A bicycle odometer (which measures distance traveled) is pg2wi- -6har 05czkewattached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicyclear w6kwegp0--i 52zch with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the 9ewj poxwt18*hzf ,d-)e di1vj6/pyirim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration?zp x9)1-wjdv ydwop8/i te, ehfj61i* For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the abg;k xp,nc9*+ oyjle)kwb: o9ngular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a uuj/a+w/+h )h.bbe ra 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 hands behind your head than whi cy4b .4, nl6g4rsi6kq3ccocen your arms are stretched out in front of you? A diagram may help you to answer tr3.6yc io k44,s6ccncgq4 ilb his.

A 21-speed bicycle has sevenw+eqr/tn6 th8l ;tn++ c8owab sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large +lah w b6;+8/ cwtrqt8eot+nnfront sprocket? Why?

Mammals that depend on being able to run fast havt w/-:xha;v:lf4ssu oe slender lower legs with flesh antsshx;w /-of4a:v: u ld muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) h* sdpomz,;8,jgeb ip3s6k8g carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net uwd8l048f ju uh 3eo9htorque on a sy04jfd ul u9h e38hwo8ustem is zero, is the net force zero?

Two inclines have the same hekbjxpxxj+ )fq-a 9 -:6.r( 3tclrgnmoight but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will ojg)xm9:lxac pkb-tfr3rjnx. q6- (+ the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) 5)cw7sivy qx . mu-yz6 e1h;ksdown an incline. One sphere has twice the radius and twice the mass of the other. Which reaches thex vsm)17ky-w;6cuyi .s 5hezq 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. Thw+-.9dalcyhz ey start from rest at the top of an incline. Which reaches the bottom first? Which has the greater sp9lw+ -.cza hydeed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular mome atu6.;ix06m:whn)ye h/ /c6r3l dwio q xxoi7ntum are conserved. Yet most moving or rotatioq 0oci/7; u6xem36y .l)wx6 h/: ahwxdniti rng objects eventually slow down and stop. Explain.

If there were a great migration of people toward the zpb9yf vw /5+aEarth’s equator, how would this affect the va9 fb5y zw/+plength of the day?

Can the diver of Fig. 8–29 do a somersault without having any initialdov).v6jj itm3n)(ghw nv9( s rotation whe3gmsjv))9 nwt.v( vjon6di(h n she leaves the board?

The moment of inertia of a rotating solid dis)v/ewohfsdj 4x 1drt9h 4 7w+ak about an axis through its center of mass is vt447+j1sdw )fw /h9 oadre hx$\frac{1}{2}WR^2$ (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 ro tza fa2 o1 a:4j/sdq*n4ayq0mtating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the a 0t2mqd oa:4qz a*sfn4yj a/1masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However umjo-fvhc1 3q5ci/4irjo5t8pt5nl3, one is hollow and the other is solid. Describe an experil /hov5 cpnu4or jm1if83-cq5tj5i3 tment to determine which is which.

The angular velocity of a wheel rotating on a ho x;4 date*hwh5rizontal 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 acceleratioa;hxe*dtwh 4 5n of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on t3:t+j)s yk)r v8djo cnhe edge of a large freely rotating turntable. What happens if you walk toward the ce+yo8 )jcr t)jkdn3v: snter?

A shortstop may leap into the air to catch a ball and throw it quickly. As he t vyu 9cd8oq(;shrows the ball, the upper part of his body rotates. If you look quickly you will notice that his hiqdu9o; s yv8c(ps and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation (pq-d ed /b6k +.,fiuqe7gpgas; cnx- of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the hegn/p6cxg- qsk.-u ;qad+bi e 7,fep(dlicopter stable.

  Express the following angm xrm9l xd9nze625g(sles 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 becauzq 86esn(w.(q 5ad9 cv ,a;oe nnec9stse of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radiansvawdnn(q6sz e.9 8notc9s (eq, eac5; ) 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. The beam diverges .q *pvljxky1fz.- nefjf9(p+ci/wj .acj yql fk .nvf-.x*./e pwpif 1jz(j+9t an 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. Whc zm g81iseo+(en the motor is turned off during 8 o+escg1(zmioperation, 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 3.5m ,rz bjdq:m68bxni0 ; m to another child. If the ball makes 15.0bjxdrmq06n,b; i:m z8 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutiontshwy3 .b3eq7 s do the wheels.h3qy we st7b3 make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotat phdnvt0e :g 36whq*.ikc5 en)es at 2500 rpm. Calculate its angular velocity tc geqk03)d i*5 enh6:vpwnh. 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 makmb1wj-x2 ic6 tes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of ajitc -xw6bm12 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 b15lo4t 6q5wxaue 7 yd-hvz3h)r ugv9velocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sog2f*b m 6x(,yz1zqz9nh orh -peed 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 centrifuge rotate if a particleb8oc;min7n6 3bkr z)w 7.0 cm from the axis of ro8zw ; rnib73bo 6n)cmktation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceler,u2(p(t t o3fztu/nvm ates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Do3t, tvnt (( f/p2uumzetermine
(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 radiu4gszx+v -b+g*po s1vs lp3ze0s $R_1$ 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, astronr7d r9p :j6tyiauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolr:t 7i9yjrp6 dution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rp-.t5 d(voscrz m in 220 s. Through how many revolutions did it turn iro( z5td-cs v.n this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcul y;jevkd+lnh29wi;p) ate
(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 o9:qmj6ksy6bfiy, nc1 f flying highspeed jets in a whirling “human centrifuge,” which takeq i 6j1:c,fk9sbny6mys 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rp o/pybwo/ l (k(rxld9u,ns7l w+ 9wlo )rmor,.m in 6.5 s. How far will a point on the edge of the wheel ha rowll7rs9+,lky()bw,m o.(ro/n w 9l/uxodp ve traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revo nb ,g;i92.pqrqq r suiq4*r/ulutions before it comessrqqp*nq ., brr / uiu4;g29iq 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 xbie:s r1aa:4 0ca8 fmthe car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.:a:8 e0 xim4s1ca abrf80 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 6 z9a*tv r4sw0gh5/aczl:6rd l 5 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a dzl hcrz va5d*tw06g:/l9as4riameter 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 w q5.oep z7ecl;,z psby 326t4xvs ;iwa bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radizw27; ie 4cvpy6s sp; 5eq,obxz.wlt3 us 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 t6p5+q la 7dnu,hlirf/ he end of a door 74 cm wide. What is the magnitude of the torque if the force is epr/7l5ah dn ulf+6 q,ixerted
(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 torqucg; 8.mt j :rj+.gpqks4m; rfxvi3 6voe about the axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4;: j+4.fx6 so pm8k mi;tvqcg .gr3jrv $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of, r3;tilt nyoz 9i4eso6o 94dw a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizont szwyo9 n; e4ir,3td4iotl69 oal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening toop( wj8.;lg g3fb ,ict a torque of 38 i3tg.,gf wcbo8l( pj;$m \cdot N$ 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 sphere of radius 0.648 m when the 15qxmdp0q-l r ax5-1pd qqmrxl0 is of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm auz4* 0a3iqjil f*0kkin diameter. The rim and tire have a combined mass of 1.zj lk30*fu*iq0ka i a425 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 rod is rotated in a az j,y7b5q12u 0w2vw(dxkb duhorizontal circle of radius 1.2 m. 50d1ww jb(z2b 7 qukauyd,v2xCalculate
(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 bmq*xqd0m(s6/d 5vrz *ksei8 on a potter’s wheel rotating at constant angular speed (Fig.vzs/0sdxmke *qri*d8m ( q b56 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in t4hmwh6ci,r:coixxo(d-ki7ev1-8 t Fig. 8–43 abouth cx 8-1c7vrtd4:-i6iek ootimxwh ,(
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose tota0 0z k jno/qp jd69:-)cdknewpl mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, engia sj8e;*n*s*1xx gqa1lzin(kneers fire four tangential rockets as show8zaq s(x* *e1l;1xsnani *g jkn 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 uniform cylinder with48e his u:tf h-(et6cn a radius of 8.50 cm and a mass of 0.580 kg. Cal 6fu-hh8(ets:i4t c enculate
(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 batl a8qkj n4up(8, 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 m9 0p+4 k0eojyh5o8,npgsqraa small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the tos j5qo mreohg4890kp, 0npy +arque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatinml-jj+m :gg3 vw+f v5yg at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional g+ m fj j-+m3lvyw:v5gtorque 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 3.6fb+ytc /mpm1w 4o/l:v-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 acti w fca*z))e*qxp4ua.g on of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acca4 gc*. afepwq *))xzuelerated 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, 9 q;gtshmu72 gmc,pt4as shown in Fig. 8–46. ;tm 9 g72tp4s,ugq mhc
(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 twotjk1q0 u;v ,t5xerfic/iu10g och11b 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 info2 fx(l5e. within four full turns (revolutions) and releases it at a speed of 2o e.(if5fn2lx 8 $m/s$ 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 inerti/r,yv4r:btenr m9j 5fa 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 ofb0)0 s/i9 ,ekewjcnp okiog0 9 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and rads u(00ms+xdr nius 9.0 cm rolls without slipping down a lane at 3.ums(+0xnrds0 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earkk /rrt5n xm22rx dr2b..2nk4h/jpx hth with respect to the Sun as the sum of two terms, .2xj/rk hrtmxbkrk 22h4/ 2p. xrnd5n
(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 i gbjv/ ukq5ou)-.a, tkg and a radius of 7.50 m. How much net work is requauj gvu.t-k,q/5ibo) ired 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 rey v9r75(jmpj qu+ )mkpst and rolls without s y +57)mk9pr pjj(vuqmlipping 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 its tip. It starts to fall atsbr4h7e rc 0rm: z68lnd 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 energyl:rbcsrthm078 4ze6 r .]    $m/s$

  What is the angular momentum rweha4)uh7*(/pa qfhof a 0.210-kg ball rotating on the end of a thin string in a circle of7/ hu pqh()aae*wf hr4 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 r0fe) r+zws/cz)e * 6ehzce 3q2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 eec)e h cew/ fzzz0)r*6+3sqr rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform tho7w8 rz/.fdpzeky( t0 at is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreasesk8zo(0 yz 7pt .erw/df 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 mome*bu9f/lvq (ds nt 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 1.5 s when in the tuck position, uq 9vsbl(/d*fwhat is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an ini;+;zscv 5+f io0 kvz4zm )ubhotial rate of 1.0 rev every 2.0 s to a final ratik;f ozzmo)v h54;zvu+sc0b+e 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 ab 87-ij1swx weround a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg sj-b 87 e1wwixand 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 ska) s-o /-h5pbopdgs5aal k 6ii(ter spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Eihkvb(exwf -bl2fxe1 u 87 ,y(arth
(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 m6- jxppg 0i/h)3v svua, avnuss :t4l5oment of inertia I is dropped onto an identical disk rotating at 3p :hv5xta- 6p4lssvu ,) /niav js0guangular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns w0d 2o *s9dgfiat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merryl4sy 9a2 l ec;c17ipyfih+k3 c-go-round platform of radius 3.i+ sy7a 1yce23c kf4 ;9cilhpl0 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 zstj(ack tw 2vbe-cxthsmm/ 8 *w*,+ 0an angular velocity of 0.8 *s+2 ,0jvx8t mtcm-wk/e(sbwz*a t ch $rad/s$ 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 -0ozsh5 (emlkass 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 be5les hz o-k(m0?(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 win3sf5ij 9lyp fckd/qkx7). lc 4ds 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 tm*6:l;.dj n6rm7 gosw26* odxkmv yx $ 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, :x-)fc +jgmx tt)6ldcthat can rotate freely without friction. The moment of inertia of the person plus c+ 6g)f)xd :l m-cttxjthe 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 of auerz)0xwh:: v 6.5-m diameter merry-go-round turntable that is mounted on frictionless0wv:zru) xe:h 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 rolldg scs x:3+*als 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 spas g:*3dlx+ scool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces thep .jpr x-+n5v bi9km;-wyhu/i Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treuv;-ixjikb5m9p + nr/h.w- ypat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest kl;z ,emsb4+wat a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0: law2.-f*szknxu t *t.20 m acquires a rotationalk-*.txztw au* slfn 2: rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 02.1:v z3vo ;io i:xuv afvrgp-oz6avb*m+,tx.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 calculate the linear speed *zxz : br2v;oo3v m6vpfii ug1:ot-,vax. a+vof 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 sbwq)bvaee d6k 12t 0t0peed 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 sdes6txhum8(ul g03py) , z4jt1 rcmm4ize of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of itsxdt(e0mg,lh3r 68y1cts4zmu4) muj p 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 automobile is for it to clk3a j07:vee tw-vr)w 0 dpd;use energy stored in a heavy rotating flywheel.r de3)k0 - 7jvdclpte:wwv0a; 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 illustratcragu udl+/l(( p70tof pth: 7es an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling ono.qs jxp u2 qm3f1j6/l 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 ulxm ,a2lwxpyh zqwd- s* qd67 g7a)mo29wu/-friction) about a hinge attached to a wall, as in Fig. 8–qwd7m7-zuaglxd)q,9ws6xplua wmh/-* o 22y 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 center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the flowjhjkux6 ebc): o) q9/or, and we want to exert a horizontal force F at its axle so that it will cliju )o:q )b/j9k6hxcwemb 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 a turcd55q0w c.d;h bz(tysvcs 8m-n with a radius The fomvc(q c;t.b5wshsy 0dz d5 c-8rces 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 zgz4b.q px0x11.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm bxg1.zqx zp04after 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.1z1*x rz iaax3eaa 2k* u7cwm arms as thin rods, making reasonable 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.w2 rz*1.*x7a zme a3akaxi uc1   

  You are designing a clutch assembly which consists of two cyli;-e k z,w*+pfd(5 5ps 5rwzmg-y hhh;bvnsd +ondrical plates, of masegs5-n*, hz(k 5 w przmv;-h+oph5ddf +yb;sws $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rolly1*9y-: r)pwfrq mpam s 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 p:9 )y1*amwpfyr rm- qto 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 assum2ijjt ip; )lj85a ;0fp(e kdoae $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolut 98nif :m-hz rebk7o6wions 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 acce:o -8mrezwb7 hfn9 6ikleration 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