A bicycle odometer (which measures dat9x g*auhbts1rdsbi .. u /6-istance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use.gd u.*/ h-9 bsuxrasti1b6at it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocit /d lnuuxq150gy. Does a point on the rim have radial and/or tangential ac un dg/u5qx01lceleration? 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 ofyxrpf(l fz ixs417i(0 w m6py2 the angular velocity $\omega$ Explain.

Can a small force ever exert a greatrj u6maufyqjb 0 r(:0+er torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your h lxfg0as6x pa +p4)aq ;oo7w2cands behind your head than when your arms are stretched out in f40o2c) xo w7lpp6a f; +qasxagront of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and th6 dw uny.)mff9mcksu;8:kdo, ree at the pedal cranks. In which gear is it harder to pedak.m d68:k9wso;)dc m,uf uyfn l, 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? Why?

Mammals that depend on being able to run faosmx:u71tiuims6s n7m xzne +3 s-/q+*kbyg+st have slender lower legs with flesh and muscle conmu*1e7xnu 6sos + y3g7/kitm+qxi :+ mbss-zncentrated high, close 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) carryrl1+p7eol;y i(x0th3oj 3wq x a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If thex f6+-virkwruv- kv0-ayo8+sxi q0 f, net torque on a system is zero, is the net foro6a8i k0rv -0-i+rx+ yf kf-xuvwq s,vce zero?

Two inclines have the same height but make differecrs:6s8q5r(1be fnbp-i 0rognt angles with the horizontal. Ths g(fbr5r60- n 8sqci :pbore1e same 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 simulta4-a ;qq/,kcb4:6avzptbtg ht neously start rolling (from 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 qqv 4t;p h4bb:agt6/at,z kc -greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same eonu0 -o a+ e*/8*ecff zt*ybwmass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the gr80fcu*y*efo tez-w / naoeb*+eater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving cyv15gfsj;c4dmx4atq8a11 2c+su ub or rotating objects eventually slow down and y ustdb4f5 c+aq 4vga1xj1182s;cmu c stop. Explain.

If there were a great migration bbzus e ykd(e7ly) ,g7-*5hrhof people toward the Earth’s equator, how would t57rley7u bk-ye ) ( ,bdhhs*zghis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having an2shs+lrq3u zqvveij58 6kx-( y initial rotation when she leave2ql8ves3-kr zivuj6sx +qh(5s the board?

The moment of inertia of a rotating solid disk about an axis through its centerkj2xjr 1 h 8c/aj0zk1n of m nc/ 1r8 a2hzj1kkjj0xass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each ou 1oe20u7pyc,.nq qjbhtstretched hand. If you suddenly drop the masses, will your angula 17j.qqpnbe yuo02 hc,r velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeverazz h*ks(j.ng b 1c/5 +cey6eu, one is hollow and the othc.e6yeun +b5/akszhjzc*g 1( er is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In whbiv+9o ycj3uw6nj :0lfb39*z3el cltat direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangen9byo 6cw0l etfvu39i*zl:j+jbc3l 3 ntial 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 of a la2 y(k oszie-ju8, g*lxrge freely rotating turntable. What happens if you walk toward the cel(xy-ujsz 2i*egk8,o nter?

A shortstop may leap into the air to cath7atgw8nlhnkv8 6 , f;ch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you loofh;t,68g7 lwk8nvah nk 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 angul wn . k djox(os ndh2b,(l1fnbq6j50 tb4lru:*ar momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can ojb(h0n6 oql:bsw rx1bl *,nj5 nd2 (kudo 4t.fperate to keep the helicopter stable.

  Express the following angles in radians: qn1 +osm cs8-xum+)db (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. Calculate, u(a 78u3:vwiav 4k6jyv0 toxyasing the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Mt:4 j kyw yv6xa(8iao73a v0uvoon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the M/vv-vs9, ndr woon, 380,000 km from Earth. The beam diverges at an - rwv,/v9n svdangle $\theta$ (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 anv-l.in i yi7jqnc.jd7 8. z9m rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slowm.jiii .8qj7n l.dzcvnn-79 y down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another childd-0 d,hq stcj*ggtt6pin 5 c-ol 1wn-:. If the ball makes 15.0 revolutions, what is its wph, l 5 qc isdjgtgt n--0:oc*d6t-1ndiameter?    m

  A bicycle with tires e )ik dh:s+ss+oj+ lcu).9z ul68 cm in diameter travels 8.0 km. How many revolutions do the wheels + +i)skzs.sd+ leu )l:j9 hcuomake?    $rev$

  (a) A grinding wheel 0.35 *+wqyp f/6rvf76h b s r(:keeum in diameter rotates at 2500 rpm. Calculate its angular velocpu(6r+7 s y:ewebvh6 rq*/kf fity 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 godd3t 4di *-fpdc:v4complete revolution in 4.0 s (Fig. 8–38). (a) What *ddgf3opvc 4t4id-d: is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Ear5j 7bh zf1n(nrcoqtw2)za : *wth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spe.jn)c 8a 8tl0efw,ge ied 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 the gu,tzx)e+x f96b8qpu axis of rotation is to experience an aqx,g 9xb6zf) e +8puutcceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceleraar ,9tj,69u92j m4xzulq rddftes uniformly about its center from 130 rpm to 280 rpmu,ztd amx,rq9l4 rjdjf296 u9 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 radius5 wo-dty*9asvenx- v 9hfz/ 7ts.q2wb $R_1$ 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 thy, ba3;q, 8ihdsos3tls 7cgl:ga2b j(emselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their tri8 h jbl,s 732;qgtl cd:a(oyi,asgs3bp, 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 ;ou ))ru3ip*rb;evd q/,x;khcqbdi8 from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this oi ;;k)8d; r*b,/ recqhbdxivq p u3)utime?    $rev$

  An automobile engine slows down from 4500 rpm to 12d u7njes .q/9 +hkvb*f00 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 i3n;.u.vpm5sz cj*w wjets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its fin mjzi5p.suv;.w3c *wn al 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 6.5 sx nye zd,w:/3z. How far will a point on the edge of the wheel have traveled in this time?nexwy,: zzd /3    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 rc+dbumx .*.iw pl.bm4xwt l:ukq1y5awk84 u8 evolutions before it c+.mkikl84 my.aqbwxd ul b ux:t5184w.u*pcwomes 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 revolut0 7hfv-cf4z;d)znwb4bjgy u1ions as the car reduces its speed uniformly from 95km/h to 4 fyzzd4b)c1b;fh7guv-jw 0n45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make b: *gud9jkd0p 9:uf ng)-roxw65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.gow j0gddx9u)-p*k nu:f: rb9
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her we1rh r*w vk5z3ezm50me ight on each pedal when climbing a hill. The 5 1 zze*r50rve3kmh mwpedals 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 door 74 cm wide. What is the mnbpn5t 49 gg6r7hy1v qagnitude of the torque if the force is exerted1 phby7g465ngtv n9q r
(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 ofvac27fpp9ns; qzg) yx/ 9/ ovr the wheel shown in Fig. 8–39. Assume that a friction torque of z7fa) y /v9v/ qgn;rp9o2spcx0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massr + hd4jdz e:e yu+n(lyo.:s*iless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction dlr(iu:.y*zeh n+d: j +s 4oyeof the net torque on this system.

  The bolts on the cylinder head of ozc.z- k1w 2xw8hk+sg an engine require tightening to a torque of 381k2 o-gw kwscx hz+.8z $m \cdot N$ 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 0.648 m when dz/q88gt keziymp-r o73)j2kthe axis of rotao2/3ekptzg-z ) ik 8j87qrmd ytion is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of 0dkovle 3/ a0sa bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. Theal00kdoe /v3s 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 a v.u+ rr7c /ymshorizontal circle+r u/y .mcvr7s 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 rotatinv.db6n qs - t,-nwdvm*g at constant angular speed (Fig. 8–42). Thd vd tbs-6nm*,.nqvw -e 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 ineco 5t.3svl1 z:ffy6zprtia of the array of point objects shown in Fig. 8–43t. lspcy3 :f6vz51zfo about
(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 oxydgl a+uqet *,:gen 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 satellite spinning at the corrm(awc;s 2l xydi.7fx( ect 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 ste.m (asx cl27(d fw;iyxady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and3c8 lbzukiog 8,sf6 1e a mass of 0.588ls ,zi31b g8o 6uckfe0 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 rese6e-w3yl c bs4fuaj 72t 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 sm. otz*,h gj-vsall 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 ,o-jstg *z.vhtwo 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 shut off and is eventua wmpa,1r-zf h+)g i)tnlly brought uniformly to rest by a frictional torque of 1.2n1gafphmt)+zi)r w-, $m \cdot N$ 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 ball at fr6j+ 97hvk 4lzlh7xruc6)sx7 $m/s^2$ 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 5un/z+tz* qe4gi40-tjp3y wamv j z-dthe forearm, which rotap vijzzj y5 +0/ttdz4-q34aen u*wgm- tes about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a longdyo1r/etzbm1r(4 r :h thin rod, as shown in Fig. 8–4o(/rbeh41yr1 :t drm z6.
(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 consib/ aptti :k5p*mi-)dasts 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 accelerates the hammer from rest within four fuled8 ) :1 sfi,1eezrzdhl turns (revolutions) and releases it :h sz )8edefr,i1d e1zat 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 u mmlsgf -c590p3k)5 uav/dbxinertia 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 torque of al/0rhn2+p 6j wfvs1w280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg0:ll nz3i1zjw and radius 9.0 cm rolls without slipping down a lane at 3zji:30l w1nz l.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the s0 r1nl 3adfd7g1i fo2qum of two tea1 r2ff 1lniodg3q 0d7rms,
(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 ofvz4d./aejay0 b9o +k c 1640 kg and a radius of 7.50 m. How much net work is requkoaz.davcb e40/ y j9+ired to accelerate it from rest 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 fro2rtw-6g-,k ugu -epu fm rest and rolls without slipping down a 30.ru-e 6-fgp -ug,wkt2 u0 $^{\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 falli;qrn3ne o52h and its lower end does nqie5r no3h;2n ot slip. What 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-kg ball rotating on the end of a thinsk17 gb45df7 hdoaneedeqs, 21m/g /t string in a circle of radius 1.10 m at an angular sp1dseg a4dgh m 5 ,7bk seq17tf2/n/eodeed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentu +qf1o0;:eg8f usgywkm of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? 0og8f; 1yw:gke us +fq    $kg \cdot m^2$
(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 pla8qo l8hqd 7i6htform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decrehq 7li 68ohdq8ases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one skb 7ct e-(l h(.mf1ckihown in 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 ma -kc1.(kebl(h7fmict kes 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 sp q:fycirb-iuyh)w -a3e *o,) xin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3 ru aw3yb: fq,* -ici)hoyx)e-$rev/s$ 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 e 5- qsvqip3)waxis 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 a -q3 eips5wv q)3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spusej, a4(qotz,y8 fn6inning 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 h (78trcixt9ql /i/f x,-x0l sj mqk0iEarth
(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 Id, g tf((gao5q1 jjq,f is dropped onto an identical disk rotating o(jgagfqd,qj 1 tf( ,5at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4xw(h /2irs xy, $rev/s$ 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 u4 nxcxjv5 5u+/(/ xc(pey- x lafxzs3of a rotating merry-go-round platform of radius 3.0 m ande4(p u (3lnyx5/ a zcxvu5 jfx+/xcs-x 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-roub1u vwt4;raa5nd is rotating freely with an angular velocity of 0b 4 uartaw1;5v.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 v84o x;:rsgeaa white dwarf, losing about half its mass in the process, and winding up with as:ex 8ov4g;ar 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 involvazm 71 -pzkso)e z5k8we winds 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 lc)1qk*r qj wbe/ hl/ l5;c(ah$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can ron0n k(y +k;vaotate freely without friction. The moment of inertia of the person pl(;nkk +0avonyus 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 di9w w7ri qvf7q;ameter merry-go-round turntable that is mounted on frictionless bearings and has aiq w97 fv7qrw; 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 exj f+) av+f3g e9ns-zwnd of the rope lying on the t3+fw9)f+ xszv-jaeng op 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 does the spool’s center of mass move?

  The Moon orbits the Earth such that the sah;2 9c7s;l+5pyjjb*z oqt j ykme side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbita+b *y;yk5hljs7pj 9 qjocz;t2 l angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m;5 zxadmamcbrps+* 5 0/$s^2$ 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 o5mxcy9z/ xa70mh3/om hmy,a b f radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculacax903m7 myhxmoz 5/ hy/ab,m te the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylin upg1 vnw4shdtw:csv 88 s08-wdrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the y:8dw1wtwuh vn80s4 ssgcp8-v o-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 a:0yydn 0 w4mlhngular 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 greaty;2 wmg+xe)pr, were rotating at a speed of 1.0 revolution every 12 e2g ;m+)wrp xydays. 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 angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobisgk- b6e1tt :ele 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 be able to 6e-gsk:1e btt 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 illustrat:of i2l 0i9zryjb5 p hxuf.eb6183yutes 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 horizontal1z,,und to x3k +kovy( surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., rhb6j9/d v nef58 sgc+we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleratiove /n+6cfdjr8h5b9sgn 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 verticaap l3d,;2ujnqlly on the floor, and we want to exert a horizontal force F at its axle so that itaq ud2jl ;p3,n will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat0 ghzx 6h;scww1(toa3 road is making a turn with a radius The forces acting on the 6;s(g0hoc31zh twxa w 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-k 3jrbe14uf :3tegwt .pg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it fuf4rjt bweg3p te3 :.1rom rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s bodx(4 a9s4zop kjy 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 spinxsa kp44oj 9(zning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cy/ bo m)awzagt.21s gz+fs pnb+,-s 9wwlindrical plates, of massa2w.stfznbsz9+m) a,po bs1g+-ww / g $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roug ba74fjl 5py8svk 0s+dh track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leav vsjdkay40+5slp b8 f7ing the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but domcwac7r9h/ qf5 ave, / r/k g*sk(x.gh not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reducesh3vb .pgdx6 6k its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.93xd6kp v.6bg h0 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