A bicycle odometer (which measures distance traveled) )r(dre.*;ryzdf 5r gg is attached near the wheel hu rdr);e(z5rrg.fd*ygb and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates a t/d.htvrx5d:; 6hdr yt constant 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 tangendx 5 v/6 ;rydd:trhh.ttial acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of t7qv17 jdsjj8h +crc2 hhe angular velocity $\omega$ Explain.

Can a small force ever exert c 1v)e,haoj7z a 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 hands behind your head than gj;n0 :9ocrlg1:h*owl(cdfq w(toe5when your arms are grndfo c w(;g:(ho1l:j0*cw9 lo tq5estretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has sfqmx0l;gka/wn : f-cif;e ;)jeven 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 f/;x:- gf);iwa0;c l mjfqke nfront sprocket? Why?

Mammals that depend on being able to run fast j3l-rckdr 0jc/c( q11ri j(rzhave slender lower legs with flesh and muscle concentrated high, close to the body (Fig(-jir1k1 j0j(/ cr rrlq3cdc z. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (F+efs6mkhlo ;gx6h (f0ig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zerjpc c41 ky8qvak0 f4g+o? If the net torque on a system is zero, is the net force zero18 f c+ycjp0v4kg4aqk?

Two inclines have the same height but make different angl5c0j pgpsh5: 0.ogsgles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the0 hs5ppg :jsocl.gg50 bottom be greater? Explain.

Two solid spheres simultaneously sta:3zlpcxx 7-zepr,d :r 3m-nqrrt 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? Whic-3 l mr: -ernx :rzdc,z73xpqph has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They sybefu1 4kdzxvf*g sv(e 9urv1 m ,i5p/2wz/w(tart from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Whicdvvv muiffz*5w(241ypeu w(b/ ,z 91e r sxgk/h has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most m9k4y zz9na qxnni/-d.x /y1hdoving or rotating objects eventually slow down andyniz9 9.zh-a/dnnqx/kx4yd 1 stop. Explain.

If there were a great migraticysj0z. py48ry a,5 kson of people toward the Earth’s equator, how would this affect5j0. 8 sakcyzsy4,pyr the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial ikvmxh ,pku- h6og;0)4 .uobvrotation when she leaves the bo hvvoob;x6uug-p.) m h0,k 4ikard?

The moment of inertia of a xp6p0j e3/:;pyupy a7cmdk,ux7e/xrrotating solid disk about an axis through its center of mas/mpupx 7pxyxje6ucd7/0 p 3:er,ky ;a s is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each y3 z 1boiy)g0nu01 jwbx,vquxep4a18outstretched hand. If you suddenly drop the masses, will yo v0qgw 0)1 ,enpz841o3yuib baxyj1xuur angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identicalj dss12s i3e; wmgjt +v2t15pq and have the same mass. However, one is hollow and the other is solid. Describe an expe 1 vm12 53sjweq+itdt;2jg spsriment to determine which is which.

The angular velocity of a wheel rotating on a hnz:pu. .1xw,zxpdp y: u7mj 2xorizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of thi,1uupx zm .::nxzpwx j72p yd.s point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standed6g4u y 2(oxqing on the edge of a large freely rotating turntable. What happens if you walk oe yu62dx4g(q toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly:qo ,0.ze*a vra+jhuc . As he throws the ball, the upper part of his bod:a .u,ze h+*0cao qjrvy rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, dispp9 b y1;j rh+)hu.zx g2r,ssvcuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways ths gr,9 )u+hhsvj2bxzpy r;1p.e second propeller can operate to keep the helicopter stable.

  Express the following angles in radians t 4/fxunth4bmo xr1*6okq5h.x,-coh : (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an ah6(1 q+f*8o8nbef oq .zi nqx odzcf40gw b)u)mazing coincidence. Calculate, using the information insu 8h8 )qz 6fic* oqbf0f. (eo4d1woznqgx+bn)ide the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divergesx xws3; )tmj:dt0im5p j/q2h tu.pw;r at an anglerw0p ;ipu/j t;:m3dxtth j). sxm5w q2 $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the me glgd:6k5c9 t*2 1k;doqnho kotor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accntkl*qc d;g9oo1d 56 k2ek g:heleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If theg+dzbh3kdo a2 .)lr.m ball makes 15.0 revo 2d.mrd.)aozg k bl3h+lutions, what is its diameter?    m

  A bicycle with tires 68 cm i kb/pw3bltb: z:c bc6)n diameter travels 8.0 km. How many revolutions do the whb /b3ccwp zl6b:bt:)k eels make?    $rev$

  (a) A grinding wheel 0.35 m in d u3n0oj2sw ixkh9 8r9siameter rotates at 2500 rpm. Calculate its angular velocity ioh9k8suxjw n9203r is n $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolutionu/fzh( i5pn2 v io/e-f in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m fromepi -oi2uz5/( fhv nf/ the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in it 3c,*6ol :vutcpupm7x s orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spmj i/x7di n60h8jv1 y7bx( sfbeed 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) mu* +fau (qwnpjy27/mp bst a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an awpu2a/q 7*( fpymbjn+cceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerat n lfw4q)x4yk-7yf j kfwc2-f7es uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determckfx w4-2fj fn)k7q f-y4 lwy7ine
(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 radiusgwko(ne/a ;; d $R_1$ 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 aboao;c601q n/tlp.e p (ofyp(r7m lzird*rd 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 ro7t ic6dr*(yr pe(1/lzm.;n qo0of plptation 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 rest to 15,000 rpm in 220 33 g92t* yxa hyr;tfjhs. Through howt*fyg2h;j hr33axy t 9 many revolutions did it turn in this time?    $rev$

  An automobile engine slow*lie0 cppk;o)dlsc-r0g 1uh9s down from 4500 rpm 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 kdv9a6du swsre-u v 64, *hz )we8/cpchighspeed jets in a whirling “human centrifuge,” whics6)pwseew/cvu u vk*4z9rdadh, c- 86h takes 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 acceleczih6uqyxtt b) bsj8 q 7a6rrpuo-n-)9tq0 9-rates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a po) y htq-tb- cj067q9xtpurz i68nuqsr9ba- )oint on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/minizdc/,bu -kt+,dq ul5lg31; : si rnhi It turns 1500 revolutions before it comes to a stop.nd-3+r ll1d:;iqis,k5h i g , cu/tubz
(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 caq /cg4) f*pfhq)bgx:hr reduces its speed uniformly from 95:qfg4hq bgf*p/ h))cxkm/h to 45km/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 carei-yzxd wp +g*,o)ot-r6 mk *a reduces its speed uniformly from 95km/h to 45k gty,x6z pm+ ir)--o*odw*a kem/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

  A 55-kg person ridingi,bafr11bli 4 a bike puts all her weight on each pedal when climbing a hill. The pedals rotate1,ai1b lib4fr 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 umf9hp: bvt3 3the end of a door 74 cm wide. What is the mag:fvupm39 thb3 nitude 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 wheel sh mf(,lcwpv):m *wb 9gaown in Fig. 8–39. Assume that a friction torque of:vcm g9) ,wplw am*b(f 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of m+g:9ucw(k*r nr4si azass m, are attached to 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. Caw:*rrk ig c9un (z+s4alculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of affnohf*nd63h bc ejx.d7e/)- n engine require tightening to a torque of 38 6bfc7 noxehdn) ff /*3j-ehd. $m \cdot N$ 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 inerti 0gmhre 0.pvki7tx 5c pfk4wssf8 91:va of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through itsfxv 0s.si c5k:p9 km7v1 ep48 fg0htwr center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm3wa -(rqgn(u c in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignorcr unqaw3-(g (ed (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizmbzlbyhdh 4,zb. *jc dk*k1 7:ontal circle of radius 1.2mdzk 4b l kh,*d.b1bzhy*j7c: 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 potterxywgi;q pvur-*xy 2v2)x;;ug ’s wheel rotating at constant angular speed (Fig. 8–42). The ;u*v)i;2 pvqy;xx2 wx yrg-ugfriction 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 Fig. 8–x *m(t6e*bsrzvxw0 x*ygh2n243 gys6trbzm x*0 (xeh xn*vw22*about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule conw (snw (h ztjlj)0sa87sc*iy7sists 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 e73*tzj rit(ow ltn0l lj/79qsatellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocke(0ti erw7o3zl tjlj7 l9*t/qnt if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm an09v8zu6lykx5oh a r6f d a mass of 0.580 kg. Calculat06 v8yu5xfo k6a 9zrhle
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from res;gpq dbnf0.gko(ng v6d);.n u t 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 hheh m f;vtv.:3and-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 mas.:vt he3 h;mfvs of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 5-mt3bg3 lo rc10,300 rpm is shut off and is eventually brought uniform3otb cm3 g5l-rly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 acceleratep* uk-7yzcn-gs 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 opu.n-v1ufnb 694gi4 3 siebdsf the forearm, which rotates about the elbow joint under the action of the tricepf i 1enubbd4g vn43-p9iu .6sss muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can beov:w :wdl9 *cwa6q1tn considered a long thin rod, as shown in Fig. 8–46.td* 1o::lwcn9qv6w aw
(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 t8w4tudz 9*g kwte+ (iwwo 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 hamm mg dehxr acwk9/ xkeh16qvq7z/5 0/,uer from rest within four full turns (revolutions) and releases it at a speedm a5 /07zwd/r,h9 /xk vhegck16 qeqxu 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 inertia 2xl7xrf 8 i1erof $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqu6l4uvpplm/5bng sh f e, 61ij+e of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slippi.f0u;ugt l/m/ e)hnq eng down a lane/.f0 /u;mgqut l)he ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as theltjv -8d/rf,vxq*u)a sum of tuq,*vaxrfd/8-) jv tl wo 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 7.50 m. How much)+t2hs.;oa 7o tsjzkd net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assu2ks+t;o hjt zd.7)s aome it is a solid cylinder.    J

  A sphere of radius 20.0 08 z lgldoy5g5cm and mass 1.80 kg starts from rest and rolls without slipping dow0 zdy8l5gglo 5n 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 verticall 20zclh2dx*iky on its tip. It starts to fall 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:*l0zxh22c dki Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0cy/((e q k9+v4m jc/)5inz hpxezklf;.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.4 cm qxl 5/z;f/ )z9yne +c(4jhkv( peki$rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8- i1wuhl ;(rs:mkg uniform cylindrical grinding wheel of(ru l1miw:;hs radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that z0++ar3an+nf ihqj ;r is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, thzqfj irn0+; ++ra3 anhe 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 jvo dy24*r+q8h3pq iqher moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed j q3+o4 d 2pqy8*vqihr($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from xsm* o3k ty vu7x .)h,s0 db58nogj9hyan initial rate of 1.0 rev every 2.0 s to a finals8 9bgs*o t5.) y ,07yv3hjohkdnxxu m rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a frvh ov *4p /y:xmf ld s72hf+.svdmgw/5equency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chun7x vms. dy2hl+fg mf5//v: *ph4sdvwok 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 1(y4xbc.8 v3q cxha jkfigure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Eaeh7 8j+ty;up4 : sblk(pl irp)rth
(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 783. o3 ssu 6md dnyk;nwnv4rlof moment of inertia I is dropped onto an identical disk rotating at angular sssn6d.l4r8 n;kn uyd m33o7vw peed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4j7+ r,j dvj)cm $rev/s$ 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 *bgs :l1/ wsvjrotating merry-go-round platform of1sjg :vlsw*b / radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocidi+s11+ spa5buz 2b7.wp k qyek5t6 yuty of 0ewy s ksy5ki6+dqubp.bat p7+12u1 5z .8 $rad/s$ 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 5c ,dcczth;)p8pfo4k2u:eq1 m i (h9efu.xpt 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?(r9ek,p.t2u :iftuc5qm) 8hdc; c z4px(e1 fohpound 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 itrp k+apjh*5 myi )8u4n 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 ij-ak l (omy,hhv6v7gw9w0p7 $ 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, initiallecx/w2o6kr 7a3 git6zy at rest, that can rotate freely without friction. The moment of inertia of thegex62awi k 3c/7r to6z 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 edge of a 6.5-m diameter merry-go-rouj()xq*jn2 a kfnd turntable that is mo2fq)knxa jj( *unted 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 with the end of the rope c5vyea1 fo(b1lying on the top edge of the spool.fob1(cy5a1ve A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth+bhlvc5zcb *t33k fj* such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axcj 3*l*tf53+zb cbvkh is) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from reu*ppuk64a . iqst 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 in the shape of a uniform cyl 6 vxlop4rbfh 35b-qq z bb;cs85.xkd7inder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the mobr.5v 4;oc x-87xbpl6f sz5qbq 3khdbtor.    $m \cdot N$

  (a) A yo-yo is made of todo r,t:dd/r, wo solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end o/ dt,or odd,r:f 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 :) :rd o6ttpjpwheel ($\omega_R$) 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, buowr 63mi dph;503qucs ml- o2tt.vbe 6t 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 its mass in the process, what would its rotation speed be? Assume that the star islsotu . r 306i6mp5mvb-3q;ewdt2och 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-pollutv)k);nf c *omlion 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 cylindrical flywhl )fok*;vmc)neel 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 s7k,hmbu z5z6 m*b w+g$H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at sp szgvj,kug*ayn. a(;: eed 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 pivo ctlp2kb5j7/3j zi2ray2 l 8lgt freely (i.e., we ignore friction) about a hinge attached to a wall, as ij8tl2 352i2pc/l rblk zyj ag7n 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 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 fl/y;rmj ej)w9 bagt+ e9oor, and we want to exert a horizontal force F at its axle so that it will climb a step agai)9wmee;tjg+9y rb aj/nst 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 t( ugy41c+ glvm.t z(buurn with a radius The forces acv.g1u( mtb cz (4u+lgyting 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 1.5 m and bdl ;fzynt9;+ fegins whirling the rock in a nearly horizontal circle above hi ldt+zn; fy9f;s 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 soli ii jhn,5l)gmjc 3hb9.d cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculamcbjgh3i.n9,5 ) ihj lte 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 c ie z(1a ii-uotxx k7,vcez),6lutch assembly which consists of two cylindrical plates, of mas1 -,iei axecx,v)(tuziz7ok6 s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the loope urk:1k 3wl2ucd rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop :wrk3ul1 c2k uwithout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumdxhg;)-g)u4i 2c vmoc e $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifor gut76 v,g5cu9z:srnrmly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was95 ucg:u sr6tzgn,7vr 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