A bicycle odometer (which measures distance traveledqgew/nbiq p:9f 7arfz 0w*3o-) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 2pq fg n793fo-iwae*0 :/zbwqr 4-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on tq ) br5tkz(kb )6w.b. 3zalwjthe rim have radial and/or tangential acceleration? If the disk’s angular vel k6.)rbtztlawzb( q3 w)bjk5.ocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body xemyp3g:mp6 hon :gv1+gn,9x be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explalm.aor p0x s,:in.

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 yq(b1uvuv4g83, iy b bmour head than when your ar4 3bi8mq v,(uu1bv ygbms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thrn5xg jv+7g eff9i n:q7b27yrdee at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which g9rqfn2vd+i fbjxn 7ge 57:7ygear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to 5 kq*ev k7qfv*run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the b5 *7q*qevkvfk asis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a longn l 9h2qcmw8otks)1,9a k,iko, narrow beam?

If the net force on a system is zero, is thcb+v)7qu1dkieu 3e 8ie net torque also zero? If the net torque on a system is zeeqke31+ucv 87du i)bi ro, is the net force zero?

Two inclines have the same height but make different angles we 65 *fq gej0ixcd7-vrlmcn u+6mro30ith the horizontal. The same steel ball is rolled down each inclinng meqfi d 6c0-rvcjrum5ox3 l7 +60*ee. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simomfs.0+0uw hr ultaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Who hw0 fsum+0.rich 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 hhn r5mr, jt:3save the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? W m5nts3 :jr,hrhich 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 angular mb e n.k lww5aogum-);+omentum are conserved. Yet most moving or rotating objects eventually slow down and mkgw5a l-.bn ;+o)uwestop. Explain.

If there were a great migratio5c8e+qld)h68qm,ia3n jt;cvde )ax d n of people toward the Earth’s equator, how would this affect tq)xe;8tv ae hin5q 8dadmlcjc3d)+ 6,he length of the day?

Can the diver of Fig. 8–29 do a somersault withou1k2 cxbpz2hf4 t having any initial rotation when she leaves the bo24p12 khbfcx zard?

The moment of inertia of a rotating solid d8-f, s qh)wnqc,xoi c6isk about an axis through its center of mass i q)f8- wci,h, sn6coqxs $\frac{1}{2}WR^2$ (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 sitti 0xw0y+6qemnfwf wk) 9ng on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, wi)+x6y q0f9 wfwmknwe0ll your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and hh b+e9dt ;0ogs+w* pzoave the same mass. However, one is hollow and the other is solidh o zs0+eo*w p;9btg+d. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. Inr fe dyd218;dxiq*o6d 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 this point at the top of the wheel. Is the angular speed incre2y 1* drddq6 dfxie8o;asing or decreasing?

Suppose you are standing on the edge of a large fre(/nuof ig87ywk8xptix8h88 1 gxio x: ely rotating turntable. What hap1iux go8y8f8ipk/ i x :8 (gwxhn7o8txpens if you walk toward the center?

A shortstop may leap into the air to catch a ball and s eq1kf z;7r4 zfk3;nfsx f/t.throw it quickly. As he throwtf re4xffs.n s/kq z371;kf;zs the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss whybc zui2pwm,xgk. 47: b a helicopter must have more than one rotor (or propeller). Discuss one or more wxpu2:k g,c.4ibbz7 wm ays the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) oqfuh4 s2n-a 930 $^{\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, usjj - ky2+n1imia4:8s8r/ ew4tfxrfpving the information inside the Front Cover, the angular diamrjp r4a/ix+2wm4i8fe j:-1yvf kstn 8eters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 3x6o1 6u.i1mkguo oc6apx.l z7 80,000 km from Earth. The beam diverges at an ockz6u.oim o1 67pg6a. 1xu xlangle $\theta$ (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 :ajdyra9zj z v4m-+4u.nd k;xlm* 0ur* dqp9xrpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is tzqd y9m:m.jaud k-n+zra4;*x9vj* rdpl ux 4 0he angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m tni h 51a/qoo)po another child. If the ball makes 15.0 revolutions,ono5hqa/p )1i what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Hou2t1- gt6 dw8bbt4a kow many revolutions do the wheels makb w26ta1- tdobgutk84 e?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its anggftl+-7m t ,bdultg -lt, +mdf7bar velocity 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-rout g jo.s:6z;ate p2y2znd makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed .e; 2:azpy ztsj26gtoof 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 velocit 9w;i-qguuq0q9 *olye xz mvi6*42o9t9ssvof y 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 speed of*)(m 7t r*2,gdjawbgv2ly+m hidnf r4 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 7tlwr** o4pk4oqf)v 1y wn5pe5.0 cm from the axis of rotation is to experko rtw1poq)4np5*5wf 4 ve* lyience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unif-pwmvgkkizv5fy3 ts)+ q +-y*ormly about its center from 130 rpm to 280 rpm in 4.0 s. Dev-- +s tk5v3qkmz*+y)wg fi pytermine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius*frq p o 4bvtkbe 16yn4*wi97s pua0g; $R_1$ 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 aboanglz 43ydc;lqv5f) t9 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 rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diamf d) ntzlly;c3 gv49q5eter 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 s. Thro q/.vg 2- elwm+mvtvz)ugh how many rel)- tqzvvg m.+w/m2vevolutions did it turn in this time?    $rev$

  An automobile engine slows down from 450/shu-+(z;jf -xrv 6 :1pwgrs.v nmld d0 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 highspeed jets in a whirl5d.k cc e) jr:3ys9nvdt tb*w ;)sovm:ing “human centrifuge,” which takes 1.0 min to turn througytndw:jcsvtk5.mo 9c:bv3;d*e r)s )h 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 249 k/p,,yqu;xo v+riuq 0 rpm to 360 rpm in 6.5 s. How far will a point 9+qru xi vqu;,/, kpoyon the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when itcpwxcm3bd bl7o. v bumta.h:4*2/by3 is running at 850rev/min It turns 1500 revolutions beforcam/lc34dmvx3u.b b2p . :yt*7bwb o he 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 reduces its of6 +lyf7i5 j//7o joxd3g-qwerg w .yspeed uniformly from 95km/h to 45km/h Tyo 6gief3 .xj7-f7o/qd w5 go/wly+rjhe 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 659 )g0/9d fg5iya,rvxxq m,xou revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80r,yxo5) f xm9diu/xg g0,av9q 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 puc mhth9df41bxw.3zz 1ts all her weight on each pedal when climbing a hill. The pedals rotate in a cir1w xh fc4mzdb.hzt319cle 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 foryq fea5 *,o+4pew.irace of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the forap w 5e iroy*+.e,fa4qce 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 th-z0+giwa ;pzme wheel shown in Fig. 8–39. Assume that a friction tgpz-i m;z0+aworque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a masslesr57 1 gkr(,i8zhy t j:xfwn(yss rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positi(y:s ,7t5izx kfygrhn r(j w81on and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engyjmj052d/(s i0d 3; pjb ldlby3py(sgine require tightening to a torque of 38 dds3jb i3 ;pm2yg0yl d(5j/p l(0sby j$m \cdot N$ 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 opu:t*r 6fr (hof a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through rf*6:(tr phuo its center.    $kg \cdot m^2$

  Calculate the moment of inerr(ny-td8 sdl /tia of a bicycle wheel 66.7 cm in diameter. The rim and tire have as rt d8-ldyn(/ combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizm(7a0naaxkx9s hm ,4c ontal cira4m97m0 ahk s(c, xnaxcle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl. w(ibpi+uvy 1 on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and thi(vbyipu 1+ w.e 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 s9vaiqo (.jp/t hown in Fig. 8–43 aboua9 ./ ipjovtq(t
(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 oxygenqlo c.tin)1e 5 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 corri8 .e9y1 zgeync erq/.ect 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 rpy.rcz9/ye1i.qg ee8 nm 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 a-a(rvai 3wk-0bqm7 t fz.1 ldhnd a mass of 0.580 kg. Calcd(w0bi. 7 kalm3 zvrqt1hf- a-ulate
(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,n49wfk- bfee/v2ikmb) 97eqkg ,+es x accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-dh r26/frwu-xd.k5nx acb2e 4l riven 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 ot5frw2uxbea 2 hrk.dxcl46 -n/her 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 evv 2qhajrm5jmyn 1;5m .entually brought uniforml1vm qn ;h5mjmy2.a rj5y 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. 8–45l4w3edd ht3y * accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ba1swm(fqfa (78hxh- bkll is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acceleratexf8(71hf wkmha sq(-bd 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 shown in Fig. 8t33 ze-mukwb:kowbn3 a3 n8m9 –46.9we8nmt3am33bw3 on bk-uzk :
(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 consis*( ) 9di(w9fqr5 vdqxego7kqqts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower acceler d6w1 v2il8x q8uhgbbdj7e9m,ates the hammer from rest within four full turns (revolutiojb,q l x 871ewhvg8bu 9mi2dd6ns) and releases it at 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 hasi,k orle0gxfom5q26c lq/k p8 oss49* a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develoosoc8rf a;u/1vkl,v ogi)3awa w:i53yai) y4ps a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of ma:.h0qeyy* g jbss 7.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.3 y.:h*e gybq0j$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the rb uuubuu zk4e:0)4j:Sun as the sum of two term4u e4):br0ujubu :zkus,
(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. H1tdp2mk h7y/y ow much net work i dmh2yk 7y1pt/s required 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 sjq2wfi7 ) f5ep*s+te.80 kg starts from rest and rolls without slip*+wt pf2 eqes7)f5jisping 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 and its 4 qt;nuu- dln// 9yklolower end does not slip. What will be the speed of the upper eo nn -/u49dtqu;ykll/nd of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momen2pn7jaukmal5d ;ty -3 tum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.tnj7a2m ;alk- uyp35d 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 wh8*6ybbrv;w s5yva g4fd*w q,heel of radigr wa5vfdq6*y ,b*v y s4b8hw;us 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 is rotatingkdy51g6*l p sh at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotatpd*lhky1s6 g5ion 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. abjk pw:ga; w32ufd)8 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position 8fk3ba2wgp)u ;a:wd j. 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 c 4/k vmll3q;drotation rate from an initial rate of 1.0 rev/d;lv3 mk4cl q every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating aroun98kayg k 6m5obd a vertical axis through its center at a frequency of 1.5rev/s The wheel can be ckky8o9gb 6ma 5onsidered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at79 xbguqp2h4 9up727myyzvsv 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 thep 3vm/44msu vwfle6( m9xodd;)in y8 v 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 jktnvz60dxh uc5: j): is dropped onto an identical disk rotating akt0jj6: d unh:c)5z vxt angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.l/b x0a1;5-rbdmogm n4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry- )8pn qstmv zl,da-o1;go-round platform of radius 3.0 m and momea1n;q8m p)s-dv,l to znt 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 velocity ri/x;.lv4pi dof 0p rid.x4v ;li/.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 intitq tn/ m;u -a +fnz7qq(r.hm,o a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass c.q+; mu7-n( tan,fq/mqhiztr arries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involvegyc 8k91m4 /atnf3epz winds 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 ,s o e;ks65xs qax(zc2$ 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, initqurz8f;ymq jum+-1 f.ially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform is ur1fj yf;8.+qmuqmz- $I_P$ 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 mmzwt:+bc ;6 n 8iyv-pverry-go-round turntable that is mounted on frictionless bearings and has a pw8cv 6 + mnyvtz-bi:;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 roppbndv27efdl+j n* q35n5by7 xe rolls 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 robnldxbe5yqn*7 372vp nj5 fd+lls 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 such that the same side always faces t +y 5 azlmz1g8je hdi6qh::ggl6-hma-he Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis-g:a -6mmhllg:idz 6hjhq5y+ 1 8 geza) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rateh0*rr3xv4;q kslspe n;j0lz: 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 rad;wf zsaohmc.e x14y -(ius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculach4em (wx f. s-zo1ya;te the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two so( bhx g4vc/fw8lid 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 o4chwx(v gfb/ 8f 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 aqc, zlm*o 26awngular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as grd8lm3ue 6z+k osr;)wgeat, 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-qs3l8 +6roe;z)wgdm ukuarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy+((lls frd3-a 6rimag4 jcw, f stored in a heavy rotating flywheel. Suppose suchrj+ (fsd ,l f- 4wi3rc6malg(a 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 illustrates an w ljp 9hs,4o85 h10mv5joefzw$H_2O$ 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 ag4mrm+az-)vyb pf 9 h9 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 f u..(a2c;tmsgg-q 1 .2n xtchg+b rdunh )d*suriction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–212.hh( bsqn ;u.dsncrc+1xg g magu-d*) ut2t.g.]

A wheel of mass M has radius R. It is standi7r4o q: nl q6,uohpx5rng vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a ste lohp n:o5x,u4qr76 qrp 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 :gt1 jwzjg)hfjfk )(.making a turn with a radius The forces acting on the cyclist and cycle are the normz))g ft1 fj. jk:wj(hgal 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-kghs zoo--,;kt *j (vweg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his headkvw-g t ;e,zh*so(j-o , accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rodsmxw91coo+bkl -5t/bx, making r5/x9kbo +1-xbmotwl ceasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical platefuvgcfq3s -ea; w,p;4 s, of magsf;qu4e, 3-fvac; w pss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 /59py; 0(n rgdvroor aradius 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 to reach the highest point of t5v gpr( ro0ayn9 /rd;ohe loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume7 -ootuf1t7el $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutio1 gzilw 1mq5zrik:.(d ef 3te5cx k0v.ns as the car reduces its speed uniformly from 90km/h to 60kxdvqzwet5 z1g . mi5erk.1l(0i :3fckm/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s