A bicycle odometer (which measures : hvn 61zcd98iao4yip distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it oc8zi ip9ho4 n1ya 6dv:n a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angul+sr wdda:e-.mar velocity. Does a point on the rim have radiad+: a-remwsd .l 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 of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular ;thio2v v,*d avelocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expl;gm34 ece* nz sq89 7vbnadpl7ain.

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 ) x6( cf +d2uzyr2bkurwith your hands behind your head than when your arms )+ufrb2kxrd6 zy u (c2are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at b +ubg8io -wf7the 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 front sprocket or a large front sprocket? Whgof7b wb u8-i+y?

Mammals that depend on being able to run fast have slender lower legs wae0i+kzl 5pjgm;/t-swg;: 6etz cu v.ith flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribut/z iv:gj0e zu w;t- +ctmlpa65gk .s;eion of mass is advantageous.

Why do tightrope walkers (Fig.nv+ifi5- 3ndx 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If th*qzo4ocv6 d) lvxxl1 fs* 5i3ee net torque on a system is zero, is the netvse 61)3 xo*5fixcl4*d lqvoz force zero?

Two inclines have the same height but make difox/pcz;(vm k5 fg7pn +ferent angles with the horizontal. The samkcm7pvnfog+x / z(;p5 e 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 rol7iw)pp6 b zrt6l.(cc iling (from rest) down an incline. One sphere has twice the radius aib lp6tr67.cz c)(pwind 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 7i801vq2l)ogkqalyfthe same radius and the same mass. They start from rest at tkq q2vg07 )f1l8oy alihe top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most 6u+0d 6ojxiu bmoving or rotating objects eventually slow down and x6uu+ jb0io6d stop. Explain.

If there were a great migv re ;nn-,f2yxration of people toward the Earth’s equator, how would this affect the x ;, vfnn2yer-length of the day?

Can the diver of Fig. 8–29 do a somersault without h7 e:ag h4s4t /0gf:9aii :/gmsk7mibrx5gm ftaving any initial rotation when she leaves the b7 : kg im iftxg g5m9iaf:7 tbs4gheas:/4/rm0oard?

The moment of inertia of a rotating solid disk about an agcm b-13ctft0xis through its center of masg tcc m0f-bt13s 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 sittingiw6js0sluv876pk qgu agd-2 . on a rotating stool holding a 2-kg mass in each outstretched hav.au 66ips -0ul dgsk wjg827qnd. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one iq8r.5r 8ljnr es hollow and the other is solid. Describe an experiment to determrq8 lr8je. nr5ine which is which.

The angular velocity of a wheel rotatinu(rclf cw tna() -n ft(yd36b:g on a horizontal 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, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular 3y6nrc (n:(ffttub ca -)ld(wspeed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotatingbzk uaez0,u85j tj9- e turntable. What happens if you e-8 ,u5jat0 j zk9zebuwalk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As nn-0o ;orejqbf,9m9gl7 ugw9 he throws the ball, the upper wj,o n bgo- rn0equ9 9fl97m;gpart 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 consep3mwz q7mkwe))nptc b+k16 v) rvation of angular momentum, discuss why a helicopter must have more than one rotor (or 7)wbczvw1)km tpp 6km)q n+e3propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radj* *oxt2usk 7adv*g+x8 rko;vians: (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 /jar(jt9*(mt9 ynk lp because of an amazing coincidence. Calculate, using the informatiy(/ ttjr( pjkl*nma99 on inside the 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 directed at the Moon, 380,000 km from Earth. The b/+t*8 zk4u s :si 6zw jewwlg+p9ofpt1eam diverges atwj i:s slo+14p +pkg9wzze8tft* uw /6 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 6zlar9mlj v.9 z4iqa8 5500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. Whiqzaz5v9 m49j .r lal8at is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If(h(l)qwez(fru +* u ojrr8y q* the ball makes 1o*r hf)8u qr r((wjezy*+(q lu5.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in(k aj dnm4eo76qu++qqplq5 .q diameter travels 8.0 km. How many revolutions do the wheels make?qpa6qlo.u7eq4m+q n( +djk5q    $rev$

  (a) A grinding wheel 0.35 m in diameter573 k75mezmoedjwdh u ,rz/)i rotates at 2500 rpm. Calculate its angular m5k/uddmjz z rwe3), 7h7eoi5 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 (.slmstvx9 q 3z2n8 vq h3mu)b5Fig. 8–38). (a) What is the linear sbu qmz2lq. v5sht)3 vnx3ms89peed 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 Earw/ 8ot7hk 2szj0mou;g th (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 a0bh (qxm0aamr * r *frfag+/kt 1ld9jwr)1+n t point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axis6(c47t cnjq mrx4e6p 5, ywdqh of rotation is 4t4ew hqqcp dyr67(n65 c m,xjto experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its0turzl)kb87.a 6 qufb center from 130 rpm to 280 btukz qb)l8fau70. r6 rpm 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 v g:abfo(3iu3 $R_1$ 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, astrohz,8 anw7z69l b5 vh cikf p7o.sgi0+jnauts aboard the Apollo spacecraft put themselves into a slow rotation to distri5,.cb7zsni z7 vagjwlfki p96h08 oh+bute 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. Thr6pf, u hnnv7;h.r(xpj ough how many revolutions did unhf 6p;hnv7j.rp,(x it turn in this time?    $rev$

  An automobile engine slows p, -ub/j6 7p(x2va dvhiufc4rdown 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 h7 fg4isa)ujh 2q+ 1qliighspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 clsu) f4g +qaihq1i27j omplete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accel1s(kd ;ml se7a0vcdp6erates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have tlvep cd;k7d06(1a sm sraveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 cqkdcaj*27p0*5tbbw revolutions before it comesj q0bb2w k*a5*tdp7cc 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 revolut2x-a ,n02b bokbav-, 8qskf0 3fvbgjj ions as the car reduces its speed uniformly from 95km/h to 45km/h The tok2,,bbvvj0j-8 a0s nfq -ka bgbf 32xires 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 reducif+ 3xdu620ov tdlfqboaw9/ 0 ,ohcb8es its speed uniformly from 95km/h to 45km/h The tireso9 , hf+t8duq/0ob6oxcd0lfwa i32v b 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 a bike puts all he:gm 04o oanjfie) if319 iixxcf96v1er weight on each pedal when climbing a hifiniixg13a969f mic4e10 ef o v:jox)ll. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a doonm 3iayh r5a.zms60) qr 74 cm wide. What is the magnitude m)5shi36 a.nzy marq0 of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the ax51kba 8vi6wible of the wheel shown in Fig. 8–39. Assume t5b 1awi 8i6bvkhat a friction 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 ends of a massless rod wh +bw3yxh( bk*uich pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then b+huyx k* b(w3released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head o;5wq:; wia)qytn +g:d 93n jdjh8qj pwf an engine require tightening to a torque of 38qg w;pwj;njh wdj3 )q+9y:i85:qatnd $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.6i4 ;3qr lh(//doa..kuma w kno48 m when the axis of rotation is throu//nikauol4;o. d (.kmr wa q3hgh its center.    $kg \cdot m^2$

  Calculate the moment of inertm8hkp;qtc*w:;r1z 2q/fatiolp(r-f ia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass/ ttf rzc2fpa- qo*;1:qr(hp;lm k8wi of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, li3 anda3k8+csf)/a*p kzy q 8ie3mp e/oght rod is rotated in a horizontal cne/fa8kd k paqm+o38/ca3*epsi3 z)yircle 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 rotating at co* 4wzv *n2jcp:afu/u xnstant angular speed (Fig. 8–42). The frictix2*anzuvp/c :w 4fu*jon 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 ofwzat8 /5s8sgv point objects shown in Fig. 8–43 s gst8w5/ va8zabout
(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 fi* w+ q-zpb2jwhose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correy)q /aaekm :a rbh(4u7gq ;fh,ct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 m auhhe/: ,)yga krf ;47q(qbamin? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform xlh2 uw8 rtt.6cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calcl8r 2u.t6h wtxulate
(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, accele7 tu.rtl 2mkk1vzc 4/grating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentiallytt h+g3yux )+u on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate3u++th xg) uyt the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is event.6 ( atnm qs)+jhb+lbe r)upri02gfz7ually brought uniformly to rest by a a)rs6 0mfnq i bl+e7+ut( bz2 h)pjgr.frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ballc8 3q1gnke 4te 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,n yhc1l9:w /t19k h,vid p/dhm which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 101v chhm99t h/d:,dln y/p1i wk $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod,uax. h52e- ep. wiuc;k as shown in Fig. 8–465-u.e uxepc ia;h.kw 2.
(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 massed*i104 xgfij)nx)yhfzat0 f uc*4l9us, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within fougjff qyo6nv3r9o 2j6(r full turns (revolutions) and releases it at a speed of vj9gj6oq r3fy6f (2no28 $m/s$ 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 ov g:o u1o3+ccpf $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280 il/)z bruki12 $m \cdot N$ 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 wi*z-t(szz ue -hthout slipping down a la setz(u -zz-*hne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eartrjan 53f swkp64 3wfi/:/klc4m 1tjazh with respect to the Sun as the sum of two term3fp45w1mfkjk a 4iaj6 nr 3w /t/slz:cs,
(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 kv17y6;( x:j,aqe erei1hzdv net work is required to accelerate it from r qh7,6er d;ie1 xyjekz1vv:(a est to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from restr 4k.zul iggr,u9)s 3c and rolls without slipping39 g)4 ,rzk.ru islcug 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 vertica.fc kk u, 6gec:7a8bpplly on its tip. It starts to fall 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: Use c7,kcb kp6:uc g pafe.8onservation of energy.]    $m/s$

  What is the angular momentum of a 0.21.z x0owvu*u69 d6lbrk 0-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular09ouz. x uvbkd*l6r6w speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylinds3)mno3x4eux : mxcq,u5(bjh rical grinding wheel of radius 18 cm wh3) 4:qsjhc o mnxxexuu(b3,5m en 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 lva c7cxyr1-+ at a rate of 1.3rev/s If ha1r7lvc+ cx-ye 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 nzdc1,ql u(v wgghhp l;m034:moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular spepc:0l g4vmg,;h13huldwzq (n ed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial gyxd 5 k7dloa(qisp )3ef64+ trate of 1.0 rev every 2.0 s to a final ra lp oxts3i645d()7aqyekf+d gte 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 centea h552*f f tb9fthe,xrm6-u ymr at a frequency of 1.5rev/s The wheel can be considered af5h y tah*f 52m,uftm6brx9-e uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a fxup v98awd wiz) tv(:*igure 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 momentewcity dkwupx89y 44)*j /9gmse u7/ tum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an vf 8 ud-j ho1nsqo w0;2(ioxj8identical disk rotating at angular speed-2 w qvi 08(xdj8h;f osono1uj $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.5*en.10:axtn cgnut t4 $rev/s$ 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 y/tm6o ms3l)fb:8u qz a( ;frfthe center of a rotating merry-go-round platform of radius 3.0 m and moment of iner:f 8ya/)o3f (mut 6sbfqml ;rztia 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 anm)qhk6i2tyjsh lr ,)5fuvj h6c,da/pv/h x1; gular velocity of 0.8 hj5 ryh; ,)6/sh)/cfijhtdxlk2 u m,av6v1 q p$rad/s$ 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, losingc1p;*jwp2x 8-zoz -mqkqdx-pzn z2 (u 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 rotatiodm-qznpzx *c2-1p zzwq 2ojpx 8(-;u kn rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120 mue qk05p4xwl3c p(,jck s5n; $km/h$ 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 eduj 5ds:o r:*$ 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 ao 5kvtqsb:*+ v platform, initially at rest, that can rotate freely without friction. The moment of inertia of the person pluskt s:q5vvbo*+ 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 personq12mutd ,x /j (bn cpxmma)5u3 stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inerx(1um/ m,pmna)c 5xdjb23 uq ttia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of 17h67r- vnl ztpcw0my the rope lying on the top edge of the spool. A person gr t 7mp-hy clzn670v1rwabs 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 does the spool’s center of mass move?

  The Moon orbits the Earth such that the same siptg jryzpz +6u76 1fgo0mx( 2ide always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentumtpp gzy( 6r g zo2fm1ju+60ix7. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at ad,9,4) uvxmp )kl3zubf0o dcx 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 th 0s 8mmj;c9xwb-k wtp-e shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at con0-;c k- mxbpwtm89sj wstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each ofl*( r3 s.b+a -exeehlj mass 0.050 kg and diameter 0.075 jlr-a(he*ex+el.b 3s 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 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 isul8 x eb 5zysvs0u0c+* the 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 91q ru,: pqjaugreat, 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: ,qp1ruq u9ja a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automl 2)xf;fg8bwqobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total 8bg f;w2xflq) mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates :meono/sy9pi8qb iqy fr-/;7 mux,a/ 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 speed v=3.3 r.q5*bv5qjiyvqsjeu.2 ;mp. h oa 88p$m/s$ 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 fr,t9* gzdy*esr eely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54yrz9deg, s* t*. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing verticallyj0pw.:m + bi6ploy uy2 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. 8–50wyil+: jpbop2 ymu.65). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn withr*a;lb r0ys jd:r,aj k ep,b qa/-fd25 a radius The foysjrd2 b;j 0,rk5da-pfr: b,a*lae/ qrces 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 rl3xy 7 *gzv p3/yv6k,o*fp*jl /erjdrock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does t6/plvg *,k* ejxd3l*r3/yj p fyzvro7he torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, bc9s7y1zs f nbwye ;.5making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for;e5 ysbsnf1b.w7 yz9c a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical platei)7j() w)zjkqsnf. j ss, of mass.j7))jjz)wni( sq fk s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along m)f -itj df:c:vx hgs+zg8krpbd(/. 6 the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highefc v+/s-z dhi)tx:rmgp(d 6b8jf kg.:st point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumeu:73;;jr npkixyo2 ui $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its s g*hst6h3o ,edpeed uniformly from 90km/h to 60km/h The tires have a diam3t6 *hgoe s,dheter 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