A bicycle odometer (which measu8u(qu+ uyu)5 srkueb )res distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with r )beq (ku )+8suu5uuy24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the.ta 9*bn/insg .lzmd + rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and*mn.td +/ bzs 9ln.gai/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the anrb9koi0oa j5 5gular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Exnnuyu ;pu9-k06 a(qr hplain.

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 donin3)7gi e /rs a sit-up with your hands behind your head than when your arms are stretched out in front of /i)n3i7snegr you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the peo1vxqn+*e0n xu b3s:cdal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In wuxcvnoes:xn* 0bq 1+3 hich 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 sles0f2ey r9l ;f: q9k (3;u(aegy q ;zofpc7oqoinder lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, expla9y(osy3u ( r:z qacof 2qi;ee q;9fgo07;lkpfin why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry agqfh-4sob rz-s* ( v5g9jq uv. long, narrow beam?

If the net force on a system is zero, is the net torque alsew4 jbmby3 -*io zero? If the net torquej iewb*3 m-4by on a system is zero, is the net force zero?

Two inclines have the sfow a :of..9mhpjto5 km 8d-/oame height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Ex8/pkod:wa h9oo -ft jm5.o.fmplain.

Two solid spheres simult bhe3rwuoeium)+nbl 9; m/-g0 aneously 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 u )wol ib0h9nem- e3bmu; r/g+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 the7h3ooi kfm w+/ same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greatermoifwo37kh+/ rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving onie6 1 f9fis8rr rotating objei9fes 61 fi8rncts eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s eq:rcph, bi fd28 xi;.imuator, how would this affect thhr xm;2f i8.bdpi,:c ie length of the day?

Can the diver of Fig. 8–29 do a somersafa*+6vrgsso 1 ult without having any initial rotation when she o*fvgr1+ s a6sleaves the board?

The moment of inertia of a rotating sof0ssmg0tw 9*lg /x9 aerqd(.zlid disk about an axis through its center of ma9sez9l( *0q afsxw.gg/drm 0tss 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 mas t k0g8 wn:gu2x/ftey0s in each outstretched hand. If you suddenly drop the masses, will your g08kng x t u:wey20ft/angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical anca5(du:rnl e( p: z eh(0bvts8:kyii0d have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine( h8pt(b(uca0r:z isld:ekn5 ie0v :y which is which.

The angular velocity of a wheel rotating on a hi)x 8 c8,xy8;kw2ds+zftytpiorizontal 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 td i)y,8yi+ksx;8c8 xztw2pt f he angular speed increasing or decreasing?

Suppose you are standing on-l h weshamjdrj::ur+ 7v62- b the edge of a large freely rotating turntable. What happens if you wah- l2br j w7udehavm+sj:-6: rlk toward the center?

A shortstop may leap into the air to catch a ball and3ce1z 5he t5o-sm ojm0 throw it quickly. As he throws the ball, the upper part of his body rotates. If you look ts 5mj 1oz-0ohe 5mce3quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a heh c5w;ldv) yhwy g91mh :hrd72wh pn*/licopter must have more than one rotor (or propeller). Discuss one or moh ynwm/2hg7lyh9w*drpc:h;1)v5w hd re ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3e.hmum- zz 8vvm/u3*s 0 $^{\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. Calculat4vvsmq) gqe/.t3ti.o p3vo0ze, using the information inside the Front Cover, the angular diameters (in radians) of the Sun andq.v po/ 33gti 4vmsez).tvoq0 the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at tr,y;9 4a3s ncn/7wr(dkwl nwohe Moon, 380,000 km from Earth. The beam diverges at an aancno,wy 4l73(sn9 rwrkw ;d/ngle $\theta$ (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 mot fwhl)u(qa6tx9b,r +dor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down? (xarufw bq9h ,d)6l t+   $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another 5pcf jsonuij4hc( (2/child. If the ball makes 15.0 revolutions, what is its 4u o(2h5icf p(j/jcns diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolu++bsd h o.4z:y8lzg rttions do the wheels:dgh+byzz t4.8o slr+ make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 250ku(0 st,ojn+lfkt ;xr8hq r(2 0 rpm. Calculate its angulaqt( rf,j+;l r(20 okutxs8hnk r velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.jv5g1c ug a+4p0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the cen +pg14 ja5guvcter?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around the Sunzo*co1 lq8xr+uh e7i9    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poibcqzg u)5nt d om9):(ent
(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 ala 8uu rxevzefw1f9s i9 -jdr 5b:20k: centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleraturf9 xirfu89b1:l ee:sdkawv2 j 0-5z ion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130pb;4 :ugtvaca p a3sm;)*kt2 r-h dv)x rpm to 280 rpcbv -vp;))dg43utt*ahaa:x2 ;smpr km in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius ), oh 2amclx*h2bc.- rbu2rsc$R_1$ 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 Apold)6le26nl cschb slff0/6j, plo spacecraft put themselves icf 0l2ls shf6 )6 ,pd6ej/nblcnto 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 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 re 23j sj6f/noxhb d+y:mst to 15,000 rpm in 220 s. Through how many revolutions sf63nj+b ho d2 m:y/xjdid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. 3od az jb0)kpx2;go*gCalculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling d4xl53dytg7 e“huxd354ltde y7 gman 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 acceleratespqi;2qxn c0) p7:sp wj 3cdps: uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? sp n:ipc: p)x;3 2p7jcsqd0wq   m

  A cooling fan is turned off when it is .wlwo m gsnwehx3s-+/jqy+-6 running at 850rev/min It turns 1500 revolutions before it comes to+j-q/+6wgwsmnyx.l ow -hs3 e 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 revolutionsxil aeoy+68t. as the car reduces its speed uniformly from 95km/h to 45kyoe x+ia68.tl m/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 65 revoluti65n lg1ixb(nnons as the car reduces its speed uniformly from 95km/hx5bn1 gn (nil6 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 al71fz1 f3of xowmiv1 + bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radif1fo vil17 w1xfmz o+3us 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 74rt(.r xli i yjq4ojm(1bb/t1+ cm wide. What is the magnitude of the torque if the force (/ jtix11rbj4qb(oy m t.ilr+ is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel q * :hzxzd:m(fshown in Fig. 8–39. Assume that a frictioz(qh m::fz xd*n 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 f4xy p.l7*jqjy, +z:yq, f*mj b3jr xsends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held infxj x*jjq .l,37f*4zyj p r+qsby,m:y 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 requir xr xifgpi-a-9y7 u72re tightening to a torque of 38 puyg77fx r-ixa2i-9r $m \cdot N$ 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 wh);t id hid k6w;,3f8zvs9 mlx*gpt*ynen the axis of rotation is through its cen wiy gvdt36;kfz*8*mi)hsn9d p,tlx ;ter.    $kg \cdot m^2$

  Calculate the moment j x9./ pihknlep+ /bg4of inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can b4hkp/+j/. giep b9lnxe ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is ro5g4 :zr xkw3 dluq.il1tated in a horizontal circriq z43l.dlg51 :xkuwle 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 pot n)ltcm(7o30 as9xhbk ter’s wheel rotating at constant angular spee l k o0t3mhsb7a)n(cx9d (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment ofxbk3o,q *0 bti inertia of the array of point objects shown in Fig. 8–43 about *b x3i,tq0 bko
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total ma aofq v 401fx +gbbybbdf9*.f0ss 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 thxn,xba /;7sdle correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius ,a;/dl 7nxbsx 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 radiuc0 ) g 9ogtvsets1:b;lyea; 9zs of 8.50 cm and a mass of 0.580 kg. Calculat ce 9 :0g;;l y19vz)begsstotae
(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 fxjke1 akhmld4l3o)87 rom rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small o-lyx u2gw0 y8hand-driven merry-go-round and is able to accelerate it fro0y- uwl2 xg8oym rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut offu,(heed, 1umpx )uj1 t and is eventually brought uniformly to rest by a fricth ,(,j1e um ue1dut)xpional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg( qtt1gl*m)gy 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 bal5epusalfh- au*.o 7 )zl is thrown solely by the action of the forearm, which rotates about the zp-h 5).lfsua u*aoe7elbow 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:xf pa x/ hluw2xiu08; be considered a long thin rod, as shown in Fig. 8–46.w axl: /20hfup8xx; iu
(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 ma u zz8ivb;8v47:xsyn osses, $m_1$ 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 full turns3w3+lq d-wg8fgf8; yu dpg e;s (revolutions) and releases it at a speed of 28 pdygqs8w -3gl 3+fdugwf ; 8e;$m/s$ 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 4 l) b3zz;9oto mp)rqaof inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a c-y)1ia;my2zy3a 4zl5jm z xttorque 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 and radius 9.0 cm rolls without slipping 1b8ee8st q6zjrfbe8:down a lane at 3. 1 ztqe8r8bse8 e:f6bj3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic ener41n;x;k8uqo3 ;fqav3d oorozgy of the Earth with respect to the Sun as the sum of tw o zf xqk3o;vra 4u3o;n;o1q8do 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 ah iuq4j4qs( ony3u-v3 radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume3u3q4v4 ni yujoqh(s - it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass2c6u0 jzubn sl .kdv/3 1.80 kg starts from rest and rolls without slipping down auj d./cz2bvn36 su 0lk 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically 0c.6ateuux jytr9zjr6i 27 9uh-1 teton its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole jusrr-u99atjxtj tey0ch1uz . 66t 2uei 7t before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum oxermjx6xzoq d4.0a* c*u0s0 wf a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular d4squ6x0 zc0xx e0r* mwa.o*jspeed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum 5yw9kej xkn zq ,sbax*2/j,.cof a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500yk ezx.swa9bkx, 2c *q, jn5j/ rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate ozzw,, .1z nphvf 1.3rev/s If he raises his arms to a horizontal position, Fig. nh.zp,v zz,w18–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of eyg,ju:y c6.msdwbh.oy3v8 1inertia by a factor of about 3.5 when changing from the straight position to th.odj m1h, 3ub 6yesy8 cvw.:yge 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 r0ea2c gd1 id+bx;lre+ ate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3 +0dcge12;e+ rxdli ba $rev/s$ 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 xf66v3w 9 ty+s2m1pddm fiz;g rotating around a vertical 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 1 py;+xf d6692s3 tdzmvwgmifshaped 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 spinningev9 ) 1. z.ltf3 +cji1hivjknw 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 Earth - nsa0 c/4iuou
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an idjq j:*ne:jknq 4hc4 x5entical disk rotating at angular sp :4e qkj4hj:*n5cq xnjeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 234ihdy d2:qjo.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 meqim.e2pmx lr6y3 h3 )lrry-go-round platforleiy.x3qp6 r2 lh3 m)mm of 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-rq:zl87zb g jz,d9p+-y3c k ostound is rotating freely with an angular velocity of 0.8 ljq :oz7db+kz szc p89 gt-y3,$rad/s$ 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, loykcb1uybj ( .)r449hayj t9 +z. hp+k(ycfwa qsing about half its mass in the process, and winding up with a radius 4. y1cauyrhyk9.a9kq f j cp4+(t( yzw+)jbhb1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess-tpgc).de 6d/y,v52 d mwetoj 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 x+po5od*nzom:itl3 4 $ 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 rot7h dev bl2 y4r:x5s9rhate freely without fhb4v s r xylh:d27er95riction. The moment of inertia 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 d3mdcpcsego+j1 3g9pj4 f2;qeiameter merry-go-round turntable thatde+j32e;1c94c po gmgpsjq3 f 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 ;l v)r7qba-jhemit -ir,n .b* of the rope lying on the top edge of the spool. A per ivijhrl-),b;r mtea.q7n*- bson 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 same side always faces the Earth. Determp7 vdot:jw vo7 *)v-gbine the ratio of t*w gd)jb:pot7vo-7vv he 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 f lareyp6p/ f 14 m0pu6xl6;dvdt(;hcorom rest 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 theyh:,2 r0z jhmut9 hda 3g(m,cz shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at consjm(cyhghh 0r :mza t z3d,u92,tant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cy5wp *d iex3m7ilindrical 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 s pdm37w* x5eiipeed 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 rear wheel (:ka:13 3l7km- a rz4g mtn b4vrgi je(feay1(s$\omega_R$) 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, bul+v,,1uijxl7f4tx wejz80 qbt 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 proces0 xjb+l4vulz1t e8 fiq, ,x7wjs, 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 a :ye26ppg4duis for it to use energy stored in a heavy rotating flywheel. Supposp2pu: a46 degye such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without 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 rqni-dz hr6;ani: oo q8lm8+2 $H_2O$ 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 o153ooa0 x0-hinach j hjxc/ 1an 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 and length L can piv0yuu .clp;6wrot 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 that the force of gravity acts at the center of mass pw;uc. uy0l6rof the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R+-e7, u;f slgucdvr *r. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against whc* -d ;vrfsg,ule 7+urich it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a tur5zjrr f/vyjdci /;; (t.v fgmg54ye2kn with a radius The forces acting on the cyclist and cycle are the;5y kdf y;jj/e z4igvv/tf(crrg.2m 5 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*i. wuxkd.;v7 *d0gzc 5bii opg 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 * i*i .0uwv7;g5d c ipbzokx.dtorque 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 rods, maun qx17is. 1e z(qhpm.king reasonable estimates for the dimensions. Then calc7(uq.p q.e1imn1 zxh sulate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consis .g* nt)l4mo3 b6szkdsts of two cylindrical plates, of mas. 4stk* mbsz)3nld 6gos $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alongdk-lh 0xp8)56neo v mi the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reacne lpkx 6 ho8d)-i50vmh the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do noe95)* eujb5kpzo i14qlx/ a lqp)qm7yt assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unif3x du8fuj82fjk ;q+xtormly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular ajd2tuf xk8u;83q fj +xcceleration 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