A bicycle odometer (which measures distance travp tdfnwnc/3/ yc / hx1 ox -8i9ejlqs6dq2k.f1eled) is attached near the wheel hub and is designed for 27-inch wheels. What y pdfcix hx8-s9qco 1wjnq2t. / fe/dn613kl/happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates aumou; + etc/ou45ge3ot constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? Iutu 5/3g4u;eoeoom +cf 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 bodtuzw *emb m//;bo1 o)-xokf madoj/86 y be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a gm+r 2s3zry4db15l gwjreater 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 v sgq4r.) mw.qoi:h3dto do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer th.di4 :hvo ) q3.srgqmwis.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the peda yk : *uorsfprh63*ooo/i/2gll cranks. In which gear is it harder to pedal, a smalllp/oi uhfs gor2*o6 3kry :*o/ 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 fast have slender lower lewy9j6rk ul(h-) dpv*vgs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rvdpu yw6 (*h9r)k- jvlotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) * pa(g0s) a pf(sz(he)s*al rwcarry a long, narrow beam?

If the net force on a sysxfarlr2o.s ,jx /dh+f+8lj2b mxab4+tem is zero, is the net torque also zero? If the net torque on a sy++rfl r.8jx 2fdma,x sb2h 4blxa /+jostem is zero, is the net force zero?

Two inclines have the same height but make differentv j0s hdki93,ncye,k 1 angles with the horizontal. The same steel ball i v, sj kyehcind,9k031s 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 (from rest:x vvo 98saf;k) down an incline. One sphere has twice the radius and twice the mass of the other. Which rka ox f;89:svveaches 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 radius and the same mass. They start from y.go79slui. k/,br/ets l;k trest at the top of an incline. Which reaches the bottom firs9t u,/r7i.t.ys k;b/egols lk t? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Y)7kg3 dti6p:+gqisxldl + x/ g3t/fhget most moving or rotating objectsdthlxs 7ikd/g/pg+fg tg 3x6)ql 3i+ : eventually slow down and stop. Explain.

If there were a great migration (c8fj. oa bp9bu .i+qhof people toward the Earth’s equator, how would this affect the length of the c8 qjp9..h ufbo(b+ai day?

Can the diver of Fig. 8–29 do a somersau0dulc:gqj y7.ra bz1br h44 :nlt without having any initial rotation when she ar1 bc0hbn 4zr4 gl.j:q 7u:dyleaves the board?

The moment of inertia of a rotating solid disk about an axis through its centdlz.8w9rl3p5mhq jb3 er of ma5l3w 3.hmb 9 qrl8jpdzss 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 eac.q 47zopfg5qo-ju .dk h outstretched hand. If you suddenly drop the masses, will your angular velocqz-d.p5j ofgko u47q. ity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow andra d,d-,8q d +bmy .,olpf4opn.0 gigz the other is solid. Describe an experiment tof a.r gd.zqbgnop-,dod8,lpy+ mi0,4 determine which is which.

The angular velocity of a wheel ro;k32vbozpf7q(. fwa zxp(y p-tating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decpzx a; qwfbfz v.3ypp2 -(o(7kreasing?

Suppose you are standing on the edge of a large freely rotatig wm(2-k l76vwsyt3fz ng turntable. What happens if zw76v3(2wgyt- s lk mfyou walk toward the center?

A shortstop may leap into the air to catch a ball and throw 1t3hj,sz wr,p it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hi ,,sth p1zj3rwps and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, d5gi8g2u1 iakxxw 2jy7iscuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter sti x5i1aux7jw k2ggy 28able.

  Express the following a* mmc2l8k1a8:vox lqp ngles 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. Calcul1f d q8nm2*o*iz8k ticate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.*oi i fm*t8cqzk1dn 28
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380kv +a6zjx/be0i h5+uqrf k, ,j,000 km from Earth. The beam diverges at a 5qu+k,+,k afhzrjjeb6/i x 0vn angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is zzthmk53+1 gyturned off during operation, the blades slow to rest in 3.0 s. What3gt5zz mk +h1y 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 chillsz o-ob3gvmd,t3r 7t)4 ifk;d. If the ball makes -,4oo r7k fldz3ig;mtst3 ) vb15.0 revolutions, what is its diameter?    m

  A bicycle with tires 6b 0wo(a v7x6if8 cm in diameter travels 8.0 km. How many revolutions do the wheels f 6bx(0wova7i make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Caq0whlaug b8 ovsr4ps+i 1847/sr.u ujlculate its angular velo17sl08 jh44oiuvpw q.+/arsusrb8ug city 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 rev8.i+u,5vhgn85rtydvf16e dhh fi qx 8 olution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from t t8vyx 8hq+1rvgh65i5n,. id feufd8hhe center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of t)voi iwckz y7k;26;f qhe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a6f pc+51zzo9wb k8lbr 6rqp(z 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) mu,3j eo7 tli.sy stskx. i3e)dus 7(sw)st a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experienc73 i3.xk sis st,7se(e just.)owydl)e an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unijc 9(c3pby ;ywo-( wnwformly about its center from 130 rpm to 280 rpm in 4.0 s. Det;ow n jc(b39yp- w(wcyermine
(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//p vq rd9gtd-t7 hyl: $R_1$ 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 Apo;0n qh*7w esj1h8ggs pllo 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 s* 7jqhw;sg8nep0 hs 1gpacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Througfr+m;hjtyw*f :ql3 p8h how mr:+ml3 hf yw8*;jf tpqany revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 +qh,rmt)t+ hm*8t qajs. 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 stressgiasc; t(sy d 0go5 -f2wg(,uoes of flying highspeed jets in a whirling “human centrdfayo, s (5iog 0-(sw2cgug;t ifuge,” 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 rpm zhggu/2-rcs. to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in thisg.-uh2zs /r gc time?    m

  A cooling fan is turned off when it is running at 850rev/min It tu0k5h.gxw d/ jlrns 1500 revolutions be0ldhj /5.kwg xfore 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 its st3 dvwv3o dkegcv7(o5z a9)( 0j id2eipeed uniformly from 95km/h to 45km/h The tires have a diameter e5iwdgzoc7(dvie 33avj d v0 ()t9o 2kof 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as 1-bzyj (knz6bthe car reduces its speed uniformly fron1-(bkzy 6z bjm 95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a etik :,q( bqlgvbfc d2.n6bzlr f(, 50bike puts all her weight on each pedal when climbing a hill. Threi. blg dq06f n ,qzblv,5(fb(ktc2: e pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. Whb 8;sge-n9n./s d8hmixkjr )hat is the magnitude of the sr8 eh- ;)/nhm 9jkbxd8gnsi.torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque aboumd gdixzbp/+x/0 u6v1c zeq k4;k5ma*t the axle of the wheel shown in Fig. 8–39. Assume that a friction tmgkdc k0z/+ezp5 x/b4q6mxu va;1 id*orque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are axrv 9+mgy a0s6ttached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initias g+6yxmavr09 lly 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 an engine require tighte*a;kv)mdsgt0xu d.( v qw+sr9ning to a torque of 38 tg9a.(*vsrxsmk qud)vw ; 0 +d$m \cdot N$ 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 ,*-mgq9 4fb/lm e)jf/,ig3goepx e bk of radius 0.648 m when the axis of rotm,m4lpf kg,b) e* o-xq/ 9efegj/gi3bation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a t krbwl,i4; )3k+rolt ci.xw.bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hur4.c ,l)i.xtk+ b tir3l;owwkb can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a t-4xtr xcz1n0x;w5wm shin, light rod is rotated in a horizontal circle of zwtxmn;x c- rs wx1405radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at conikj.7 o opon/o;:(q fxstant angular speed (Fig. 8–42). The friction force between her hands and the clay iko7o .(;p/o: xnojiq fs 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 i2o( kjgt2wty: hpq*.c nertia of the array of point objects shown in Fig. 8–43 ab o(:cqpyttwgk2jh . 2*out
(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 oxygegcdhv t)*lp7owaob7, 28+ pw jn 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 corr xc :j6bae1yj2ect rate, engineers fire four tangential roc x6 cbaej2j1y:kets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0.ac9k9 wzyv( tqa5w0; d580 kg. 9a0 k v9t(cw5wzqady;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 sw62xraw)+z* maa krovh ;skp; 7ings a bat, accelerating 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 tangezwfhfv 3*4t) 3udmf6 wntially on a small hand-driven merry-go-round and is able to accelerate it from restv3f*u h63wf)w t dzmf4 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 12 d4lo if(2svl0,300 rpm is shut off and is eventually brought uniformly to rest by a f ovl 2ds2l4(firictional 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 3mitbs427vwjgq /1( az-i haf6h6lgs, .6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the;q m*ky1cdoj5bl )r c5ivfp6: action of the forearm, which rlj1v5)5imy f qb6o pc;r :*kcdotates 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 canztl9 2w(5i u dj uw;ug6.e.swl be considered a long thin rod, as shown in Fig. 8–46.l9 (w. .ilj ezs d2;wu5uwgt6u
(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 masses, s:cc 03zj r ljr*axq3b7t+in *$m_1$ 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 tj )2 p8 vvaxkg38ipqlg)w:f/bhe hammer from rest within four full turns (revolutions) and releases k/)qaxbl)j2 fw3v:8g gi8pvpit at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inerti5 i; p 229xnt9m4dc-gve qeijga 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 dev:yh:m as amiqx(0pefs2rv;66 elops 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 k7a wpycjhj-yc -:hu98g and radius 9.0 cm rolls without slipping down a lane at 3.3yhw:yccup8--jj79 ah $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earee0) wa t5amxs f5i,m,th with respect to the Sun as the sum of two, m 0s5fie,5te)axwm a terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much netw*vhff .(rxd 5 v9t)ihm*a-mp)g x6 fe work is required to accelerate it from rest to a rotation rate of 1.0xmxet5rm d )a*fvp 9) h* -vwhfgfi(.60 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and masjk0;i5 ,bst 0m9rdkmqs 1.80 kg starts from rest and rolls without slipping down a 30k 0i 0m s,mb9q;kr5jtd.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 ba qn0 8ah5c7x 4c;*vrwsq l1apdlanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of th 8 ;wr5qvqx0*lapc47 cda1shne upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momc0;eq a r fy+270hyup(rmml m6g+k-jhentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular sp-(m+rya2p 6hkh0 yfc +mq l7ug 0;emjreed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical gu,q cz0k0q 6eo+da +ifz w)ah:rinding wheel of radi0,aa+qk + )hwqzeuz: fdci6 o0us 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a ptotjt uo ,unw t*1a(36latform that is rotating at a rate of 1.3rev/s If he raises his arms to a horit juu(ttoo * ,6n3tw1azontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8il2mhgxa /8mu7w uh gu87*u5v–29) can reduce her moment of inertia by a factor8ag2xuu/v* uwmm8g 5hl7u h7 i of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate fr0hv.v6 pfqxi +om an initial rate of 1.0 rev every 2.i.vq+ xf 6hvp00 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 h71/pl z*6 h3 ssex4ewyjq5vo.m,v owvertical 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 a 3.1-kg chunk of clay, approximately shaped as a flao 4jlee/3v*o615w7 mv .ypqszx,shhw t 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 momivycev/l(e:z fc1w/ 8 f:ccblgv 9z)+entum 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 momepna9:s+b5-g yv s 3qocxo7 yxi(v/zp 0ntum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindr qp,6icqbmnt 55z41e xical disk of moment of inertia I is dropped onto an identical d izqb6mt5 1 n4eq5cx,pisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2 y- 4zkaf85xnia6 xhh(omq5f,.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 stanl9j hgerc )604kply. eds at the center of a rotating merry-go-round platform of y4kcl6e .prjegh90l) radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating f38nx3uj(c h rwkl84vareely with an angular velocity of 0.a4jcvkh3r 38u wl8(xn8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about haj5 *5tn0xhpdjaj23vsd ai5s 0lf its mass in the process, and winding up with a radius 1.0% of its exjx3vp i2 aja0*s55ht d05sn djisting 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 12m mi*e.zq0 wke6vq: d90 $km/h$ 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 af4ouq:gts /i+ 89z dp4li*ix$ 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 re+jkjsd7 9 nf 6b8,yjtkst, that can rotate freely without friction. The moment of iner d t8n+bsj7fj69k,y kjtia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter meia) s7gybx( r7e4+tp l+h4im lrry-go-round turntable that is mounted on lpigbt 47h ys74+xl eiam(r+) 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 rope lying on f5czw,b72bdh the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center f7b 2hdz,cb5w of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. e( rnnt1k g0vkx6 z.t*e+6d nzDetermine the rxnd*6+kg10k ze.z6t(vnnt r eatio of the 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 rest at a rate of 1 m +e0q f2kiq(mf/$s^2$ 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 cylinde-d crru6eaq(yq5 ,zo)r of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular accelcq,rr) d(zu6a5e oyq-eration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricq/)oo9og, owls89kze al 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 yo-yo when it reaches the end of its 1.0-m-long string, if o)kgo o9s w8/ez9l,qoit is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear w(z,m/ pje bv*l::qgg sheel ($\omega_R$) 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, c;/ef:a9ul es but 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, what would its rotation speed be? Assume that the star is a uniform sphere /u:e9s;lcfea at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutisr67jqakj;+dsgg14 d z j6hr 8on automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such7sjgjhd48r;z 1kd6 6sr+ q ajg 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 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 illustrateshg 5l:h :p- ieqa2ege) 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 rollin3o7cm((4mdqtmm o3ptnh/ rm) l17l rbg on a horizontal 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 0f: 1xq3 /ped 7qxjskzand length L can pivot freely (i.e., 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 acceleration of the tip of the rod. Assume thaq0x/p7sqxfe: 3kjdz1t 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 standin 7z+idg xvbv)2g 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 rests (Fi7bzx 2 +)vgvdig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road 1 aty l60iq+uj*;pkgd is making a turn with a radius Tly;tug+ q0k6iap 1d*jhe forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-ksdttf2e.+ 5gt1/kq hi- +nijug 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 rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from? /hn ut. sgietd+q+5f2i tj-k1   $m \cdot N$

  Model a figure skater’sxn hoyh em,(+5 body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tighth+o5h( ,nmxyely against her body.   

  You are designing a clutch assembly which consi teab126 w:oyasts of two cylindrical plates, of mass bto12aae:w 6 y$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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.j. vjiq om9t:b- hs;u7 What is the minimum value of the vertical height h that the marble must drop if it m-:u7; . hisjvqbj9ot 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 fm xwe3;:s*ubdo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed un1 0e5 qsbwxq)xqh9cy(p*hr8txv+z u1iformly from 90km/h to 60km/h The tires have a 1t*)s w9hx(5xxq v0yebr1pcq8q hu+ z 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