A bicycle odometer (which measures distance traveled) is attached neamgtbp,zl z -3*3il* gu bf1km8r the wheel hub and is designed for 27-inch wheels. What happens if you use it on g l*z-m3bmbuip,z1f8l k *3tga bicycle with 24-inch wheels?

Suppose a disk rotates at tlr 1)hcm) mmbi:+w 0+viu+cc constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude tu c+ ):bmci+rhc1+lvi m) 0mwof either component of linear acceleration change?

Could a nonrigid body be described by a sf(x5b67j awg9c) t (fm1rie ksingle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque fupne. m or 8-*jelxz:)5bki;than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-upfn3h5a b1s/u/mcds3x with your hands behind your head than when y 5bms /3sxfcdna3u1h/our arms 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 whe (tkw.r 8m/poi1 /ttnbel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small fro1omkrb/8ni(p/ t.w tt nt sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower leg8sd n 6mlb-uk+s with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous nmsb-8ul6 +kd.

Why do tightrope walkers (Fig. 8–3 v2n0- bo0k;07ui eqez6coyevbn g.( f5) carry a long, narrow beam?

If the net force on a system is zero, is tu6 qw;.atpdiwj /,lihx1f 8w, he net torque also zero? If the net torque on a system is zer;jlwih. p,,/wquf aw1ix8td6 o, is the net force zero?

Two inclines have the same height but make different angles with tx 2c8u b//d4nw k,cpzna5l)t;ewhf (zhe horizontal. The same steel ball is rolled down each incline. On which incline will the speexnc zdk /;ce, b2p8n 5 /z)fhtu4w(awld of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) ujvn (hi ;/nx142lbaidown an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the ib nin /1;a2lh(xv4 ujbottom?

A sphere and a cylinder have the same radius w)f9vc,,suhyat : ,+.5bxf /tmn kic kand the same mass. They start from rest at the top of an incline. Which ctt,y5is, : a+ 9,.kc/fhxkwf)umvbn 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 angular momentum are covpe 2m/ a +8w5nkp4eoonserved. Yet most moving or rotating objects eventually slow25/poemvoawpn 8k e +4 down and stop. Explain.

If there were a great migratiygul jq17nxnaqv+(5 ;on of people toward the Earth’s equator, how would this affect t5au+ qyn1vg ;q7jl(x nhe length of the day?

Can the diver of Fig. 8–29 do a somersault without having ;n7 wmse+nde71 ,xaqer. 9f,iy w4/gezt5 rs bany initial rotation when she /gswt e,ys;r5n x94 e1 7ei+rmna.f ,dqwze b7leaves the board?

The moment of inertia of a rfu16es9pk r kt5+yk0wz -ksve h4ec /9otating solid disk about an axis through its center u esye/945 csk vekwz prktf190+6-hkof mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating st 4lq5ly*y 4 l9bhtoq2vool holding a 2-kg mass in each outstretched hand. blyqh2t ol l49 yqv54*If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and h6x:g5tv/trwn ave the same mass. However, one is hollow and the other is solid. Describe awngrvx/6t 5:tn experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points8xdju+0e7do9 p ta-yu west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decre 09+yue ddu87o-j axtpasing?

Suppose you are standing on tn8a92j xs+yf4h h.-jhrg*,pfof r)sd he edge of a large freely rotating turntable. What happens if2*a-hjy8 .f,donp)sghrf+f9rx j4hs you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it q5w2mekb p 7pw3i3;x avuickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips anpwbmwi7av pk 533;ex2d legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of courx8(f ed5g1jnservation of angular momentum, discuss why a helicopter must have more than ogjf1e5d x(u r8ne rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles rgq;7s na o*b5y.ahg7in 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. C.au,q r , p:gvtm0qy5balculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as see5qrpq, va,m byg0:.tun on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 3xu uii1vav7 -euk28)g 80,000 km from Earth. The beam diverges at v) uv ki27g-i 81axeuuan 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 the motor is turned okgy, c*v.ggfra9- rj fyf036v ff during operation, the blades slow to rest in 3.0 s. What is the angular accelerat vk c fy- 0g9fga*fy.rj6gv3,rion as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball mak4 kuc 6d)x9y/fgtoyr :es 1xu 6ry4 y9/c)df o:tgk5.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travj:kg u4w xw(xh/npw-662 y4 rlfds;o ltd1n;mels 8.0 km. How many revolutions do t dt nw sxh/m12pwlrokxujy;n g:4 lwdf ;466(-he wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Caz *y x17vb:t*qa wtlb/pgr/8f lculate its angular velocityrbwbt /8g ylzqf*7*:/xvta1p 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–ovaf7mczt b8 p .eh/9) (xhqb-38). (a) What -px zvac( em)q8fbh7ot/ 9b.his the 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 arou96l(r zjl9;xna g* aphnd the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spemc r2 1zqte3odz +(r;red of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm 0f:9q5d r,ajn px+ edp8s zoe8from the axis of rotatp z xsdd5qep08+f9o jn,ra:e8ion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from gr si4;6mey.x0 x k2kv130 rpm to 280 rpm in 4.0;ex0 ryi26g .kvxskm4 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 radiu trg +7 vq0.j lhz82jndwiytebx+0p32s $R_1$ 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 Moo7f3martcc4djt 4d,g1n, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to d4m3 fdadrt, 71gct4jcistribute 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 diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Through hu0turj z t +n5 hpcdt755f rn-2k8l3dzow many re f28d75pkzhr+t 5rtnc3dl j- z 5uu0tnvolutions did it turn in this time?    $rev$

  An automobile enginey +, sprnmv xvkr3h-)3 slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in i 3;pq7g -b gdzni4)gsa whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before n-4 gbzi g;sgq)3di7preaching 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,v uo4esbn4 8g uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edgen, 4uo v8ebgs4 of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 85cab pua:/t4l3j u0 5im0rev/min It turns 1500 revolutions before it comes to ati ua/5l4c:bp3 u0ajm 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 revolubrb37 rwe1lg;tions as the car reduces its speed uniformly from 95km/h wgre7 b;blr31 to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly fr g+xkv9lp /tg1om 95km/h to 45km/h The tires have a diameter g+p/tkv19lxg 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 all her weight onzj 8mgj8s2 ,pw each pedal when climbing a hill. The pedals rotate in a circle of r88sj ,mzpg2w jadius 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 cmtjb 3mrjy11ocznbghz90d- g5 x6d6xd*u-f d0 wide. What is the magnitude of the torque if the force is- z910ncxh6g5xdf0t1-d j z3jodgry6dumb *b 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 m,h da;cp /x/jof the wheel shown in Fig. 8–39. Assume that a fric /j, xhmac/d;ption torque 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 endx7vl s,waox o mpo,*.a;ip2q2 6w/exss of a massless rod which pivots as shown in Fig. ws,v;x.qaw x2o6e l,m*poxs2 7 iao p/8–40. Initially the rod is 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 headrf;fk b9m ufsl/g0p 8( of an engine require tightening to a torque of 38 u f/ (8mblfkfg 0psr;9$m \cdot N$ 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 a6 nenvd(i,q 8z 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its vn 6dz,in q(8ecenter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm inqp 8bs.)ihv:c diameter. The rim and tire have a combined mass qh icb.p)s :v8of 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 (o(6ecp7by76lqam1;lr u8 usy u4wzc rod is rotated in a horizontal cir;6y wl8o7bsecca1 u 4zq7uy(lru m(p6cle 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’skc6 g rv8pi5 d-:g(z 4wi eb,k12arqih wheel rotating at constant angular speed (Fig. 8–42). The friction force between her handswhge 2-q( rg i6i 5k48:rikz adcp1vb, 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 c+5xm ihslic:js2z ,i ,ajehw8ek5( 0inertia of the array of point objects shown in Fig. 8–43 ax,5m wcs iz ah2,jh0e: 8js5il(ik+cebout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whoqtr :7a5 vxp)rse 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 cylqkfmxoxu -r m f,.t:2,indrical satellite spinning at the correct rate, engine,xrokqm:x, ft m-u .2fers 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 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a masshd7bvvor0pc/ 8f7 ggn; a;l bp(8c 3zu of 0.580 kg. Calcul gc ;f8u;o8gbbp/zv7dh(c 3lpvn r70a ate
(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 7wf6;hdsi0 oprest 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 and is ap1aj rm0c3gz )ble to accelerate it from rest t) 0gr p1cmzj3ao 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 torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor robm.4nw h,r6k774f-k vkbf 7ed(vrq gh tating at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictionkv7krmwegqhn(46b 4k f 7,- 7rfhv.bd al torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 gj (e)6 znu0vpgllzn1w0+,vf 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 ball is thrown solely by the action u q2 ldj-5 nkw84gc-xmp1f(qfof the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–4j8- gudl knfq 5p4(12 xwc-qfm5. 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 l wj poc)zols.y/1m:u-ong thin rod, as shown in Fig. 8–46.wm:pjzoso-.l 1u /cy )
(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 ofe5. kbngr pwf 4h)i. zn2vs9db r b4qgd()cm7( 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 accelfokhjav)72 r8erates the hammer from rest within four full turns (revolutions) and releases it at a speed of 28h7r)a8fj2v ok $m/s$ 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 i*g3.m ybiz4ic bnd:9 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 develops a torque0(bgf h/myts7 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 slipping down a lh ,98onzs))q+ecwobzp 2(v ntane at 3.hc8wz9 vo(t)np,2 )n+q eosbz 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of tl2x ;cyedu2*m he Earth with respect to the Sun as the sum of two term*y m;dlcuex22s,
(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.v(pbm7hrcu1 ( How much net 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 cyc(1b( ph vurm7linder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg swrf2(ffd6d9b tarts from rest and rolls without slipping down rf(f2db96d fwa 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 )kn3 iu6 nw8ajth(1 rdits tip. It starts to fall and its lower end does not slip. What will be the spe6dhkjun3a8)1rtwi( ned of the 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 th yv5 v z37 mn/ov)2+jttadp3ytin string in a circle of radius 1.10 m at an angular speed of 1t/mpt)yt 33yvna7j2 5zd v+o v0.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrvr dy9; . c4sp43qptkqio;zj2ical grinding wheel of radius 18 cm when qvik2p pcq4rs.; 4ytjz3; od 9rotating 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 pl ;sd/cd.21 bailir3. h yl8wiiatform that is rotating at a rate of 1. blh 3d.2 airw1/cs iidi;8yl.3rev/s If he raises his arms to a horizontal 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. 8–29) can reduce her moment of inc1/eds.+yp 6ug;j kb9 p vofr-ertia by a factor of about 3.5 when changing from the straight9ge jkd-;6r.vu/fpsp y1 b+co 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 increasn/h fydom9 6f mh.v72al6:hlhe her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a fh: hvm9al. nm2d 6o7/hf hlyf6inal 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 c a(o xohk+ib;3etn o wvi5;0d-dr: (uaround a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a unwk +0r xc5ban(-heoo3t;vod:dui; i( iform 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 a8k23xddf g7d4jgaz (um: ca /ht 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 angulaiq24 u6by+wo ir momentum 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 ks, gfdzj:1j :I is dropped onto an identical disk rotating at angular spejg dz,: jk1fs:ed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 7ys h1of a+42 3ng.hd,8pnq hjtiuq2y 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 center of a rotfrrf :r6l *b.qating merry-go-round platformfq. lr:r*6brf of 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 velocity oflkt 1pbgx i)* g(z(uk- 0.8 i-tkg )x1uz g*pbl( k($rad/s$ 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 int r p+1et8b34z: wuhhkuo 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 1 zu4pe bk+3uhtrh8w: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 windsgt9 -ck( gv6mlq .jx/b 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,t5y 6l : ayixhzn5c$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely withojl8j e;(*lqh9q kgu e;ut friction. The moment of inertia of the p9q; jgk(hu ellq*e ;8jerson 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/t8 wyjcf bnsj7;fik(;6 4ouu-round turntable that is mounted on frictionless bearings and has a moment of inertiatjocb7wn/yu (;468;f sji k uf 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 of4zh t9k9,u1u4uxdsx7 ic1:iyalyr fut5 d3n 8 the rope lying on the top edge of the spool. A person grabs tht5nsx9zu d4lhrii11f48udu9xytcu7 a, 3yk :e 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 suqh zsf,l73-k/ pe *wgach that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axi* hqpg fwez7l/3-sak ,s) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates3r. n/uouyk wadeg0:9 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 shape ofwts+lu *ds h7ee 4lb2, m*dl;o a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculdou;bs+twl,l*4 e27l sdhe * mate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricalgi8k5qfl1amcbew 6aun;* nk;: / pj4n disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when 6na ak fk;u nw* 5n/e8:pi;4qg1cjmlbit 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 spefi:r;ak(z7x 5: 3ppm 8k ajaj ndy1lt2ed 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 dh5vmcpo) *2 yk-s 6dsof our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of 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 carrie sdop *y)kcmh52d6 sv-s off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobilep- //)c4o lawaje5*)snupe ud is for it to use energy stored in a heavy rotating flywhee-w d 5aesnl o)a *j/eup)4pu/cl. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratesjl43+2aclk)qd- ee* ipm-f z o an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is.re6bv1as m1 yc7b 0xz rolling 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 length L can pivot freelyv+m;kx g*m6/mf* hadvr mn6a-ds8i d/ (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 thea-v+ m6fsm//m*k* xr; 6iv dhdndma8g rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on th9(q01)f fdepmhm s/pb h dx s-zmx7+i.e floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it if1mp ( 7-h+/xehsbp.f mm z9dsdq0x)rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flamh+c,/x8op u jt road is making a turn with a radius The forces acting on the cyclihpo8 c jm+,x/ust 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 1w7:sg/sy or )s.5 m and begins whirling the rock in a nearly horizontal circlsg y/ orws:7)se 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, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body c: q .jh:g+lx9nsh;ijhhn/e3as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calcula ge+i n93snjl:c:hq .; hjh/xhte 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 cymc *owa/x9 g2xlindrical plates, of massag92xw com/ x* $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 r rho-csh r.,6rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the lo.6r r- ,shorchop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but - i)nxj*0qqxa do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformsbd*tt 7/7at qmay94ply from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelemtsat77 ayd9 b*p4 /qtration 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