A bicycle odometer (which measures distance traveled) is attached near the whte hb(rw/ oddx1x lb6--rw 4t;eel hub and is designed for 27-inch wheeld h6 ebol-rb1(tx;wtd /r wx-4s. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at conspj8off5k9; of2l8kwg tant angular velocity. Does a point on the rim have radial and/or tp5j 89 fko8o;fl gfk2wangential 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 +wk tw:j g u+q(+co3jwby a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forun roqfeh-5h-zg4w(); n/ghkjd8 w,xce? 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 hands behind your 4at0 j n/wm/nuhead than when your arms are stretched out in front of you? A diu4j tn0m/n/a wagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheeg, ma;x,lod(cul3gp4lol5s4 l and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or lgxo 54am,sp,lcl(gu;d 3lo4 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 fast have svjby:e27 ,fzvlender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotati72 fevj:yb v,zonal dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–:d13eix s2o: ptvqux 135) carry a long, narrow beam?

If the net force on a system is zerocwl;9b6l6sgv.b6b eb l5te d6, is the net torque also zero? If the net torque on a system is zerbws 6 6cve.lb 6l5tgb9l; ebd6o, is the net force zero?

Two inclines have the same height but make differe)sf zviwbe.)a -y.1dg pb9xd n8 zx24jrhq9b2nt angles with the horizontal. The same steel ball is rolled doi2q1)egbx. bn.989y z-zbd a jprxfd)24vs hwwn each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down ls s6d3nd 6lmiv 9u6+xcg:6o can incline. One sphere has twice th6 xn:d+i6 cco3s6mllv6d9sgue 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 bottom?

A sphere and a cylinder have the same r:bzo+ mpmdk-)-zmf1 sadius 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 tf1-+m )pzb:omkz- dmsotal kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving orlk1iy z earvg9zxk4*z ,1dx: y58tvj. rotating objects eventually slow down and stop. E9z yt8vad1k .ry1kxi jez gv4l,:z*5xxplain.

If there were a great migration of people toward the Earth’s equator, how w: spli8; r5mntould ;8lp ns:mt5rithis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without hal))e2ii.n 0y xwylb zkofu0z,vy/:i 3 ving any initial rotation when s ,nxi yilo ie3luk:z/z).w0v2 y0yfb)he leaves the board?

The moment of inertia of a rotating solid disk about an axis po0dkef/ ,aj i8suol5qn. i7; through its center of m/ispjqkooe u.0, ;a l78di5 fnass 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 oe1; +jkz 0 ;4vqbkwtkwn a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angularv +tkk1 bje;4wk q;w0z velocity increase, decrease, or stay the same? Explain.

Two spheres look idemmdq*cc5u loaj -l1:;ntical and have the same mass. However, one is hollow and the other; j *du-1amclqlmo:c5 is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel u g g2/en( fnmw9hrh9b)1)tncrotating 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 acceler/m)(ngn1hcbrh 2) 9nge twu9fation of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the ev,r) tbqi 834xw.czg vdge of a large freely rotating turntable. What happens if you walk toward the cent8gqvb .vix), w4zc 3trer?

A shortstop may leap into the air to catch a ball and throw it hyxc(qjbfqv(-8h 8 0d(0za k zquickly. As he throws the bax 0 880(f qz(dabjkhych -qzv(ll, 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 angulq:* / 2,hfhy)uxmnxjgar momentum, discuss why a helicopter mus ,hxhx)n gqju*/fm:y 2t have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a)gzu66s c-oq2fmx 3m/o 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+vcb(dm n -prta/ka 6+ of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (im(ktcbr+6vdna+/ap- n radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the M:gqkrp3zcj;5 i;tqxe;: 7gtsoon, 380,000 km from Earth. The beam diverges at anp5r 7q3q: xt;;iggkzecj: ts; 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 ca9o( r hyl4*hof 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*9 (c4 ahyolrh slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another t lwbjc(m b)) l-ml88vtgb;k4child. If the ball makes b88wtv4bm)l gtml )k( jbc-l; 15.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8+: wx xgb;7sr6:jg3t2hecaf d.0 km. How many revolutions do the wheel7s xxrfgehw:g3j+actb: 2;d6 s make?    $rev$

  (a) A grinding wheel 0.35 m inwa+hg6iq e ( 0)cz-jhe diameter rotates at 2500 rpm. Calculate its angular ve 6hceqh i0a(zg)+w-ejlocity 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 (Figjr-vpc6 9- bi er+ 4/x1ntydig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the cidre 64ity/jv -cn g19-rbp+x enter?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) inli ck kcrk2 5,15-jhib its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of aq;/h0ntvzn8* f jd fveya1.;u 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 centrifuger6vc8bgp v3apin b0i+ue1u(h .;te/b rotate if a particle 7.0 cm from the axis of rotation iegurpnvvic8 thb/ (e1+3ai 6p .b;0 ubs to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uzfhj ph1,v 8k2niformly about its center from 130 rpm to 280 rpm ih1 2vfh8z,pk jn 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 o(cv9,f/er w0ge lwj;47tpjr$R_1$ 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 Moonl7r *xs8z sfd npt- (wqx;1/ee, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder wrsn l d ;t wxf*7-p(zex8sq1e/ith 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 15,00023dy/es zp)gt .ky1 zz rpm in 220 s. Through how ma .zeyp)zsykdz 2/ 1tg3ny revolutions did it turn in this time?    $rev$

  An automobile engine slows down fromv)tpo71gpm7 r 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 flyi; ;5a,o,evndr:a(tqv 6cw+ 2b*rrdq:izvzdfng highspeed jets in a whirling “huma5aqvzz, v6acr;fqw:* rev nd;b(d t+ird :,2on centrifuge,” which takes 1.0 min to turn through 20 complete 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 accelerates uniformly from 240 +ipr*go9m4k8h8( *tpk6 vqx jjo,mvu rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have t hj (xuk +t4 ik8mvj8*or g,9o*mqpp6vraveled in this time?    m

  A cooling fan is turned off when it is running at 850r ;d 3ho8sx-1 i y(u/.dtfkqt 4merrl1aev/min It turns 1500 revolutions befo3hok t4y8rr d;/11 dtu-.ax mqls(eifre it comes 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 reduces )k c3 zr)r 9e(4relkzdits speed uniformly from 95km/h to 45km/h The tires have a diameter zl(z)erdr9 kcer34) kof 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 revolutty j9oc4h/.(q9g qjrtions as the car reduces its speed uniformly from 95km/h to 4 49j.y/ot(qjcr 9h tqg5km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on 0oz uhv z;g62 mgq*/jpbo7z8x each pedal when climbing a hill. The pedals rotate in a circle of rahgzuvx 0op/;6o*82m bq g7z jzdius 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 widez3b0r/0 q hsvo. What is the magnitude of the torque if the force is exeb 3q0/rovzh0s rted
(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 of the wheel shown in Fig. 8–39. Assum7 b ;xgxlvo*(me that a frictionx*x g vl(o;b7m 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 whichv -smwb cw1l wa8k8h-x4-5bty pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on th h wa1-88skctw b-w54v-lx mbyis system.

  The bolts on the cylinder head ( qz7hxeys)w z nl5/7uof an engine require tightening to a torque of 38 quzl5n /(h x)7w s7yze$m \cdot N$ 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 ra4brq, 65i qnsjdius 0.648 m when the axis of i54qrbn,sqj 6 rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle)5sh-c vfr br6tl9w +h wheel 66.7 cm in diameter. The rim and tire have a combinr6bhc9flstv+-5 )r h wed mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball :esy7r r:ph*v 01uaplon the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Cah0:*71alvp uy :rsr pelculate
(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 pfx5 b*sr5u; xw1c 5ojzotter’s wheel rotating at constant angular speed (Fig. 8–425sxoxzf 55buw*c1j ;r ). 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 shown in Fdk +le2mplca00sxz p - 5y)z3aig. 8–43ll az0z+-mp 30ayp2k 5 edxs)c 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 oxygen atoms whosn+2q g zjlc,c,e 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 correct rate, engi8s5-3b7bbrjg; dae -eic63ut z ka+pnneers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radiu68 ud+;ee3rcpa3 - it5zabkng7j-bs bs of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radd:3hbam12say 1 cu iwcy21j y3ius of 8.50 cm and a mass of 0.580 kg.c1yws2 j3i ah 13cy12du:aby m 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 rest t fp o4;qp-hjk)o 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 oe4 t6bt7 6msg7j i/ch zg ns;.dzc(cxd115qwsmall 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 m1zt 4ncdos7cd6 qc zh( 5b.ge t w6gj7sxm1i;/ 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 shut off and is eventually broug)m:bbw/j(i vr *ka 4x;, wdyeqht uniformly,; /bk)mjaw 4i:(wye x* vrqdb to rest by a 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 3.6y* qp. ;:l 1ffq)ocjep-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 thronx ;d4f v8r+sbwn solely by the action of the forearm, which rotates about the elbow joint undedfr +nx4bs;8v r 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 consi+w hnee q3/7abdered a long thin rod, as shown in Fig. 8–46e 73b +qnwa/eh.
(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 massern+i ehdws/aci,m3 )v*a (m h7s, $m_1$ 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 thezdaispb j:1*1 hammer from rest within four full turns (revolutions) and releases it at a *pabid jz1:1 sspeed 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 inertia ofk :da uc-;v8q;uujz7m bz .q8w $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine d +t5nfch: i+vdevelops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and5j)l j1zskl;:l0 ejo:pcru3 v radius 9.0 cm rolls without slipping down a lane atk5jzr:e1 v0 c :pujl;lj3s ol) 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of th;ulw+v)/ h9vz pidwwtv7-/0x-lv vro e Earth with respect to the Sun as the sum of two tolv;i/h w-d-vvv0) +rt/ zvp9 7wwu xlerms,
(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. Hjkvg7:zz9+ sg ow much net work is required to accelerate it from rest v9z+k: gs 7zjgto 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 uh4o-q g8s);prf2sej starts from rest and rolls without slipping down a 30.se;h 8)o-gsuqrf4jp 20 $^{\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 tiq3-ihrl 17xvbe0 r25 n6ogrggt-dx+a p. 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 conservation of energy.] 7ib2to x3+rqr0h5 1 lxg6ggrv e-na-d    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of 88ffwz9l q g9ka thin strf9 qkz8 flw89ging in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of2c1 uidn 9xej/ be*e5t a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotat1b 5/ *ecduitje9xn2 eing 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 t n2n9 j 0ma5.hpvd,tywhat is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 5mj0 2dv9nw pynht,a.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 2zx:rby9* w ay5 hsiyc5-ec y,her moment of inertia by a factor of about 3.5 when changing from the straight position to th9:z2 ,e*hc5 x-s5yayybyrc w ie tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial /vhlgyj(m 2)l rate of 1.0 rev every 2.0 s yjg(m)hlvl2/ to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical amf-z i4 7jn )frsa- nzy0rl :s1jp m+1mm5a2rvxis 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 3.1-kg chunk of clay, approximately shaped as a flmzja)0-m4zrvrs fsp 5f7n a1+:2 -mmniylr1 jat 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 momentuy,.n;n iiz)jpo2r 0p -wuaig .m 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 Er-hkp *yjc +:uarth
(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 9 by-jo6u5wteonto an identical disk ro yt 5ewuj-96botating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2lpze2b7o/3a c .4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round pn0v5 akd 3c/b, r2ihemlatform of radna2b i5m03dr/k ,hevcius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular e th;dp72q 0df hz8zh-velocity of 0.8 hqfh- pdh7 dz2te0z;8$rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a whit-zand8re0sufui 2k48) kp )vd m6wjh5 e dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular nk40rjk s )dd 2)8ua-uz6 8fvwi e5phmmomentum, 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 a rx/,*c+pn efin 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 ox) ab(l8p7o3qhy0(msr7fkd$ 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 platformb;hgr6iq / mr*j oz a1o5h1ii5, initially at rest, that can rotate freely without friction. The moment of inertia of the pe roi6b5 1zjrhm/o5i1 gaq*i;h rson 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 t cy frdu68zhznj.7 v1s9/tl ,xhe edge of a 6.5-m diameter merry-go-round turntabls6/yhnr 9x8lz,ufv 7cdt.z 1j e that is mounted on frictionless bearings and has 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 d s t7z1+d3asikr3ou; rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, h7ka u 1so;ri+d 3zstd3olding 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 sjuic7v b( 8c:vide always faces the Earth. Determine the ratio of cjuviv b :(c87the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from r+yr -vx x,epb6h(4lr hvx*ep,est 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 oeiekn1s x6r2b* few27:- or szf a uniform cylinder of radius 0.20 m acquires a rz*fneokrb 2i sx2w re-67es:1otational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050hqsw6xgm 34.q kg and diameter 0.075 m, joined by a (concentric) thin solid cylin swxhqm63.4qg drical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rewxcngt3i- ,-tt6 5 a0y*dmnrear 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 great, were rot6d6,knifg/ a 6agu16ffcf d k3ating 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, /6k6f6ff g ufn1a36da,ik gcdlosing 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 automobile is for pn5likl7ug7jd7y5y)xe12 re8rp 7dy it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kgi5 ep d7jyykr y8xd57lgnl12ue7p)r7, 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 an,raa3/e : bhzy $H_2O$ 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 spw cl:,0b*ekuen,k-v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore fric3o5pz)n 3mvm uatb9vqk:4 w n7b6a5g:im,lf x tion) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the 4f:v n6 5pxibmwzv ,)mgk73l9tnoum5q 3a:ab rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standingk qba:- s8eesxl bp5.kc* -.ww 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 rest b.5ls*w8 :a-.p exs-bcq kkwes (Fig. 8–55). The step has height h, where h

  A bicyclist travelinos quobt8 ),wmr7mx67(ler b6g with speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal forc,8mrsou7xme 7bq6wl6(b ro)te $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 ahmcup*(4 v3vz -hy)w4w 4yar rock 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 rau44 )4zc ywha(*am h vvp3w-ryte 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 solid cylinder and her arms as thin rod*,-u, kpv *ded fvi ,;e,ybejqs, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and wud,f;kq,ve pb ,**jy-iev, deith arms held tightly against her body.   

  You are designing a clutch assembly whicaut/qn9-2.gd* a e opwh consists of two cylindrical plates, of m*a2 d/n9 ag-upoew t.qass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 lu bi7)ty- q ocxyq; *eo dgovcc5x73:+ooped 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 highest point of the looy5qq ob+ev7)ug* - ydox: 7;txiccco3p without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume q:lv1qf5v92ls j 2aqq $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces u8emv0 fk4 -mgits speed uniformly from 90km/h to 60kmug4k0 fem8mv- /h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s