A bicycle odometer (which measures distance traveled) is al9i (epqin4wbj. 4gip.3h +s7o hb eg)ttached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a 4+ojeenh b)l9ii37p bi (hqw4sgp. g. bicycle with 24-inch wheels?

Suppose a disk rotates at conlv:k 1cn7hb0z.gyh kyq+ 3/sxb-n ux .stant 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 of either componeny7-3 +k:q x 1/vbylxgc.0 khnunbsh z.t of linear acceleration change?

Could a nonrigid body be described by a single vvo q.crchram8 7*r5 +z tjuj57alue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger 8t dzgcf6 a50yforce? Explain.

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

Why is it more difficult to do a sit-up with yoss v-)d ,ny cd8,:hxivur hands behind your head than when your arms h cdv,,s xy -ids):nv8are 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 f,gv)6s j8vdah ixb9/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 front sprocket or ib/sv g)a9v68d, j xhfa large front sprocket? Why?

Mammals that depend on bein3yiff- /tnm5 jg able to run fast have slender lower legs with flesh and muscle concentrated high, c35/fji-n my tflose to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry b5t0cosp s1*nus (9tia long, narrow beam?

If the net force on a system is zeroci0p11s bl.rd;e w n2 6en (xtv,j8kjl, is the net torque also zero? If the net torque on a systct1,r 2pv d;x.n jle(1sn80w jleikb6em is zero, is the net force zero?

Two inclines have the same,d fi3 hxrz +,7eac+jv8xhs.k height but make different angles with the horizontal. The same steel +f , 7a.d+h8zh,i3 jvc xxreksball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (f/s qvdm r (etgr57)l1krom 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 greater speed there? Which has the greater total kinetic energy at the bott/ k7e qr5)mrg(1svltd om?

A sphere and a cylinder have the same radiuxf )ols+ 3srzf3p7i 1is and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total ki3 +r)17f 3fzslsipo xinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most yi,/)v 2mjfrsmoving or rotating objects eventually slomir2 j/ y)f,vsw down and stop. Explain.

If there were a greajt :yzxz7h x6t96kcu-:yr ad6t migration of people toward the Earth’s equator, how would this affect the length of the day?xduxyy7 zza tt6:j6- :69ck hr

Can the diver of Fig. 8–29 do a somersault without having any initiau;;ias sct,.o6 zch c:0y4zkml rotation wh4 c.6: u;izm,sacc0ks y;ot zhen she leaves the board?

The moment of inertia of a rotatinro4 /p43u i yqysi3m kbnt50/sg solid disk about an axis through its center of mass ip04n t sk34 iyi5mou/sbqr y3/s $\frac{1}{2}WR^2$ (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*rx hm c:u,(zk stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the massk zr :*hxm(,cues, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, ,vf2q0p bygj2one is hollow and the other is solid. Describ2jf 2bvpq0,yge an experiment to determine which is which.

The angular velocity z 7 ode7eke ,)*k0l*b rsb6fypof a wheel rotating 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 poinb)lyse , *ee6 zr77kbdpo0f *kts east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on th:x7 aau2ak e5zg*lk x1e edge of a large freely rotating turntable. What happens if you walk towxaeag7l 1*a:xk5zuk2 ard the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he;z 6 i-ehiuglszj;f12 throws the bfz-ge2 ;jih; 6zu1sliall, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuv i3d z*rn2zhv)1k2cydi;; zuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second prv2*v1iy nz;k3z rdu;2zic)dh opeller can operate to keep the helicopter stable.

  Express the following a 9;8pjp8uq 7gr*k ivqz.xss n6ngles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Cfy/ p mmn;y+l;8;)bo nvnsp5oalculate, using the i;vop n pns;yl)yn5;o 8fmmb+/nformation 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,ar*q)wo/6 mzhk;: ps x 380,000 km from Earth. The beam diverges at an anso6rzp)hq wak;:mx/ *gle $\theta$ (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 r 7t s(vs +,pe5 faie:9qktx5td3tmz5motor is turned off during operation, the blades kdm( ptz qttisavsf3:5+ex 9r,t557eslow to rest in 3.0 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 to another cu194cz *nghk x0 /vlge e2oj,ghild. If the ball makes 15.0 revolutions, what ig 12uvxg9n0hl 4c,z/ gjko ee*s its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manhl)s9 /1e jg ouk4;kpwy revolutions do thew9spk u l1hj /g;o)4ke wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diam;8yy(46r sl1cybz hyb eter rotates at 2500 rpm. Calculate its angular velocity in r1 ly6byzhs4by;8 c(y $rad/s$ $\omega$ =    $rad/sec$
(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. 8–4;zr 0 ojoryckt0/;wd 38). (a) What is the linear speed of a child seated 1.2 m from the centetky/0o4w0 r ;dcj;z ror?    $m/s$
(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 ehh1bs4 /c ;yeits orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sp; jk kj.2wwi)k*yh6 gjeed 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 from tn; -vwj+mhc6w he axis of rotation is to ex+ww h6;mn-vcjperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpf0 3wnbq5+ )dr+ /ymzru9g veom to 280 rpm in 4.0 s. D9oyvwnfbg3u/r re+) 5m +0zqd etermine
(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 wnady..e/4osccwf 2s5i1l .p$R_1$ 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 put tg: ngpkg65an9l9h yv3 h3d .jrrap5 8khemselves into a slow rotati g3h gd r85ay5k ahp3ln: 99rvnk.j6pgon 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 accelerates uniformly from rest to 1gui3.pb.+.wr erpcii t93 g4a5,000 rpm in 220 s. Through how many revolutions34 . r ga9iiwt+rpb3 .ipcgeu. did it turn in this time?    $rev$

  An automobile engine03 kyj3r-jaoh7h5 s w f9/peyq 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 a whirling :7wmoyb* t t,z“human centrifuge,” which takes 1.0 min to turn through 20 complete revoluti * tztowb:m7y,ons before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.f k /er p4:s0ddz/0h;+ig sfkr5 s. How far will a point on the edge of the whefge0s //k+s: 0 4 khdrrpz;idfel have traveled in this time?    m

  A cooling fan is turned off when it is running at 87vuls 6k- ix0z50rev/min It turns 1500 revolutions before it comes zvxu0si7-kl6 to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car r l1 ykc/mo.sju /;s,tpeduces its speed uniformly from 95km/h to 45km/h The tires havejc/s. ku; l,smt/o1yp 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 revolution)i6bko t 3f1atit)z: ds as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.8016 b3od i):i)zfttatk 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 bik7fszdva(j6w tc+v p/2m-r+uh e puts all her weight on each pedal when climbing a hill. The pedals r j+zu-dc+m(/frt7 6v2 vpwahsotate 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 aj 71n kd2rdz1 op,zp9f 22cfeo door 74 cm wide. What is the magnitude of the torque if odk,f2 21e zp2d 9jc7 fp1onrzthe force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle oozuzp4/ ox6t2 f the wheel shown in Fig. 8–39. Assume that a friczox / p46toz2ution torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attac35 y0yzbz(+.rh*4 ueedqjoas hed to the ends of a massless rod which pivots as shown in Fig. 8–40. edhr*y3u5 ybzaezo(s 04. qj+ 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 head of an2zo. dce5- bwk engine require tightening to a torque of 38ke5 z2.w-bcdo $m \cdot N$ 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 radiwv7 bp7b6.x;c*c m uhnus 0.648 m when the axis of rotation is nm7uh*w 7c6p;b .x bvcthrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheex9 lar c*7+zqehr 4l ioex,9w1(+flryj gb,p )l 66.7 cm in diameter. The rim and tire have a ce* l,r xlp x7a (4rlf,i1erj+hc 9bz+yqwo9g)ombined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end o ebu fu7y 8sq8caj(k3+f a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Csa (qu+ j8u 8k7yfe3bcalculate
(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 t7k; g*a(hjc5 q5hgxl potter’s wheel rotating at constant angular speed (Fig. 8x ;qc*gagj hl 7h5(t5k–42). The friction 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 point objects showna 6r:nzcmuo ;9dw;ir 6 in Fig. 8–43 about ur :6r ;io ca6dznwm9;
(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 whose total mass sx:drj5 2,mlxn/7d.wehoxm 5is $5.3 \times10^{ -26}$ 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 corre qmuz1ftu:u 2 ;mt8yi3ct 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 satellityt82zu1;m:uifu qm t3e 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 mas-t7rh*t7ig yx s of 0.580 kg. Calculatxhrt7 t-7*gyie
(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, acce4qsor2g(td)r qfmy-8lerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merr/wt8 le(ti8wstz; + amy-go-round and is able to accelerate it fromt;i ( wl t8w/+8zmtesa rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shufy q2h63a;-dqsj zmj4 t off and is eventually brought uniformly to rest by a frictional tor3d 6zj jam2fsq ;q4yh-que 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. 8–4((k5njv0zrcw ee - z(x5 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 thni,ya0f*0sdlan n4 y9 rown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. Th9af i d0*4na,0sln yyne 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 long thin rod, r2t;7j cw utvio,l+o)as shown in Fig. 8–46. tl;)crt7v, w uoo2j+i
(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 massecb zbm*ri09 0bs, $m_1$ 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 w1)8kz, nnpd zjithin four full turns (revolutions) and releases it at a snpj81z, z nd)kpeed 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 5jpsz vd(49nk 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 torswhqb n/a;rh ug6m;yo)hk:1 + que 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 kgfdwg5a 0ri) 7p e)q3uy and radius 9.0 cm rolls without slipping down a lane ) iw7ea 30ypud5)rgfqat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of 0(lddhk ;ait-two ter d 0tal;id-hk(ms,
(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 ne 0ubsz:aj co-9bt4*c op ,h4ue8qz(xpt work is required to accelerate it from eqcbzjhtc z (9ps8a 0u,:b* 4o-puo4xrest 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 masx2d uu vw8+h of4zqc2.s 1.80 kg starts from rest and rolls without sd+hxuqv42cw .u28 z folipping 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. x23sm1 r(fjj7e mt*kg*ohcl (It starts to fall and its lower end does not slip. Wgjm o*t *((1xerm fc 7sh2klj3hat will be the speed 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-ks, hrs4vffr 897x zmzs(b -7pl:rap1zg ball rotating on the end of a thin string in a circle of radius:7fb shxarsm7, zsp98v r1z -(r4zlf p 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg unifor 8o*zucob xe0r0xu9x1nm6t- dm cylindrical grinding wheel of radius 18 cm w nzd*x1c9u8-0t eoxbo6 umrx0hen 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 c3l sl*uzup1 +j4 xu2xa rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.84cupzu*32 xl+xu 1slj $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown inivz xu1 f1ay11 Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is h 1fy1uz1vxai1 er angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of rj44kp; p7n er1.0 rep 7enr; 4p4kjrv every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a verticae( i*f nbu:el4r/vbc;l axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws (u/be*bf:i ;r4nvcel 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 mccb+ffl /pt(75:*h*vjh smb w/t9mt vomentum 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 the Eart9h j omi8a4a op0a ej8-c2hgx2h
(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 identn ,14gd kq)ktg i9s*sldf)7weical disk rotating at a 4n* kq sg)e t9kdgd71si,wf)lngular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ax1 l/ zht-l4ozt 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 ce dl-r 0 s7d0l,4dw.kmp rbcdr(nter of a rotating merry-go-round platform of radius 3.0 m and moment o0rd r. d m 4-llkc,7sdd(wprb0f 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-roun8yctc 1sr.)e+ cvzuz w;jm8 y.d is rotating freely with an angular velocity of 0.8 zc+ .1cy8rj e8ysu ;ct )mwz.v$rad/s$ 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 dwarfqijz / foka2tj.rd+ke45r8 q9 , losing about half its mass in the process, and 8i59 r/4k.r jfa kj2+dqoqtezwinding 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?(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 +ys5d e6;l1t,y5bhlxb ak3st120 $km/h$ 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 hlg9;,/ jilet 8z lr:l 77d djdvb93ef$ 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 a4ezt vkwp3. v+t rest, that can rotate freely without friction. The moment of inertiazt.v+e v3kw4p 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 div04ymywi .j 0c/ykw9g ameter merry-go-round turntable that is mounted on frictionless bearings and hay .4ykwm w0v0 i/c9gjys a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope l xe/y cssa5-bz 2)oq)xying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding o)esxo)x/2bz q-y5 asc nto 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 side alw;2sza+ltd dx.h a(2sq o)nc++j) u vaxays faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to ox ljsq v(n) daa2hzc+s++;)xda.tu 2its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from r;1epuy9;fqr2d bn) h oest 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 acqu u -3:le3y0zeuisd6., u:3eko xs juhwires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculat u3yk, 3ss0le -jxu:ueh :iuezd o6.3we the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.05019leqs 3l.beie145 y fgcy8 uc kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg y8bg. ciyqs 145e3 9e 1culfeland 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 a5l uqt(/ja7q6fqtm/p ngular 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, b cc2tk2:t jcc0v zc9z*w7yf 8kut 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,87 * tw0kz2c :fzckv92ycjt cc what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use x w ho5wmnk:*;)gqldl u;6+ z)ph( rbtenergy 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 be able to travel 350 km without zg; ld6now;t)kbphmwxr(5 + : )* qlhuneeding 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 illustratezela0,;8i7ii / p4gwf ya5 krbow u1j4s 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 wpm,+*gw jbqo-73 5h1br4tfse non) h$m/s$ 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.eahoc8 x* *a.oze18b10vm ygrd., 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 linearhx 8d.aa*r *8 veb1moo1zy c0g 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.ok+3p ,c ;k5qgzl.w-qss z/z h It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it w/zq3gh p ,.q+5kzzos-;clksrests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road iskyl98s fqg79t.dz 7l o making a turn with a radius The forces acting on the cyclist and cycle a.lt 9g7 z9syqofk d87lre the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins w wpx:-tf;r d7ihirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rawp;x tfi7dr -:te of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solidmeb :p0sco t.- cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio oo- p b0e.sc:tmf the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly w c,ez e v3tk91q+i)qkmhich consists of two cylindrical plates, of mascv z,qk)3e1t ie9 qmk+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 the looped rough track of Fig. 8–58..zd9a 9 b)asew 9f)ahe What is the minimum value of the vertical height h that the marbleefb9. dza9)9was ah)e 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 ass)(023l.tgme zhswmf+ tr:0u,ssr w uhume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unif e+nwim1 2nn+qormly from 90km/h to 60km/h The tires have a di21nneqiw+ mn +ameter 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