A bicycle odometer (which measures distdmdk.;/rf d() jqzv9 dance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 2/kd;d fd)j.dqm9r(v z4-inch wheels?

Suppose a disk rotates at consfr ggdcovj4,iq n (9* hu5kv9)tant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point havnk4f)g9q*9 c(rg j,uvvdho 5i e radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angun7a.zmsrmi3**pziz 0eeo:v d s ) t,4ular velocity $\omega$ Explain.

Can a small force ever exert a greater to51azziv1 u5 hcrque than a larger force? Explain.

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

Why is it more difficult to do a sit-up w*(r q-n 8hsv.q(bsw :,ajq hzpith your hands behind your head than when your arms are stretched out in front of you? A h 8 pnsaqv(s:, hwq.(qbrjz -*diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three aptskv)3xss. m3e ;5 3 l5bhjzrt the pedal cranks. In which gear is it harder to pedal, a small rear sprocsse z3 b 55vhr)spj3 ;3xkmtl.ket 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 runtlgd9f90x chon a a;kt54r9e 6 fast have slender lower legs with flesh and muscle concentrated oatlgf 699r9tch; a4xe0d5 nkhigh, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35,p2:fi lh :ygi 2tyy:s7vd ry;) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the n1f7g:baw3 ,5u oh mv ypy*hiecci+*6q3,qsxqet torque o:y 6 yuq,, ghpc*+ cxboisa q3mhf wei5*317vqn a system is zero, is the net force zero?

Two inclines have the same height but make doa lp5 +2lqhm4ifferent angles with the horizontal. The same steel ball is rhq+5o24llp a molled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simuv2 j*i.klv4sxltaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic e42ijkv. xlvs *nergy at the bottom?

A sphere and a cylinder gbw-82g wofba20xj7qd4 .coz have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the 2gc w47dgab2ob8 -fx.qwj0 ozbottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved.btbokx9 );zp, c. hm;y Yet most moving or rotating objects eventually slow down and sto )yk9x bcob.tph;;zm,p. Explain.

If there were a gread/9.l w)njhvza *,o ept migration of people toward the Earth’s equator, how would this affect the lengtv n,awphjdo./ *e9z )lh of the day?

Can the diver of Fig. 8–29 do a somersault without having any init4nux. m7owepb silja k **y*/(ial rotation when she leaven e/l .ix7 skaop*um**(4bj wys the board?

The moment of inertia of a rotating solid disk about an axis through its centqo2 (39qy - juyzayr-eer of( q-9qareyzjyoy2 - u3 mass 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 rot+7t tijvci+ntl1 fi(/ ating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay tjctl i1+( tt/fi7+nvi he same? Explain.

Two spheres look identical and have the same mass. Howeqzs5n1k xupn embyyu+e)q u3p22 7 w66ver, one is hollow and the other is solid. Describe an experi 25qyzpe13mq6nu)uby kw2n+ 6 es pux7ment to determine which is which.

The angular velocity of a wheel rotating on a horizwdt sxd937x i93v 7rwsontal axle points west. In what direction is the linear velocity of a point on the to3i s rw79d ws397txvxdp 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 decreasing?

Suppose you are standing on the edge of a large freelag5b23hnar1 (q(fhecy rotating turntable. What happens if you walk toward the cra g3e(qh1b2af hn(5center?

A shortstop may leap into the air to catch a ball and throw it quickle(g,uhr.(7uc8 z:xvukw+ o mry. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the o7(+ o u.rgrh8v ukeuwm z:x,(cpposite direction (Fig. 8–36). Explain.

On the basis of the lakx(od)1w/7 u8mqudlh:.x m/bv 3k xpiw of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller)bl3xpixk/d.)7v wm81hduqk:umo( / x. Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following an k;h2k( 1ved41qvtgp pgles 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. Ca n9lwqlq f,ks;pg clcqn (7*x6t5t d50lculate, using the inpgnq, cnt 9c;0 d57lqf(6 sl*wq5ktxl formation inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the vpcmw scuu;s15 .a,357p8 sl ava 8ksoMoon, 380,000 km from Earth. The beam diverges at an anglecl a w, m;8ospusa5cv k 173a8pssuv5. $\theta$ (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 5dvq7v0m 14)ns odbiq motor is turned off during operation, the blades slow to rest in 3.0 s. What is the aqiqvm5bvdo0)714 d nsngular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the b q jz an/ t(*hfxvpn ly/ws-)gdn./8-qall makes 15.0 revolutions,twdfna/).pgs-q8n vz/xn(l h q-*yj/ what is its diameter?    m

  A bicycle with tires 68 cm in diameter tmo-2 arb f1 agx6fgp13v1iajink4y9 0ravels 8.0 km. How many revolutions do the wheels makeo6bnaja1 g410x9p 2m-f iykrgv1 ai3 f?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. shw,dkxv(eq f56ge 7:Calculate its angular velocity in d5,: xv76(hsfqwegek $rad/s$ $\omega$ =    $rad/sec$
(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 j074 u) vbq k60ttfh*dl0gk dfs (Fig. 8–38). (a) What is the linear speed oflkq*t fu 76df0tj)h 0dvbgk0 4 a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth;)cd xpa2p kt) (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sp:ws g.lg a+irov g5dk;0/c;uieed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must9j5s v0u a;k6+jeb mhh a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,09hbh jj0;ak6v+e m su500 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm gf(o2e hx1bu uc 9lq;,to 28, f2gqehcb(9;1lxu uo0 rpm 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 bd9cq.qp,q4z $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put e ,f 5mie*yd1dthemselves 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 revoluti,im* feyed5 d1on every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Through how.kn rzn qns,k t-6ee6+ many revolutions did it turn in this time?.n -66nesqek n+t,rzk    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.7vdmg2luohc()x rjbh 49 qd.vtx59qs7- yv2d Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling owpcj/7n8pb :“humaw/7o bc8np :jpn 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 rpm to 360 rpm 27s: 6 x enke gbmo3ymu .e.mvk;(vra)in 6.5 s. How far will a point on the edge of the wheel have traveled mn) mge76k: 3;bkyu m 2vsx(eva.ore.in this time?    m

  A cooling fan is turned ofsg5d,c+oki.. nw/oj4 heh/arf when it is running at 850rev/min It turns 1500 revolutions before it comes /i+d/o . g h4hwrs ea5o.c,njkto 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 ; e+u),bten:x8 ithw u 5u-xb-rkx g/fcar reduces its speed uniformly from 95km/h to 45km/h The tires have a diametert:uu b 8+x-,enxxg;5iw ebt /rkhu)- f 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 revol7cvr- 2d.hm5hgtz4 lxutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamg 2xht4 mv.h-5lrzcd7eter 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 each pedal;m eicnx)r;t vidxb *6*k*r- 2mp6mix when climbing a hill. The pedals n6 vi*c- e)x rt;dp6mrim*mkxi;*xb2 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 p2re;vgnq4q n0 p0la vc9 9j( v1f4celw(hg3oof a door 74 cm wide. What is the magnitude og(1pneca;h0 n(wrflg3vqv qcj492 v4po0l 9e f the 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 ab cbv; q-ecu 3k-cw4t5oout the axle of the wheel shown in Fig. 8–39. Assume that a frictio ;c-wu 3qvb5ctc4eok -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 ends of a massless rodnp6r5glmh t./p2d d+c which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction ofnd65gp mprc 2/l.t+dh the net torque on this system.

  The bolts on the cyliod-1 2j6hzfb ynder head of an engine require tightening to a torque of 382b zjy1-o 6dhf $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when the a-k(nvv q1 (fu 3qvoj6t0sk a0exis osu-03nt avve01 q(kko(vfq j6 f rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diam1plhcano: )r5-ly a x (5:menpeter. The rim and tire have a combined mass of 1.25 kg. The mass of thl5eapn)m -ynoh:lr( a1:xpc5 e hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a zr:,m+s:d l pphorizontal circle of radius 1.2 m.:+ pprz,d ls: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 constant yot ta(0;+e:fi s;sckangular speed (Fi(+tyk sts cf;e:;i0ao g. 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 of inertia of the array of d1tdap6kpb wo0:wil / c(+n8 gpoint objects shown in Fig. 8–43 about 1+ dc a8d6kw/:(n 0wtbg olpip
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mass h34gjx* /chq ngf 81wjis $5.3 \times10^{ -26}$ 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, engy8w;2bqb0yllg 3y .odineers fire four tangential rockets as shown 3q0;.d o 28ygwlylbbyin 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 csx;e 8fb:z/ sbylinder with a radius of 8.50 cm and a mass of 0.580 kg. Casfzx:bes/ 8b;lculate
(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, -f/ g,s7 z6qk ekern4waccelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hb xqeipa*-/if2-xyd( bpv.x +and-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque -vfxxiy dap-/i+*2.b(bpeq x required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating ah3 +na jv9fc:8f2fz jmt 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictionalj+nh3 fv9mca:2z f8fj 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 ball0k*rfl v1-e7bun;uy4hzqeex s g9 7; b 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 c0yxy8 or ef)slr3d -9solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The balfs orex380c ly-y)dr9l 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 (pjdk9ztc2+qxd x9k0be considered a long thin rod, as shown in Fig. 8–46. kxdj +9 t0pk2zcqx9 d(
(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 sy.fh+a4:yje masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hamc;2n5pn +w cdg/es;l rcl* t3qmer from rest within four full turns (revolutions) and releases it at a speed 3clwl edq/;st2p n5g +c*nc r;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 inerti3hdq3vx: tew- t ov.(sa 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 torqga fxq;52vn+p ue 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 rollsaei10pm;x(-ld7 bd:;(g g cpfs; mrug without slipping down a lane atsl7 mcm1d;0:ai(gudep xb ;-fggp (;r 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Swp/(ptfnb 5k:n jh05 uun as the sum of two:/n5tbpkn(f 05 hju pw 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. H5tlz+llywm7cg 5, (o sow much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a socgmsl,+tl7loy5w5 ( zlid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest ani25.4q dsy,ap jvmwp (d rolls without slipping down a 30.0 pdyai2q(j4m., w ps5v$^{\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 itd8fh:gt5v.ou n*e mgsp zt , *c2;9uses tip. 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 eneh .tug*c, n9;*s sovtzme5:u28d epgfrgy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end ouof/7r;dqzl+o k5ao erpqif /s qa: 0m,(( p;if a thin string in a circle of radius 1.10 m at an angular speed oil0 z,rqpfq//(ikoqs5ue 7;;aprm: + fo d(oaf 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kgv:gpg3ma.dztk58 e oq *p l31c uniform cylindrical grinding wheel *.q3 8kd5 3:lgatepo 1pzmcgvof radius 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 atjn//aq0co/ 6+mtifo o his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the spq ot ma6o0/+cno/jf/i eed 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) mamy lz1212 ju sz++krcan reduce her moment of inertia by a factor of as+2mj2u1 1kr m lzyza+bout 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 fr1y c1md.t l-koom an initial rate of 1.0 rev every 2.0 s to a1mc-1.old y kt 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 axis through its cenj8vk pjx 9-xdyy6(1i3s :i4ty+ b xdenter at a frequency of 1.5r4+ xs 9-yn:bi3 8dxj6d1(xki vey tpyjev/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 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 figurewzh y)wb2du(; 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 theqa 8;c8f*qb bg 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 cylindrical disk of moment of inertia I is drb 1f; impuo)p - i:jqunc3g/)popped onto an identical disk r n b)pcigu/u3j:o-pmf)i1 ;qpotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2p8lvx-qx9t8k iu0 a ,mo5c bc,.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 rota 1( o7(whxxwkfting merry-go-round platform of radiusxkx ( wfhw(o71 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 w2vdme 6k6k rq2ith an angular velocity of 0e2 vdr6 mqkk62.8 $rad/s$ 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 col+ru ;gvx+s p*s99e0u 2rt c yv-lmlm5glapses into a white 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 momentum, what would the Sum5;lrp0y+ 9ltr2 vc+xes-vgu*sg9mu n’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 ky/8zn xt:hlngz 2p9 -ngk;s8 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 x57z1/bz ))heosbgx j$ 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 rotate freely withw o dn0c9x28iu,.vm;afkq7 kpout friction. T;cnim k7902.k vqxaw f8pd,o uhe 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 6.5-04wc4fw trq(k m diameter merry-go-round turntable that is mounted on frictifcwtrk (w44 0qonless 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 z88)j 9er2dyiaepv ,g6nar 7pwith the end of the rope lying on 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 of mass movevrjd,8ya rzieae )pg 7n28 96p?

  The Moon orbits the Earth such that the same side always faces th p87qww,6y( rxxit7dm e Earth. Determine the ratio of the Moon’s spin angular momentum (axw7t(xpdy wm8q 7i6r ,bout 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 mizh6*k8 r d5i l tl2p9nxgu5x5/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder ou k-iaewiwb : +2)hd3ff radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular afiaui ):d+e w-h2b3 kwcceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.001lh 61l:c7w 7sujimxmeqxw050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindr :1qh17uw6ix esmc lx m0ljw70ical 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 gwpk, 4g ,blzigh7589ig1 rgathe rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the s5pg/p1is 6t;bolg* lk ize of our Sun, 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, /* ik5t6;1 golp blpgslosing 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 autoqwk6nx cd f5c2ksst 6 (q9a(q2mobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diametec sws96q kfa( xnd(t2 5kcq2q6r 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 illustrat0hu*hg6fy:h mes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizont *:-ayjdhcpv9xp/5 ff3. dlmhal 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 Mw4c(j8f k:iei and 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 ic:ekif wj 8(4acceleration 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 rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, ah b8ateu)xwnj- 9(y) oho )0xhnd we want toj) (aoexh)wt b8yo) xh9u0- nh exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=adu+47ya w( 2( (xsbnncdjmzdz 21,bm4.2m/s on a flat road is making a turn with a radius Th(ybb zn4(xun2j s+da ( a ,mwc1d27zmde 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 xqb-sk)u-k-8wc fe j20.50-kg 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 f -bfj8xu)w- kek2-cqsrom?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her atvxf kivzzkw *c, c4+8. r.nf0rms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning c. kv8, n wxf0kr*.tc f+4zivzskater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists oa w1 *qaauf.ev36blu v; at*p5f two cylindrical plates, of masb wvu.5v3qaaua;*e1lft a6 p*s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of F, pi*yfic xx wj-,x3l(:fe9p2btgh e3ig. 8–58. What ,pihwb9 y3ctx, je exf23(* fp-xi g:lis the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but th:-zmu2ri5 u do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 rev,. xs/ px/m4mls .lmadolutions as the car reduces its speed uniformly from. ,/mmallp4/ dx.sms x 90km/h to 60km/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