A bicycle odometer (which measures distance traveled) is attacr b78p; ewg/rghed near the wheel hub and is designed for 27-inch wheels. What happens ifge8; rprg/7bw you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim havx8,56n bx f:van,g ki8 izwvk*e radial and/or tangential acceleration? If the disk’ bvaf* , kzk86:85ivnni xgx,ws angular velocity 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 of3yv,qn3bmo gz( 8z.r e the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than pmp 4t2c in3a(ugo/vf 8uyck 3rs65-s 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 e 4gvseeuf leex-e, n6 m24z.*with your hands behind your head than when your arms are stretched ou*e- efxns 24 zgeme46e,.uelvt in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheebhepf+i-04n el and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? Ie+ pb ni0e-fh4n which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend o4emo4h+ s*xda77.vhp v: ubaqn being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageouq. xd:p4hsb*74aeo+m7huvavs.

Why do tightrope walkers (Fig. 8–35r+tyao*eh( p9:jns d: ) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also z/kzi i4/6-sdie7 v-ao -yissol/pq+ pero? If the net torque /-i id+4az /y/ipkios7 qsve-pl so6-on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontalzy gy *ha:q:5uigkr9 1. The same steel ball is rolled down :yyggi 5ak: 9qz *1hureach incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (frh caco :d/.cfwf)yi-3om rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the gre yhcdffic :3)co/-w.aater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same rad,iswiz )u 9 su5dmc:r1ius and the same mass. They start from rest at the top of an incline. Whiusm ) i i15wud:c,zrs9ch 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 conserved.e c.4tusm+ s mz((nu;lcwio +3 Yet most moving or rotating objects eventually slow down wuu.lcm+4 s(oemz n3+;cst i (and stop. Explain.

If there were a great melf1+6o 0 pfnvigration of people toward the Earth’s equator, how would this affect the length of te1 of f6v0pn+lhe day?

Can the diver of Fig. 8–29 do a som.r10 krd2nan,wgv ;v zersault without having any initial rotation when 1 g2rn,n zd ka0v.wr;vshe leaves the board?

The moment of inertia of a rotating solid disk2g/ge,ye n:kby p2u)w about an axis through its center of mass isey:wy kb,up2)/2n gge $\frac{1}{2}WR^2$ (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 am, cijp i;0sn/uj sg0 cqla a4+x6ai/1 rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velo0/jauxlnc1s/,a;+ p ii6m s0ai4cjqgcity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is : .h/edijo6 :f: rrevtpf oq96hollow and the other is solid. Describe an experiment to determine which is whic/q:rtede6rop:fvf:o.i9j 6 h h.

The angular velocity of a wheel rotating on a h9m.f.xa4fdwg-0f7x ,zen cqi orizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, descri fm4fq.9 g,.7w-cd0 zfeixanxbe 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 oflua2n c+qrsyo4* h2ms65le (l a large freely rotating turntable. What happens if you walk toward the2slculmos y n4(6eq2 +hl5 ra* center?

A shortstop may leap into the air to catch a ballq /ik5 i3gco622mmnhe and throw it quickly. As he throws the ball, the m2q m3 2cghikioen /65upper 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 conse70nx8ecai bj/uf0 vr*rvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stavrf/80x7ca e0bin uj* ble.

  Express the following a;p6pldl)n 9wfngles 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 bec0gl9cf nb3y0i k vgfkzn7n5b2ebrz q+1s3 6/qause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.zc6 y0q1rn fb2ig9v+qsk3kg /7fn3z5bblne0
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at tmhdi7dyz f(/lt3fadz -b4.k :he Moon, 380,000 km from Earth. The beam diverges at mf(47id3: /dlay-.d bzk t zhfan 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 moko-tz7r.c 2tvtor is turned off during operation, the blades slow to rest in 3.0rzo -k. 2tvct7 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to8bo6 upcuc+n 9 another child. If the ball makes 15.0 revolutions, what is its diametec bc6+8uo nup9r?    m

  A bicycle with tires 68 cm in diameter travelssk:e8jwy sp ps )i1 rjq,*ln9. 8.0 km. How many revolutions do the wheels make? j) yn1w9i: *r8js l., qpepsks   $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its an2 d5 ,xvdg*abigular velocity in*vai gbd5 x,d2 $rad/s$ $\omega$ =    $rad/sec$
(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. rj8ti6czc8 gy7qe + h(u;yx.z0 s (Fig. 8–38). (a) What is the linear speed of a child seag.ciq7yhzru z( tj8;6 ey+8 xcted 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 velocny-o ap9-8k wyity 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 a pointw1zyoeizei0ol9q6;0 t/f d(pn8r d(g
(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 ct6g7uhh 4(r f 3xdkh6om from the axis of rotation is to experience an accel gr3xhohdh( u664fk7t eration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm t dxw3mr3- 917in crkryo 280 rpmic1x 933ry-d rnr7 wkm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius 9k0 x(rm( j(u2vhdig1olcu + l$R_1$ 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 aboard the Apollo spacecraft nrpjt*; 0ga 8k lbf )m4*8mmafput themselves into ak;ra*fnbltp0mmmj)8g* f4 8a 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 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 acceleratess+ :2c 7a je-monevcd; uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this t:+c7jad2 v;cee mns-oime?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in s1ek3bbp jyn ,um2m912.5 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 str2 )g+ b,f mgc3ki p4s8kua.ylaesses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete rev.+pg2cs)l i4ab3km f8aykug, olutions 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 uni4mmj , 0jxxw62+b 8juqlt/sf yo2n+hxformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the whee/0uwyqbtn42mf6xjx +j jxmohl 82s,+ l have traveled in this time?    m

  A cooling fan is turned off when ithwv m48/euq+zv5 rx: z is running at 850rev/min It turns 1500 revolutions before it comesrq8h:m+xvw5ezv uz/ 4 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 9fji jnx0tje093m/ rncar reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.fx 9j jirj m9t3/0en0n
(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 *spdv h 1; ikgwb.:ny)reduces its speed uniformly from 95 gv)hb*k yn.;s:i dw1pkm/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding az0ho35 dlfe m./mm+cu bike puts all her weight on each pedal when climbing a hil.3cf u dmom0/5el mh+zl. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on th8*klw z 5dc ) zwy*b/f5qvp*gte end of a door 74 cm wide. What is the magnitude of 8p /qz)gdcfytlw*vbz*k 5 w*5the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about thsczc1;o9q+phh;r v 8 ee axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4 shcpr+9; ;qceh1 oz v8$m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached fyhso x(n+6 :wto the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then releasehnx6: o+(w ysfd. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tighl hedezh4a 16)tening to a torque of 38 dh146za )he le$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere jzmw -n7hflpe/ c/ q.)of radius 0.648 m when the axis of rotation is throwec p/-mnhj fz7)./ lqugh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The8wr 4:s-jk: e4mqmk5 ck*f3dweaa2uk rim and tire have a combined mass of 1.25 kg.cm8kuw5 -sfr:4 kdk4:m 2aaewjke*3q 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 7.nb zmr ek9p jhu;fa1yy 8k*;a horizontal circle of radius 1.2 m. Calculatp ;*n b rkm.;k8 9yzey1ufjh7ae
(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 rotating at cons kw z;bxn 8 ycyub0.:**a f),cym3ys8q iwcth1tant angular speed (Fig. 8–42). The f *0)xy1. ,icbcwtk*3 wm:8fhynauz8bc syqy;riction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of pointn rl k)3j0e0ew objects shown in Fig. 8–43 abouer00wje lkn 3)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 o/, t kmvjbi(zn( m5/cuxygen 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 tdrraf7i) j*r3,9 varsatellite spinning at the correct rate, engineers fire four tangential rockets as show3r t*vr7,fi9r)j aardn 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 8.4b s oyyc4c(xc:5g np750 cm and a mass of 0.580cx47: bygsc5co yp4n( kg. Calculate
(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 rem9, xrk+v3j , j0zzqp(l( inpbst 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 a7+h, -me f4tvrxl lw-ww bk:3vnr47ugble 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 :7gvnk luf7xbh3r w+ mle ,-wrt44w v-of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shu)ijq q)h2lby-t off and is eventually brought uniformly to rest by a fricti lyh)-2ib )qjqonal 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 accelerates a 3)pk;vn iy8.jcn y5gx4.6-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 the forearm, whee4*tw.3acnbp eq. / pich rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformlnp.bt* q.a4e p ec3we/y 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 cant5;uvjy-ir+ suak j 764:twq/ rb)oyi be considered a long thin rod, as shown in Fig. 8–46b7 oui6/t5)-rats:y+ j yk w4viquj r;.
(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 consi lucflreqn ye34y 7 -i21xhl4;e9z/yn sts 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*iv)b;1zop 7nft cemrbyf*j/;2f 4 jzates the hammer from rest within four full turns (revolutions) anyt4eo fr;*bc 1p)*7j zvzb ;fmni/f 2jd 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 has a moment of inert* 0clkrt6b/ dfm5v si.ia 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/rwqi(p.4p6ily 1iuv (1 wecp 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 mass 7.3 kg and radius 9.0 cmr0fi0id(, m0 isbao8m rolls without slipping down a lane at 3.3,d(mmi8ro ia0if b 00s $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eh kh i yh125whg5r8f.sarth with respect to the Sun as the sum of t 1h5gwfishrh.yh82 5kwo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How,f n8j7h a hhnqn.vn5/a/f-ibep- e-q much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution pfnhn an i7 afbh-p/ e.jq8v -n/h,5eq-er 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts mlvn (t b0/zvfl0b4g) from rest and rolls without slipmnblvtlf() vz0bg 0 4/ping 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 9c*/a.) ytuoy gvan* pfall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: .*/9ngto)y*va pyuca Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.4jzo1r d;t3lsz9k h6f210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular spet41l hf z ko3dr9z;js6ed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a+ wki4r1;8(exx qzl0iakic3 f 2.8-kg uniform cylindrical grinding wheel of radiuxxw zfak;qkr30i1lec4 + (i8i s 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 rotating at a rate oqoqq(3 3 2oozvf 1.3rev/s If he raises his arms to a horizontal pozq3qqoov23( osition, 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 inertia by*jimy7wi1(7 :: jomcawz3zg y a factor of about 3.5 when changing from the straight position to the tuck position. If syo :z7:c( iaym 3*jz1wgjwm i7he 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 rotxhl93ly 0 8wema1p807mgl:vlqod9t i ation rate from an initial rate of 1.0 rev every 2.0 s81q9l7lo hgex d3pivll0890 m:ta ywm to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis thql5nv9wb 0 jze n:l,7drough its center at a frequency b9w 5v7j nz:ql0n,ledof 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 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 momen2v7z8pthk e i;tum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of thae9ix4-lk.:53mi-md6 pdw o u4kmet a e 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 dejhf;e,k/t 1zd u2u 7eisk of moment of inertia I is dropped onto an identical disk rotating at angular e/uuf h2tee,71;d j kzspeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2z 9t ovf0 w/a47omu9sy.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 rotating merry-go-round platfo6 +qv6pxwl7eprm q wvp 67lx+p6eof 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 rotawe( f,yp4fdfg,w ,n8 tting freely with an angular velocity of 0dw, f8wy pnff4g, t(,e.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 w/feixis s 9m8y;e*ql 9jzz 0a op1a+6uhite 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 carries away no angular momentum, what would the Sun’s new rotation rate be?(roz0iy9 zesp68fiosquaj1 9x* /;am l+eund 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 windkutd*t2 nq8 0zp31wh js 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 ;ab3;i)yjn6p +cq f9y agzwo1+zh8 hy $ 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 pla1kvc/s45 w l n7ayv;aptform, initially at rest, that can rotate freely without friction. The mo5y 7/1s kvna4 ;plvwacment 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-rounn i3ad)y+hmjj-*; bmld turntable that is mounted on frictionless bearings and has a moment of inertia of 1700 j3ji;nmm )-l*yahbd+$kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on th nlcqb5g08.y (276pgqpiqxt/ 8e fj cae top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far i pg60ce5cbn88 q /y a 7t.2ql(jpxqgfdoes the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the E7zx1t*vv,ptd3 5xozh arth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momxvtv* top3zh7 z, d15xentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fro 9awszm i-eg8d15fgd2fwd/w iiu5 -e )m rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m aye.d7aa-bh exgke;- 9cquires a rotational rate of from rest over a 6.0-s interval at constant angu.b7 ea;aykx9-dg eh-elar acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass6: qrui4ct nd7 0.050 kg and diameter 0.075 m, joined by a q7u n d4c:6tri(concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end 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 speed of the rear wheel -c:o9e8dyb-( tw5vbm(zvrj4 3k nl ek($\omega_R$) 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 tim 4iua.v+ n(pdmes as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angulap.v mnd+ai4(u r momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutlr39+ d qwqz1e0f2bpdf26un d zj2w5w ion automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should 1uzqlwzn2 wwfj2d5 3d +2 6r0bf9deqpbe 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 +26giyqx.h6 bqtm5d n 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 rolling on a horizontal surface at spee *1xw3 g;vorw2w0anced 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 )ic sxrb9 3kr :7ifap9ignore 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 cifa:px7k 9sbr 3 9ri)the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is sta 3esrhj -a;h*nnding vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step againste*h3ha njr ;-s which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with spe51dqg 8zwy,t eed v=4.2m/s on a flat road is making a turn with awgd qz81yet5 , 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 leng+ux hha06 ozi;uf0 zp9th 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come hhpazou z;0iu0 xf9 +6from?    $m \cdot N$

  Model a figure skater s,p-rihzb4j83x.8o nxk0vce ’s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning 408ki-xvn3hr e.o cx8s j pb,zskater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of tw 5y x78nsx88eqnvlv4o o cylindrical plates, of maseq nyv no8s8v87xxl 45s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. 8–5i8t0am h-sy ,s7fny0q8. What is the minimum value of the vertytm8-0 ,assnihf70 q yical height 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 +8f7 sgp;1 lh5yfbcaj assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as thetmkn66clt7 h6a2fdr / car reduces its speed uniformly from 90km/h to 60km/h The tdal6t6h 2fn rm/t ck76ires 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