A bicycle odometer (which measures distance traveled) is atta xs 2t(sksq;z t0cdhr 7u 8q2.rz.vsl*ched near the wheel hub and is designed for 27-inch wheels. Whq x8t. s * 72ld0.tuzsc;2hsqvzsrrk(at happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular ve-g(os 9g6,a1vc2bpki1nvv fzlocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular ve2vc1- i,6a 1znk9 vsog (gvfpblocity 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 be described by a single value of the angul3urs8wm l ;q+z:izt4yar velocity $\omega$ Explain.

Can a small force ever exert a greater torque tk6ru 100 n-hjgn oqbrtl((ui-han 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 wha .8v(bo h57akjr37bkap7d+sy ugk 9gen your arms are stretched out in front of you? A diak(7kgayp +a5. vobkj3a 7r suh79gbd8gram may help you to answer this.

A 21-speed bicycle has seven sprockets at twclf c;y7.e,z he 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;c7,lfwz.c ey pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being abls*cs 5.g ml-ske to run fast have slender lower legs with flesh and muscle concentrated high, close .*5c -kgslsmsto the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry k b:2/j-mbo x6hnak)va long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If tn lzxg06.b8wj he net torque on a system isn gxzj086bwl. zero, is the net force zero?

Two inclines have the same height but make differn*osbkiy 00f k, ahx3d ,k9bk.ent angles with the horizontal. The 9 ykh0kbf.a o k0xn*bsid,,k3same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline0 .dvm mj4cow0 7zq /vz)2lb vp(kib1c. One sphere has twice the ri4l)j/vp w 7z0cc2o1z vq v(0kbmmbd.adius 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 qu5ywo d5 1/gwsame mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Whicu5g/ dq15 ywowh has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most m+r )r;a2rwzh hoving or rotating objects eventually slow down and sto)+zarr h;r2 whp. Explain.

If there were a great mp:54s 6l7z 0c3 h 8pcuu8ctpm af5ebmsigration of people toward the Earth’s equator, how would this affect ucbcp aspcflt0m75e:pzum8h 3584s6 the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rota v w9ei/h3z(nawmz dmc;g*+5 ation when she leaves thn*da(ac ;zwmh/z 5vgi3we9 +m e board?

The moment of inertia of a rotating solid disk about an axis thr p)ldxc 6 2mxc- d,m7za-e+ergough its center of mass is 2+m ldg-ra mx6,)c-exz d7 cep$\frac{1}{2}WR^2$ (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 ro2/uze a q-g45jmzf-ritating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your an4jr / qige-2zzam 5-ufgular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have thes91nnj s m1do1 same mass. However, one is hollow and the ot nd1ms11j 9sonher is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle poc (max(y5xo8wje: 4ln ints west. In what direction is the linear velocity of a point on the top of the wheel? If the anguly en 4:cxax5 wjmo8((lar acceleration points 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 opnwd 8+)jc-yfspk wadmz (*gog8u( s.ru) 2/ff a large freely rotating turntable. What happens if you walk townuw my +ugpfpw)f.*d gc2-s8 /rk)(j8osdz( aard the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he tgp)n hbvcc+9 utem* ):e l;8y): bwxglhrows the ball;g 8pv:+bywuthbcgm l elex:)cn*))9, 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 momen;b jnms /z(sv0tum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or mvb ssm/(z j0n;ore ways the second propeller can operate to keep the helicopter stable.

  Express the following angl-j sy y.mo(fce p(x/d2es in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because.pa nl90p:ax w of an amazing coincidence. Calculate, using the information inside the ppalw90.a:nx 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 direcpfzi 5ky+dyeqr- kj o 76/(q.qted at the Moon, 380,000 km from Earth. The beam diverges a6j+r./e k5(- y qqkqpfy7 izdot an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When th kgz5eldbt-m5/.c2c f;/gkck e motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blade;g5 dcceb kl5k/m/c-f.kgz2t s slow down?    $rad/s^2$

  A child rolls a ball.c)rb 05ac;:fzcech a on a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is ia. ;cbcc)h5cfze0ar: ts diameter?    m

  A bicycle with tires 68 cm dfr))8ug ks4t in diameter travels 8.0 km. How many revolutions do the wheet 4rdfuk gs)8)ls make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angulem ,k5 6e1jr+atxrk)t8ti8 d lare+tid t186a8lrj kx)et 5mk,r 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-round makes one complete revolution in 4.0 s (Fig. 8–38). 33i f nni q.qfzj4j.tmn k88:1qgx-qp(a) What is the linear speed of a child seated 1.2 m.qptfxik8 . n3z:j m 4qfqj-1ngi83q n 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) f+ bfz8;-ihub4 8dapwin its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a puxeg zvk; c *.w6cy0g-oint
(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 rofi/s ffqiq 3* 7l:7c1ttjcne/tate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,000 q:sfe ftnci7 3f q*t//ljc 71i$g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its clao)r b5j aqw314lcz*enter from 130 rpm to 280 rpm in 4.0 s. Determin4cl w*a1jqlb)zo 5r 3ae
(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 ld *m8,u0wcc 4piee -ffqp:w1 $R_1$ 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, astrona vk*70s.n xlvr94okkxs; 0yhruts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of x* s.kxr rhvnsvko l;y0k4079 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 fn*c qgb: rom, ihr)*a2rom rest to 15,000 rpm in 220 s. Through how hr:*n2o, bgr* ai )qcmmany revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm .+.vwm4m gqutpb xh/qm3dd4 ,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 whirling “hu,b q22rtbh/uvqgm 47nam7hg lg5: +tuman centrifuge,” which takes 1.0 min to turn through 20 complete revohb2:l4ur/gah tgt7nmu 5b 2m g7v+,qqlutions 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 240bl-/x/06 t:u3ka amghds+:y lzffj1s rpm to 360 rpm in 6.5 s. How far will a point on 60:f:z-s/s/b+gtxyj dk 31lfamah ul the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 154n7 jzfy.wl)bj mjgi) 5 (ule200 revolutions bl2z.) )ym7lei gjunw5jf(j4 before 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 red h f7kw9u5xo+huces its speed uniformly from 95km/h to 459kfh5ohw 7u+x km/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 car redu92 v6nws4txz i7 kci+dces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.t+vzn wicid794s 6kx280 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all hen.q 65v y llfg8ku74obr weight on each pedal when climbing a hill. The pedals rotate in a circlu 8v 5yl6ln .7fkg4qboe 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 end of a door 74 cm wide. What q6l21 qf+-vf0o(b r fpdsrp9 ris the magnitude of the torql 1foqs 0 -db2f96rfppvrr (+que 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 shown itfgvtg,wt6 ()-vvh* b n Fig. 8–39. Assume that a friction torque of 0.-w) g vbtvfv*h6(, ttg4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the endy,w m+:ts1nml3l3l wor/w cr;s of a massless rod which pivots as shown in Fig. 8–40. Initially the rod ic nw1 m,olw:l+ sl/y;rtr 3mw3s held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tig6 fgl)a lk6+z: ,bn-*tpb +dsojxde)khtening to a torque of 38 :g)dl*f )tebnpj6z+, dkobsx6 kal+ -$m \cdot N$ 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*6p dv+vp6p vj3tdfbr 8)og2w sphere of radius 0.648 m when the axis of rotation is through its center. pv6 pj*)pgr28+t3 bo6dv dw fv   $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel1fqoy 1 jk6hn3 z4b+lbig0po4 66.7 cm in diameter. The rim agqop+0fnh 46o1lbzbi4k y 1j3nd tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rofbehw,;f4h1 o tated in a horizontal cir4 bwef1;h, ohfcle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotatingnv5;.uqtb -f2l5jkcr at constant angular speed (Fig. 8–42). The friction force between her hands and t f j bvt525q.lkr-ncu;he 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 a z2dvl(7ptq0ph-,fdpoint objects shown in Fig. 8–43 aboup 7qda ,2hvpdtl0z(-ft
(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 consiss2zf80j9 miz lr7okz7 ts 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 cylindu2yqjgv1o( ; hp.nj+jrical satellite 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 rocket if the satellite is to reach 32 rpm(q1jnv+;jo gy 2hj p.u 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 and a mass szhw0 t1ympd-,mv z (2d7wd *uof 0.580 kg. Cadth m1,07zsv d-wmpudy 2(*zw lculate
(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 frol79kk ar6. xj)izx; /voucp0qm 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-driven merry-go-round anda*p,gbyr lpz q6/.x8 r is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torquegq r*.8ax/ l,pbp yzr6. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor ronr+ogw7dgd b840 nmp/tating at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torq/w0m+ndrp bg84on 7dgue 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 accelerasl(1 sie0s/ 5sk x.celtes a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of ff /:e;wn.fmqthe forearm, which rotates about the elbow joint under the action of the triceps muscle, :;q. fm /fwfneFig. 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 blada8nj7zpu6+8;f6a-axacg7 1 dm voevz e can be considered a long thin rod, as shown in Fig. 8–46.n +68zaza;g v-6 c dx7 fvueom1aja78p
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two mas)5) spgpd/maqfyvr1e6 vkv y g22 9hm8ses, $m_1$ 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 accelera1qouo*qhy ;u6t p-: yates the hammer from rest within four full turns (revolutions) and releases it at a speed of 16-q pyou;t *:quahoy 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 of z nd-/x *bbvaoisg:lia /h 7pt;(1v; v$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque ofm;of)n lhm; d8 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 r yh9k:xg9 ee:,xvai4fm0 raxy(rwbt: -4/ cj badius 9.0 cm rolls without slipping down a lane at tkmwej::vxy 4x f4- 0r a/9 9bercahiy (xg,b:3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as 6 -bk+ntq/iqj-psdt 7the sum of two t- +n d s6p-kj7qq/ibtterms,
(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 nebs4mz)y8 d+ec t work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylmc bzd+ey8s4 )inder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and y mxo6q 2yme*t-,h tz+1j nz1if-7fpfrolls without sl11q -e6m2y ff+m* p7-t xf y,tjiohznzipping 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 starf(xp pbiezssfe0 3q8)z01nu( ts to fall and its lower end does not slip. What will be the speed of thes00z fxfnp8p 31 z(s ue)qi(be upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin sz.uid as2qj/rdwq) sy 96w7:q tring in a circle of radius 1.10 m at an angular speed of 9s :/ .qsq2zrddaqj6w7uyw i)10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cyliu2nau :0qgq.kta 9 0hwndrical grinding wheel o q2hauwkn00at. g:9qu f 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 tha (p;l/r(mid8sm; ntt mt is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the sptm ;dns8r (/;t(miplm eed 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 her momenzph i:/v5xv +ji)x 5bgt of inertia by a factor oji:i x5h vpx v)zb5/+gf 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 rotati e-u/5ly isnm9on rate from an initial rate of 1.0 rev every 2.0 s to a finalneliy5 mu /9s- 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 gram l2aee 6,.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 shaped as a agme.ael ,r6 2flat 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 sbd qih7v)yj1 +a+.votpinning 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 mxz (t bf-aj z55w+pdg;omentum 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 iner6sp ,ww1gu8coq;edo 2tia I is dropped onto an identical dis6cgeq swp2 ;,8ud1o wok rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsik:r:ix- e8h552va1de gpxq c at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the cent+ /w +vk)d t+lpmgqx;0j d3cve9k /egver of a rotating merry-go-round platform of radius 3.0 m and moment of inertia3tj q lk/ev+pvgwc+d+ x0e /v; mgk)d9 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-rode 2ifn,w8h 8wund is rotating freely with an angular velocity of 0.8 nwdfw,h28ie 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 aboc)9 s (iucm/;v o;vtdjut half its mass in the process, and winding up with a radius 1.0% of its existing radius. Ass )9com;c /vjts;iud v(uming the lost mass carries 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 involve winds in exce w;0dlbw l4*cafcr*n7ss 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 gn+73cycesx (xi()n m$ 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 platformxj2 ap6+3cx gy, initially at rest, that can rotate freely withoutxyg6j+x32acp friction. The moment of inertia of the 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-rounvau +ndlx 7l3,d turntable that is mounted on frictionless beari ld+v7u la,3nxngs 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 wkpq2e mx +o*p-.z7 wu vh2f2yeith the end of the rope lying on the top edge of the spool. A person grabs tq+7fkz2y2w. o-m* u vppxehe2 he 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 such that the same s3 vnr9 m:q69od/y;c+nyywx fbide always faces the Earth. Determine the ratio of th9c 9wxb; y ryofndm+v6nq:3y/e Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratesl+iq1:;-ck; u.oswo 8ygvfh u from 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 shapus f :axjk)9g1e of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constanuag9)ksj:1 xf t angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disksr 3ewvzfe61x vn7b3edo8 . l,x, 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 energyer 313nz wfx7 6vbe.ex,8oldv 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 t+y71xxsyn;-pt )lgu0h6h w,uy* u khkhe angular 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 great, were rbmeezx. (b 4-qrcuw,/) l+xh kotating 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 tl-u .b(+hc wz / k)bx,qrem4xeimes, 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 enepoo7*cl fco -m+di a,:rgy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform c7+mc oflo*pai,:c -odylindrical 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 a- s*ps2ejwrm :gz/t5s,cm p1un $H_2O$ 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 rol9+u vgt;oexzhuzy 9qn06 *)zkling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and len0o8b/n lvg 0 kad.wks:gth L can pivot freely (i.e., 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 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. [Hin0 v/ko8 kw0s.algd:nbt: See Fig. 8–21g.]

A wheel of mass M has radius R. It is stand tx6jmz)gf2c )ing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has hxtjfz ))c2g m6eight h, where h

  A bicyclist traveling with speed v=d+fk qc s5gbw ,jna./)4.2m/s on a flat road is making a turn with ad5n.,f b+/ )cqwk asgj radius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 ,lsn; ,hpy, i zg1.kw(jm*zozm and begins whirling the rock in a nearly horizontal circle above his head, accelerating sz.;y*zpz hw(mlg,,kno1 j i,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 cylinde:k*g;1,3x:kllsx lssqs d p5er and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular s1ss;sksgdl l,:3plxx5*kq :epeeds 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 cylindrica+d40j:10 rh*k4uf evuiavl, zy 4lojpl plates, of vif0hu 4okzlp 40 yar*uj1 :4dl j,+evmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 looped rough track of Fig.k6, yckq zb 9h.t2ygd0 8–58. What is the minimum value of the vertical heih.d c0k69 b,gy2 yqzktght h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumfx, i0 sqz+oyk69g9wfe $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly frrvlyodm8rzm g80o6 +5om 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleyod 6rrv 50 8g8mzlom+ration 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