A bicycle odometer (which measures distance traveled) is attachs.j y818 uxd89dfjnrded near the wheel hub and is designed for 27-inch wheels. What happens iu8fjxdnyj.8rd98 s1 d f you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does arcw:mao . xv z9b-25it point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For whiwboc9r5:zax2- vit m.ch cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angut . kn6jz9oc,ae8qj e8lar velocity $\omega$ Explain.

Can a small force ever exert a greater torque wqggw ./-8zb tthan 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 4xyf7 v0 y(fo8l ru5j1mmegm, a sit-up with your hands behind your head than when your arms are stretched out in front f405fmm(ryy x ,gelv71jomu 8of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the ped5ozh 7 +jsjwm,al cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why?j ms7zj5wh,+ o 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 slender98. q*rid .,+u lr+cvuzymq gv lower legs with flesh and muscle concentrated high, *rc .uqyrdz9+um8g.+i v v,ql 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) carry a .j2zl n,d:;+bvxb uiolong, narrow beam?

If the net force on a system is zero, is the net torque also z(9idj iytop.ry s.1( kucy0t) ero? If the net torque on a k(.iiyt1 9spyur0ydj )o .(ctsystem is zero, is the net force zero?

Two inclines have the same height but makeu-cu3k,f 1+ euhml.: mlwe*oh different angles with the horizontal. The same steel ball is u .*le,ul+heo1 u-mwck hfm3: 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) down an)ylm/npy db 3snbypp22e(8w5 incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Whicb38 np5/2ys wny p 2ldpb(m)eyh 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 samz0 i n,)dbxdr 9z7g+dx+ cufh,e mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has0hgr+d n7uzf+d ,9 dxcx )b,zi 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 momentu1rj 1x5.dj7o 6vtephbm are conserved. Yet most moving or rotating objects eventually slow down and stop. Explaoh65xt. pr j bj1vd71ein.

If there were a great migration of people toward t4t:5u kgq0yyg q .3l5rzhm 4ephe Earth’s equator, how would this affect the length of the d h3pkrq4.yq4e u55l0y:z g mtgay?

Can the diver of Fig. 8–29 do a somersault wit;-mu k(5mlf2v wv b)zq)hk2cghout having any initial rotation when she leaves thgz v )2k-bv);m wc2k fqml5u(he board?

The moment of inertiabhip-rx5e( 2*+uqip v of a rotating solid disk about an axis through its center of mass ib*x-r(vi i5 q 2phpu+es $\frac{1}{2}WR^2$ (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 i *8 z-cmnpbl3vn each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, l bc38vnm- z*pdecrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howevblu u7dd*z/4 ler, one is hollow and the other is solid. Describe an experiment to determine which is whlu */lzub d74dich.

The angular velocityf61mgae)duu 3:t0zy7, rlp boas( y el;,+e dy of a wheel rotating 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.1dapgy3moytlzl7a d,,6+ :;re)f0u e(u esby Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freev 4hbi2(xcng)y 5ri)yly rotating turntable. What happens if you walk towarcg 4(y) bvnxyr)2i hi5d the center?

A shortstop may leap into the air to cath(+ . ,as5dyu-issgj4 dc7sfm ch a ball and throw it quickly. 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 5m-ds+, csy sg hsj(ufdai74. in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentumv h5tn;yz*pn1f9 1h .hgnca 6o, discuss why a helicopter must have more than one rotor (or propeller). Discuss one orngf 9z 1*c.vhho1t;p5 anhy 6n more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radia;)2/1zkii+ohkq tvn:so 3m r1baq z:lns: (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 amaud-x9 +yf:+ aavin (vmzing coincidence. Calculate, using the information inside the Front Cover, the ufav y(+:a+ix n-d9vmangular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Eatu hx5y*j82gurx fdg2-fw8(brth. The beam diverges at an anglety2*rbxjgf2u8 g-u( x hwf8d5 $\theta$ (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 65ck:ee,pd.e72)gkr qm 00 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow :7 r)e2edqpk eckm g,.down?    $rad/s^2$

  A child rolls a ball on a lx*brdp s)agwqwk 6sif0iwl8w9 +34w5w zh z/.evel floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its di kf/wz *h4 )ps85rwx wswwbgi+azq 0.9dw63liameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. H.t9bv*q5w bg fow many revolutions do the whe*b.tf5b vq9wg els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 r;t7/7ihos j ,avw ;wnov zp1a.pm. Calculate its angul ,tsjna vh ;;/a7pv.o 1zw7woiar 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 4.0 s (Figogy;rq, -dh/q 2w (lro. 8–38). (a) What is the linear ,or oh-dq q2wyg;(l/rspeed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular veu.p.nn - jxwd7locity of the 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 a point /ud*zoc :da u3
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particlbehp5xf1uf49lm2j ,rq1m 8h( rm hk0g e 7.0 cm from the axis of rotation is4m8ux2g hkjm(0fe5l m,qhb1 hr1 frp9 to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm t ; k bhdxuwkjn44h8r jcc.65nk 9 ge4.h)2zmygo 280 rpm in 4.0 s. Determin;mhexu.bg4 h4hkw2dj n kk gjzc95)n6.48ryc e
(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-.umsnn/+a gb,3oz cm $R_1$ 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 Monwyn1do1yf(+ 9kgu v6 on, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thoongw19 16knyufd+v (y ught 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 uniformly8v4z+z ag(ld g :(hbbl from rest to 15,000 rpm in 220 s. Through how many revolutio:hgz dvzlb a (8l(4+gbns did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Caxrnhgx 0b5c 2e+dm,/,kw v1ym lculate
(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 stres7j* n:d 6-2bncqo xcwxses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions bcdnb wc* 2o 7-j:xn6xqefore 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 in tap2sfoa,xk :. d1; ea:gmye2 6.5 s. How far will a point on the eoeds2 gkxy:p afma, 1:;2. taedge of the wheel have traveled in this time?    m

  A cooling fan is turned o/txtb:k, kvr. ff when it is running at 850rev/min It turns 1500 revolutions before it comkr bt,.xk/ :tves 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 revolutionsh:c34snr9l*i9 8doknu2op k w as the car reduces its speed uniformly from 95km/h to 4o ni4n9:rukpskd 9*832wh lc o5km/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 revolutions as the car rvgj8wv m-p/ln/k7+m peduces its speed uniformly from 95km/h to 45km/h The tires have aj-l8/p vwmv /ngk+m7p diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight o6xjj05ig. h5jjw jj m7n each pedal when climbing a hill. The pedals rotate in a circle of radius 17 c6 jj.jwgjx0jm7 i55jhm.
(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 end1:vy qqw6;c+p0 as7 x7rknaxc of a door 74 cm wide. What is the magnitude of the torquev1 wra qy:a776p;c n +x0kcqsx 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 about the axle of the wc d wdh7got5zfv;901 vheel shown in Fig. 8–39. Assume that wd95 v; 10vf7 zgdthcoa friction 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 thext.yq) p4wl o- ends of a massless rod which pivots as shown yp.x4ot l-qw)in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cyliiy3;rvv34mj s nder head of an engine require tightening to a torque of 38 m34 ry;vis3j v$m \cdot N$ 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 7pq 8a7qc.p+iq mv v5u- d;kqfradius 0.648 m when the axis of rotation is through its cente.q pmv ia fq7 pq-7kcq5u8+vd;r.    $kg \cdot m^2$

  Calculate the moment of inertia (zm zc jhpq76iacx;45of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the x7;ihmcj qa zc54p6z(hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod ij (y 3bhxeej +b:5mw/ts rotated in a horizontal circle of rxj3 +:mty whj5/beeb (adius 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 pottv- 5ke.1z-fm kgo,i 1ipw5t vler’s wheel rotating at constant angular speed (Fig. 8–42). Thelv,f.pi-gtmz 5 1ei5wv k1ko- friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown 9pq5kn +ry*tein Fig. 8–43 about 9npr*5e+ qtk y
(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 is g74gkb97ym e)wvq2 wcwb( ba.$5.3 \times10^{ -26}$ 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 corre8qdc5po9su eom:y9u r v c;9 vr(;0espct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32qup8cs e(9po5vv9 e9;r0sdc;m: uyro 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 a n5f3dtzraky*5dzet-(s/vn * nd a mass of 0.580 kg. Calculate3f zk5 d(e*anzr*s y5v/tdt-n
(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, accelerz15z c;g3po8 8rpqgp 2vuono,ating 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 hand-driven merry-go-*xn g: bje;tw+dwv62n hi 1j8around 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 childri vw t2n hd16exn*+wja:jgb;8en (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off+os.h-9;7qqdm jxe t/npo kz ) and is eventually brought uniformly to rest by a hed./njt ) -zqq7xs 9k+mo; pofrictional 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 accelerattoci::byw y8 w g:-wr/es a 3.6-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 *x75fnh ,kkzl9ps usfti;j+ 7 solely by the action of the forearm, which rota,jhn7; pssf u*9lxi+kft k75ztes about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long t e8jjoyve791. afvp;apd6 y49b ;im zmhin rod, as shown in Fig. 8–4679fye vz6;jp;.jpay m a1mi e 9bvd4o8.
(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 ht7d 9j.//z)5ga4 *efbqnaz bcm 1e ihtwo 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 ham:av8qghl0; vp1*0 vbjnq m-qkmer from rest within four full turns (revolutions) and releasvj*q hnv 0 k8:-01a qgqvbmp;les it 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 inertia of/sxxo9 2j8/ c7ozv ccnvp qu:3a3ib6j $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque(ez 9o: /bnmn3:kkyjr 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. 7* muxzejyf4m+wd*3f apiy030 cm rolls without slipping down a lane ap mj37*30dyfua ef y+*m ziwx4t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic enenh15o7/wkntl 5l/a4 avihec ,rgy of the Earth with respect to the Sun as the sum of twoalncwt5l/ vi 5 o,4hah/e 7n1k 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 nn6l jvurw .5)k m(iv/cet work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cyli(/wkvni.) 5rum6 vclj nder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rcrp0ic01j s )pest and rolls without slipping down a 30.0 pij00s1r)cpc$^{\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 verticall k: *jfwd x,mq1kprc8.y on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the,cw:qxr 1d*fp jk.8 km pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotatingbex9v gmlwfcck 2ih) :ti xk:.*wpqef) ((8t/ on the end of a thin stbx8lwx*g .me)c:c9 ph i e2qkwftk f(:vti/ )(ring in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of 2kvua0bz;jb 4a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpmb;a2 ubkv4jz0?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, ons8 ys7pj;2qcp3 qhd o au tgp:yzh;0/: a platform that is rotating at a rate of 1.3rev/spuq73 8thd sc /g0 q;pzj:syy:oh2;p a If he raises his arms to a horizontal 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. 8–29) can /ed+(xcb /a ibj7n+wht 0is h9reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rot/ab7 sxie dnit 0 (b+w9j+ch/hations 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 fromz0dy bz-oa)ng9k 3 zc, an initial rate of 1.0 rev every 2.0 s tnkczz do)z9 -30g bya,o 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 aroun9qs2 n(vw;lsy k8l,/jv8n bzyd 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 shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel 2 vwn n,(8sl/9z jkvsy8;qby lafter the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skat w1 lf 3poeh o;lqg-ktdu911q/er 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 angularx19 fo-9xcmk v momentum 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 cylindrical disk of moment of inerstw otjf0+0c 8tia I is dropped onto an identical disk rotating at angular sp8jct ft +ow00seed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 i4+md+pl- jsuo;kij81c 9xmj $rev/s$ 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 me gcj/ q.zq2m(:i zf,idrry-go-round platform of radius 3.0 m and momenm q/. cid:2jzgfi q(z,t 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 wit r8wuyp 8. ovrd1.8bw fo9zr(zh an angular velocity of 0.8 ( .1 fz rdwuzbyr8.ro8pw8vo9$rad/s$ 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 abouh ocuo8-g-z b/t 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 Sun’s new rotation rate be?- h cgu/zoob-8(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 e,ke3* ftw6pjd xcess 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 +v3 qo/io5wn5)v2xs,mopqgus- d-s 2c9 a y cl$ 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 free5p:6;vxls o 8b hgzb:gly without friction. The moment of inertiz5 ol h6 vs;pbb8x::gga 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 9rr,vfk p)+ 1wyto;rvfx *wd( the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a frv+);t 9xork1y, w w(rdpfv*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 mwd /0mrh*ap6 rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the 0*h rm w6a/dpmrope 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 bnev/lk 6ct:u n)9xlvkm60jq (7 twb9o/jqr 4same side always faces the Earth. Determine the ratio of the 0 :qb/)v qnj9mkjb t4tc7nx u6ew/ 6kl 9(vorlMoon’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 at1g(gva*m v4hj a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylindel wxts7iw)z/ 2r of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque ws/2ztl )7ixwdelivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrica98zk-7 s)(z wwuo3dm t6iplrdl disks, each of mass 0.050 kg and diameter 0kzd-m8z)i6s9tlw w r3(7 podu.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 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 nle,l:7at y* arear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rota9y8vpnry)lljy2-w yac *s ,p-16it ltting at a speed of 1.0 revolution every 12 days. If it were to v6yl--p t*nl yijc1spty9y,28ral w )undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution auto0j (w5d tov-zmmobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a ( 0t5 mzjdv-woflywheel “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 je03n ghp/yg8 /e v1dx$H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal g- d1p0+vtyjk7hyqf .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 canthnc(bk, w;7z 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 ron(zwh, c k7tb;d, 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, and wewp(pyzm +s q-vr920vg want to exert a horizontal force F at its axle so that it will climb a st s9-qzp r2ywmgvv(+0 pep against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on agukrpjq( w, /i.k b4,v flat road is making a turn with a radius The forces acting on the cyclist and cycle are the w.krvu 4 i, q,(jkbp/gnormal 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-/i8i7gk*x7tl nkl1w ckg rock into a sling of length 1.5 m and begins whirli7g/k ci1tl7 nxwl*8ki ng 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?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and r 68pd,7u tc3bbur3zx her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angb3 bt 7d,zx3ur ucr6p8ular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, o4,jky ;xdb pz:f;bxz4 jdy:k ,p mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ozfcx*5gzu7 w1 bbcc/ i++ tiu6f Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop witho5f +/6 i uxciwbbcg t71+cuzz*ut leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assupkc1qdp;81d;t) 9 z avpqtj3si6pb, ml*9ew zme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its sp,xogbus 5r90;wdo)l2wz (qx i eed uniformly from 90km/h to 60km/h The tires have a diameted9wix wz)g( rx lubq;52,o0 osr 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