A bicycle odometer (which measures distance traveled) is attached near the whec4q50xr+ln sl9ryw c *ui8l9dy/* jkvel hub and is designed for 27-inch wheels. What happens if you use itvrl+jiwsc5yn u cq99/ kl0*yrd 8x*4l on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular ve9vqsbmxa-8 j+z5jtz jc 75m7ulocity. 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 magniz5 9xtqbumj75 sv jz7-8 +mcjatude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the acdq:w h1w 2ys.ngular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a :v6m uor3f lhvd)* az6larger 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 b8-r aie0f kr9mptx3b8 y ;hzt,-x*xtsit-up with your hands behind your head than whenix8 t0, bma9 *tk-b8pz;retxx r3h-yf your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven spros2ldl9l ( ptc2 wkg.b2ckets 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 p9.tld(g2lbs22wlc k it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on bein :jyg1uzrpdn qviq4/ebe26) 5/p/z ohg able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of ro)qvu : hzge/p/ie/n1yzb4 q pd52o6rjtational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a fqq 7fd5 )ptm0long, narrow beam?

If the net force on a system is zero, isct. t4pe9q .zw the net torque also zero? If the net torque on a syste. .ewq9tzp4t cm is zero, is the net force zero?

Two inclines have the sam.4,tc cxjnr1a/8 jvwhe height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the h.1/8 wvjt ncj,cxa4 rbottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an im4gs j:hx- k4jmhe2,e ncline. One sphere has mmsj 2j4,h :h 4xkge-etwice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the saxn-hq3h1u0rczg , fn0me mass. They start from rest atnz x gq0,hfuc03hnr 1- 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? Which has the greater rotational KE?

We claim that momentum and angul97 cj3pt3iypa z (revw30;ufsm6p j6iar momentum are conserved. Yet most moving or rotating objects eventually slow vps03erpu6mi yc3j 6(9 z;p ijafw37tdown and stop. Explain.

If there were a great migration of people toward the Earth’s eqn)og53gx+n0 kaj de:n- +nrr17jpydm uator, how would this affect+- o+ :gaddxrn njnm301p )7e5kjrgyn the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotation,quumul. g6g: when she leaves tluumg .gu6,:q he board?

The moment of inertia of a rotating solid disk about,wec0 xs6+ysd an axis through its center of mass we+sy s0, x6cdis $\frac{1}{2}WR^2$ (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 6afwq*ivj75./ sfxrwmoty*42 e.m kgoutstretched hand. If you suddenly drop *m/gr 4is wmaqefv*7 .65o w.2kxjtyfthe masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow andk3dgmqs182qh edly 2-r+u+dt the other is solid. Describe an experiment to ddr+q t8 +eu mys2 l-d21d3gkhqetermine which is which.

The angular velocity of a wheel rotating on a hol x 9izw(/hh6grizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration poigwliz/h6(h9 xnts east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freypd.;u6zfil 4 t 2;urnely rotating turntable. What happens if you walk towf;i rupuz4 l2y. nt6;dard the center?

A shortstop may leap into the air to catch a ball and thh xiwi5wd4q m3mzoz( 2v */ed/row 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 xmmdqwz/ied2w*4ziv/ o( 35 hthe opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a helhg0s:ns 3rto. d 8fxk7r01jr ) x-bvmlicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can fx:dhb)xsls 3n k.7tg8omrr jrv-0 10 operate to keep the helicopter stable.

  Express the following angles if ef8zg0oj r+5n 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 because of an amazing coincidence. Calculate, usingk 8yizum+04j h the information inside the Front Cover, the angular diameters u8 k zjy+mih04(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 frh +-usa1fb3a:usdi+k y j 7c,bom Earth. The beam diverges at an asu3b yi,b1 - +aachj+:7ksduf ngle $\theta$ (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 ra+m 50 e4rqfpwbc1e 6xate of 6500 rpm. When the motor is turned off during operation, the blades slo +pe56b 0mefc aq4wrx1w 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 anothe0gg g)kp43 rik ,zxt,zr child. If the ball makes 15.0 revolutions, what is i i3zzgrpkk, ,)g xt04gts diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km.ipeaf7hidd4tp y)-hb h.o40xu)jl 0q+yi (0w How many revolutions do th4 hq0. 7uf d) -p)x0ojepyh y4iiw(ta0bhlid+e wheels make?    $rev$

  (a) A grinding wheel 0.3506jcmer wlx2e544- ygunsh)y :m eb4y m in diameter rotates at 2500 rpm. Calculate its angular velocity i2m5)6y u4rw yc4 e- s0eghjxbmy4nl:en $rad/s$ $\omega$ =    $rad/sec$
(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 mak7g1o jdw. /p boish-ir 9,la4kes one complete revolution in 4.0 s (Fig. 8–38). (a) What is ths1 ,hpw/d.ob7kiji4o gar-9l e linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around24pn;5m r: l0wf/poo9 c jdxhz/.oonisuej:- the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ootinjq i(i(lo1 b 45 4f.hrkv;:qgd-rf 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 particle 7.0 cm from the axisd8 xksghd)a .5 of rodxks5a.h gd8 )tation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center o;b9i 4l 2l q4fgu9kxwfrom 130 rpm to 280 rp o 4l9k4;xiqf9 uwgbl2m in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiuskyljahg *9 7g. v9gc/8( la,ajrhcm,h $R_1$ 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 aboar xnxqv,6x z;kqye-7sncf *1 8td 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 revolution every mi ny6 xxq8 ,v7tqs*-;zc1knxefnute 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 frox6zhrdi 00g*t 4awep.3q b4 dem rest to 15,000 rpm in 220 s. Through how made004t bpx.di4rz *ah 3e 6wgqny revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5*r4 8wqyi ta1b r8z6fh 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 1dnfq65oclmt9z, ib 9the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete re z,tl9m69bid5cqf 1onvolutions 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 unifh g xu,)d*naiipyz4)g.-i j0/g muz3formly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this fgg0y mg a.i-xu* u4)i),nzjdp3h/z itime?    m

  A cooling fan is turned off when it is running at 850 i; zb/ x8z)hyh2 vldgoa1vv0+rev/min It turns 1500 revolutions bhl 1bh2 + ay)z/v80ogv;iz vdxefore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduce 1)- plpkop;tbs its speed uniformly from 95km/h to 45km/h The tiretbo)1-pk pp; ls 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 z ma7jnmj7 f6iafks3w vv0:(uh(4 ;ubthe car reduces its speed uniformly from 95km/h to 45km/h The tires have a dia(w0 j n( afvmm7uau 64:z;fhi7v jsb3kmeter 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 algjpf i0 i74;kff10qi ll her weight on each pedal when climbing a hilifq i0lki41;f 7gf0jpl. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the enp-kjg(jeh dz 9nd u654d of a door 74 cm wide. What is the magnitude of g(-dh6d9zk j4 pun5ejthe 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 whg6n f 9:bkeks(hdnjbg7kr3s6)r:s,veel shown in Fig. 8–39. Assume that a friction torqkdfbrbk6s n(vsg,k: 69:7 )rn jsge3hue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are atsmjk9h 8 f*bes8 xme20tached 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. Calculate the mkf9bmme0s8eh jx*2 8s agnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightenixtew4;+ v:n b0v/v cezng to a torque of 38 b0c e:v+vz4/v et xnw;$m \cdot N$ 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 08 6b pelg (ozjn1y,6uu.648 m when the axis of r ,z(nuo68gpyb ju 1el6otation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diaq-syca4mg g24f ;us 0mmeter. The rim and tire have a combined mass of 1.25 kg. The mass of the h 2ysucs0-q4ma4gf; mg ub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of eeba :p*3 eiba1go+p1a thin, light rod is rotated in a horizontal circle of radius 1.2aagb1: ep 31i+ee* opb 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 potte08)9esdvz dt wr’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her han wts8z edvd)09ds 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 ii2om4sj 5wfnsk4o ,(h h)d)*:f o r9cec:fxjof point objects shown in Fig. 8–43 a e2micoc 4rf9s 5:*(hjiowds:f)kx, jf 4 nh)obout
(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 consistsglhgln1c.-5k+ ;dz t h of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correcnbjyuho/ud)b s7v pr07e g)1c5( o2vb t 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 rocket if the satellite is to reach 32 rpm in 5./2do p)bvh7su n1 roy(0ev)g75 ucb jb0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder wiswsj st ,l6e.5;ue fhr:f6g)l s,if) lth a radius of 8.50 cm and a mass of 0.580 kg. Calculatigf)l 6,swsestlhjl) .;u6: fse,r 5fe
(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 resis2a j:r-hxvo 2imr6 yt*9j9 4ll)apmt to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merryfcx6,jmia3do.r-qb m p+dp 0+-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 6q d 0rmb,+p ocj+ixdp-mfa 3.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 frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is evoz5rfx ,-zc.kentually brought uniformly to rest by a frictional torquzz , k5of-c.rxe of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-k y, mu,obp6n(hfq9h: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 9hvx 8 /rk/ajlsolely by the action of the forearm, which rotates about t8/h/ jk vx9larhe elbow joint under the action of the triceps 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 be considered a long thin rod, as sv7j1vy ek5j .mhown in Fig. 8–46vyev.7 jmkj 15.
(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 two0awv:6 rmk/ 3r: 9xdcojju+wv 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 1-mp;vyz-o5ja bfga*9r y 7ae within four full turns (revolutions) and releases it atjf9-rym;-o5 7e1zv*ya bagap a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inkypv.ik 7 yj 2;oy/fp myg,kd uw-ydh )d9-p(1ertia 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 :l h)y0e2t 6jasxx 3 r9zi6qi tcn-td,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 y. t7ts. 5s fefa)ry:pslipping down a lane at 3sp. e. )ayffy5: ts7tr.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respei)uz* p/62amj po pif9ct to the Sun as the sum of t ) p/2op9mip*z6ia ufjwo 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. Hn+ t46l efdk*row much net work is required to accelerate it frol6 +4* ekdnrftm rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.2yjmnc52qe b- 0 cm and mass 1.80 kg starts from rest and rolls without slippi5cb2 2jyqnme- ng 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 balanc35xqs w gb:*jued vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the ups:q* x5u3jbg wper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum 1af+ an 8yf1f9uw (mdcof a 0.210-kg ball rotating on the end of a thin strcf9daym18fa(+1wnu f ing in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheelt7.n*sg9lqb k of radius 18 cm ws*7q . btkng9lhen 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 si:jy,jsps8a*z k-d f r4de, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a 4yf*8,:- djr sza kjsphorizontal 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. 8e0bf9 5jkdm0a *r x4tz–29) can reduce her moment of inertia by a factjk b0dxr5e ma 4*0fz9tor 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 ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate fr b 09,hc2gpq0m n om4pfydk9k8om an initial rate of 1.0 rev every 2.4ck q o9fg kym008pdn ,29bphm0 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 thro*rwv iffgg*- nsl6n /*ugh its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately sh*fl i6 vrg**gfn n-ws/aped 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 mome.+hs7 h0iexyt b vkwht1*/y m4ntum 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 momenzg ,gnt3f c1l0tum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is drxd6 v0azd q*s1opped onto an identical disk rotating at angular1sdq a6 0dxz*v speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atnlr,pk4 +d m*+u5n;axjk uh: e 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 t/j kzr)cekjs-d ;tr0 5fz:iu *he center of a rotating merry-go-round platform oft)kzrej /s-r5;0* kfizuc d:j 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 velocitd* x1x 4+hn /0v xbhw;mb7 3sjyv;dwgpy of 0 xw;xjws+h7bbd0vm x d;n3g1/yvh4* p.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 .8w gv8kq0:dauz xycbj7fx //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 ro7bwzvxg/kyuc8f8 dq a/:.0x jtation 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 120 /0 d g/fsxj+ce-rtkt li h2o8-$km/h$ 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 2a tur911xk :*yjwms i1e+ oyp6f;yek$ 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 plap 6xg0tcmmd+:n v4s y*tform, initially at rest, that can rotate freely without friction. The moment of inertia of t x vd4p*+:0yc nstm6gmhe 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 merrar axlgwn ;pmmlwn (.2;3; 0y5qpo/ah y-go-round turntable that is mounte0nw2agrax;35qywn (po/.;lpm l ha ; md 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 lying ,fqr,k5 wcdbw24 c6;s8l j1t e v*ugvcon 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 wi4*5q 1gc8sel,u f;vb r6c2 ,twdvcjwkthout slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces txd3t5t1) w )pztvv1vai,ei z 5he Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, tret1tp5 v1 zvxa)z)e5d,tiv3iwat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fk ro-lh1t0 sgaaltg )vqr +g*l(1oy/,rom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniformlwfcb565. ei4(rwz7(i aje r w cylinder of radius 0.20 m acquires a rotational rate of from rest ovwiejf4r c(w(e. l5za6 bwi 5r7er 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 )dtxx5(a:lk eqan4. ovq1u;lsolid 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 k;.dxx(ke4 lq) nq 5vaa:1 utlog 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 angular sp)1 ) bp1ksvxnzeed 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 mass 8eie 2-pmkvt+n9nh mr ;/7yx +b.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular mh /b-i+k2e9rmnn +m pt;xeyv7 omentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pon+bj1l 4qe5 9hq56uog9q3 s lt5e9yr gor8sdmllution 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 flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km withou 9g99rh53qoqmuee51nb lq+8 4otl6g r5djssyt 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 anxu 4gdmb tv6e93.m tqos)o :o, $H_2O$ 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 o4.h:qbfde bmm6hj:1 ge -;aukqc-4jin 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., a *s7) uqwe ir,ilm6uw d.r*z*we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rodw di*r*mwualzqeur *, 7s).i6 , 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 tgxr g egi;2w+,he floor, and we want to exert a horizong rg+ ;g,wxe2ital force F at 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 spx). pdje cu xntlr(, hc4c (;:lx)mp*zeed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are tpdjp:xu;()lc nc .le rx4) hxzc(*tm,he 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 sllw 2vaku9vt;sg 8lw w.34p3n ring of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, vw lwp4t2w3 .;urslk3agv 8 n9and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as ::oav 7 jtdywok 7b6gu79 kqxx.e2j9fthin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstk7jewxqa t:7 ugfj96 b d.ov:y29ox7 kretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrdh)h+ 1urtts 3va (c9iical plates, of mas913i)ch d+aru (tthvs 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 anlpvh;yeh6a1()ymo; 7h 2 u6skuwj9 wrd radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is t6jyk )u r wy1u(2 wmshal6;;h7poe9hv o 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 asstcu d-ipo;, f4s1cgyo 9z8a,gume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduc 2;, ybtwi9apav)w: rvzg(dz3es its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelez tvv wz9wr(2d;b, py)a ag:3iration 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