0 :z 5xon8e) )x 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 dropp zrewxo-skqf;(c h7,,u8ov 2g ed onto an identical disk rotating at angular spr(kz8 oc eqg-2 wuv, oh7;fs,xeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 -tvenh8:cu u.$rev/s$ 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-ro +8whzcn ygymr2/g m04und platform of radius 3.0 m and moment of inertia 9/+4 yrcm8 0gygn2whzm20 $kg \cdot m^2$ 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 (j3.r3 5ugi.g p7szzihm/ghr 0.8 .z j g35z pmh7i(r/gi.gs3rhu $rad/s$ 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 gc,m+xbo1:q za white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sug1: +qo,mbcxzn’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 excess of 10;;u e aw0(cfpftc4swq ou t,620 $km/h$ 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 :v k7l(7t-ivoga7 xq d$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freym5b f: 1gx gsjgg9b5l x7e.02fyim2jely without friction. The moment of inertia of the pye5xj2s :17j gy25b bmgigl. x9 f0gfmerson plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge h;)xyi02:d arnyo0j7mt(s s7a i 0qaiof a 6.5-m diameter merry-go-round turnthmi0aj x27 a i)0n 0yars7 ytq;sdi(o:able that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground withob((kbyx bd qtjeu* s5x-) noo8s4 s+5 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 with8xkto)sb5(obx4n 5*oss+b ed-yuj(qout slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the lxc5 pyh8/gt 1Earth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to itycgl1 5hx8/pt s orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at aolm1s2auub*ifj:b / 4rc.h:z rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylif.x/kl 7-(xoppi 5r l-lc(itt nder of radius 0.20 m acquires a rotational rate of from rt(pilo fxl rc5/(-ip7.xk -ltest 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 0.050 kg an-uv0l0q8l(( /qgf g p 7xmf:lcbhmr3h d diameter 0.075 m, joined by (cvhq-mll8bg (3 0 fur0f7pqm:/xhlga (concentric) thin solid cylindrical 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 angxckzm +dhp99opf4* en4sr ;p 8ular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with massu)6+h (ndvatl 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 s(nv ldatu6)h+ peed 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 lor)vb(s*c5n*f ;qboij w: a0hu w-pollution automobile 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 cylic 0b*vu ra sf:)jwbq*o(5i h;nndrical 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 1b(s :* ks1myaadjv;y$H_2O$ 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 (ho-e 8lkw)c)ber(f c/a90irz ;ms tu,xtop) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore .r4 x1en:zmm m 8mvorpv.m 92afriction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the cenzmmrmxm 2rva194p : e.vmno8.ter of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vert+++/ze7d-cnp f axg (pz5pejkically on the floor, and we want to exert a horizontal force F atdxz( nepa 5e/cp+k+pgjz+ f7- its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making as-j:izvk.-;syh ta06 o 1d fkfb*bjk; turn with azkjfb*k-so6.y: a;h b;kdfj1v s0 ti- radius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 0 f(dasiq3f9m1.5 m and begins whirling the rock in a nearly horizont0f9 f(aisq3d mal 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 cylinder and her arms as thin rof-73 0 jx2cwj j:y+fvzdg5yow ds, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning sjdco3fyg25+7j0jvxzww: -y f kater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clut67s ,dnk k+:kgobzkd4ch assembly which consists of two cylindrical plates, of maskd46bk,g n :s o+zkd7ks $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ri -jnmh xadg5p.3 h8i(olls along the looped rough track of Fig. 8–58. What is the mini5 ngdh3.jm-i 8ihx ap(mum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assum58rasbkf d(na1tc *9 be $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniform:k8 sgjchr y0r:/v-y tly from y -v/ gc0:kt sry8:rjh90km/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