A bicycle odometer (which measures distance traveled) is attachedlh4f . gm l 6o-1(g,j,stwpgoe near the wheel hub and is designed for 27-ig s,gt .o,61 4ojgp(h -fmelwlnch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates egh cxh;xb()e8( hp(h at constant 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 have radial and/or tangential acceleration? For which cases we h(8eh;xx)(hc ( pgbhould the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by anf 7qd9jyo(1x single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain.s33ncpdjh7y *

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

Why is it more difficult to do a sit-up with your hands behind yourmjg/7a)n f/ tc head than when your arms are stretched out in front of you? A diagram may help you j/ta7 g f/c)nmto answer this.

A 21-speed bicycle has seven sprockets at the rea rj78l;n k6tnj vjsplh, b/::)r.hrsnr wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front.6lsjsk , nrp:rtl:b) rjj/nh8 ;n7hv sprocket or a large front sprocket? Why?

Mammals that depend on being ablen ,t9g. t)xq4siep9tnv /lzw: to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the biqt: )w 94z etps,n.ln9gxt /vasis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carrya s2rak)ie 3fa y9vq68 a long, narrow beam?

If the net force on a system is ze 2jvw,;-vmkv c(-r ueso.nb2fgz7(wero, is the net torque also zero? If the net torque on a system is zero, is the nef(or.7 ,-;cuwkz2vv(mv eswgj2bn-et force zero?

Two inclines have the same height but make different angles with the h;b9 n-mk70bbr u5be qworizontal. The same steel ball is rolled down e 5bbn 9rwu ;mb0-7bekqach 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 in p6kntxu/ 6dipvnv( 1 /qg+pz(cline. 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 g/k6tdgqvuvx6z+/1pipp(n n ( reater total kinetic energy at the bottom?

A sphere and a cylinder have fh zafh i6vpv* 0upgp 7/)2)puthe same radius and the same mass. They start from rest at tfz*)vfa60v/ pu 7uphig)2h pphe 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 greater rotational KE?

We claim that momentum and angular momentum are conserved. nsn zg(l 8 41ftb un(8,cnb)ltYet most moving or rotating objects eventually cst 8lgu )f8,1(n 4bbn (lnntzslow down and stop. Explain.

If there were a great m 12 l,c2qdnyxcigration of people toward the Earth’s equator, how would this affect the leq ny2c,dlc2 x1ngth of the day?

Can the diver of Fig. 8–28d fs/jk--l0 lyh4pb0 dwx v1l9 do a somersault without having any initial rotation when she leaves the l8y-s-d bdxwjf ll00h14pk/vboard?

The moment of inertia of a rotatinri/0 h0lp1vi f-9pst+li el+iv9cb4e g solid disk about an axis through its center of ml104i90cii+vvpihr l9let /ps+ e fb- ass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outst ( -9+ tvpt;mk, 0-e2qkb8ecpfr hbulzretched hand. If you suddenly drop the masses, will your an;pk tf9z0p8 e(ltu+qrb 2, v e-mkbh-cgular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeva cs(s5pyxgw7 gh2l94er, one is hollow and the other is 7hg2 sswa(x4cl p5gy 9solid. Describe an experiment to determine which is which.

The angular velocity5mi p1v sevm0qk jp778 yew8;w of a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of thpemms5y 8qv7wwj1epk0 v; 8i7 e 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 stan2xpag9 2+-qg 4mc wv qzv7mq)hding on the edge of a large freely rotating turntable. What happens if you walk tq v-ag2hmg9q p4xm zwcq2)+ v7oward the center?

A shortstop may leap into the air to co/st hy)t8t gidoy818 atch a ball and throw it quickly. As he thr/d88 yys hgt8o)i1 ttoows the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why axjxk u p;gmg,kw4; t6kcw+e,)rw 2zz; helicopter must have more than one roxt u kwr,kw 4;;e2cpzg ,6 jg+x)wk;mztor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following 1u:bvy-r uos91do x+tangles 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 coz/q w5hyh x9x5incidence. Calculate, using the59qxw 5y hhz/x information 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 Moon, 380,000 km from Earth. The zt13i)sr5eq o0 7ytacbeam diverges at ansq )iy0 1r7ztcto3a5 e angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500qkop 64)wj x7pxze *9h rpm. When the motor is turned off during operation,7kzpjqxxh4oe69w *p ) the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a ley tiou:w/z z)46pw;hq vel floor 3.5 m to another child. If the ball makes 15.0 revolutionz:4h6)woq /i;zw pu tys, what is its diameter?    m

  A bicycle with tires 68 cm in di j ,c94yrr*u7tmo -t og6qkd3eameter travels 8.0 km. How many revolutions do the wheelqjo- 47t rtuegc3y 9o,*6dkmrs make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 sa0 lhb1x0mpo o)s6f+ rpm. Calculate its angular velocit s6hoo001+px)mlbs f ay 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 compl5d1p8x+gntcpw(k8 yogu +obns- ; hs,ete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated8gw, s8k b+-ghtcx+s15on npu o; y(pd 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 (a) in its orbit arou f1cdy4gd29zknd the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poi9+f;qyp 9+-rubcx y hwnt
(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 pjbkevf1g3v 9w48+x; adqf av 2article 7.0 cm from the axis of rotatiojvbgkqwd;f493f v8xa2e v+a 1n is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates un e*kdg 5yqk+)v(f1 eguiformly about its center from 130 rpm to 280 rpm in 4.0 s. Determef 5*y qk(g vk)1deu+gine
(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 radiusv) hflei, d-gou8 :nztbh w9a(6*ijp; $R_1$ 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 themsel* s-,jpdu xr)g( dx1 0v ,ixjjrafd5n.ves into a slow rotatija xu5xi)d*d ,.v 1gsjxp r,d n0j(-rfon 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 rest to-/1tfex as-d j 15,000 rpm in 220 s. Through how -sjt e/ xaf-1dmany revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1201m j -s/ k,:*;jxrc yggmk,xmj0 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses ohn/3u0fi*3 vy lo7 mssf flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn throvso30h *nl3y mius/f7 ugh 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 accelerate 65uhd+n6voxu2 rxex ,s uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a poih 2v5nxreu6 o,u6 d+xxnt on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It t4 hry,- *dxdsvurns 1500 revolutihdsr x4*v,d-yons before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed bm ihxs(eu 9q0q+a/k(e zhb/w bn3o8+7rn ky2uniformly from o 7h + 9r/mwsknyqqb(ae0u8eb 2 3i+(knzbhx/ 95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly/jg.ld2lzx8j from 95km/h to 45km/h The tires havegjjz/xl2 8dl. a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal whosth 4b/ mdehq-1b)2x en climbing a hill. The pmtd)-4 1qhhx2bs oeb/edals 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 forcg0tmv p78j.ax)ua f p,e of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exeu7g.,atpx 0apj 8mv)f rted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque nyeg7sx(c 3 ,kabout the axle of the wheel shown in Fig. 8–39. Assume that a friction tor 7,en ygxs(c3kque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, ahl) 7*sd)rmmpwaw6pl1r- o;4f nn(q hre attached to the ends of a massless rod which piv;omwdal) 4 npmw p( qh1l s-)nh6*7rfrots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder 5.ac2hs1 pdl yhead of an engine require tightening to a torque of 38 l512ay.dc psh $m \cdot N$ 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 (mtugqd++ r9pt 7ll)aof radius 0.648 m when the axis of rotation i +dtg( +latrp97q)um ls through its center.    $kg \cdot m^2$

  Calculate the moment of e4fxc-pnw* y61k4fmqa2i0xlinertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mapw 6 x42 *iy4-xq0cmk1naffelss of 1.25 kg. The mass of the 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 oiw+ 068dzcif horizontal circle of +0df zoic8w i6radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating a(5x z 4ppm .eepg*nv+ot constant angular speed (Fig. 8–42). The friction force between hmev(+ n pex5gpoz4. p*er 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 o wi be5aiqsyb5a;;jrh / .xq5d.(m( ozf the array of point objects shown in Fig. 8–43 ab;hd; wrqizbqmoe(ysxba.(j5i 5 5.a/out
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists qrp +qy*hj/dn9pn* k.g86sl t3-jdvv of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satelli3 k,9z9 z wf:uukdxq1gte spinning at the 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 of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 3zkd 1:gu9zu 9 wfk,3xq2 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a u /a62xfjab g 8joloi*7niform cylinder with a radius of 8.50 cm and a mass of 0.58joj*a2 xi 87f6ga bl/o0 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it fromvtuy h(+ j)po) 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 smalxi .mrtepzqg n8e)x,(95 vze: l hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mavix,qn 89g :eee 5zprz.tx(m)ss of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventuallvd;b 3z0cnc 4mq)uwy,hm l4:f y brought uniformly to rest by a frictional torbw d,)hm nmu 3lyf qvc;0cz44:que 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 accel 3vm 7u(bhp3cw8vl6oq erates 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 *d8g (khbtd a3aj8i6ssolely by the action of the forearm, which rotates about thek6(*jat8dia h3dbsg8 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 consimi; a duq9y*gsdtq +97dered a long thin rod, as shown in Fig. 8–46.sq79m9 y qdua;it*d +g
(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 cowy8psb) e(lq1 nsists of two 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 hammer 9dv5;d jc,jmq2pkn, r from rest within four full turns (revolutions) and releases it acknj ,qvjp9 d d,2m;r5t 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 han4r3j zc . 8atxry3z4gs a moment of 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 t5. pf uxuucr04ju8wd wj*9ju*orque 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 withon+5sl 96b( ydygz d7hbut slipping down a lane at 3.3+ db 6l 7g5z9yysbdn(h $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of 2t):g2jgiq; idae ea0the Earth with respect to the Sun as the sum of two ter2at qdi:e ga;)0 i2jgems,
(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 masi0q +a:duns ht 00hsm7s of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotati0ma7qhh+du 0 ss:0ti non rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and opfrv cx:n9 q1ss ui-+h 4uy51mass 1.80 kg starts from rest and rolls without slipping down a 30.0vq sxous4r c:h if91p n5u-1y+ $^{\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 only(1kt-ur h2yi;b, av its tip. It starts to fall and its lower end does not slip. What will be the speed of thehby1i,(ul;k2 r -yta v upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum dbf/::;v ynaqut8ff 4of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular spf4:;bfd /qvt: nya fu8eed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding ss;**,qvt m+v rsck;c0o2 r,idv (mhr wheel of ;m sd+, mo* q0crr,str ;hv *vsv2(cikradius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rot r e+,d)q04eaj)nccfqating at a rate of 1.3rev/s If he raises hic)q f edrc+a)jq4ne 0,s 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 reduce her momentucvs8:2+,km+ chjsdg of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makk:h+vdmsc g,2jc 8s+u es 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 f65luu mgp/g2edk8f);smb9b k pa(gp 6rom an initial rate of 1.0 rev every 2.0 s to a final rate of kd9pp2fuu) sp; a 5l g(m68k6bmbg ge/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 center at a fr6z af38:ggjub equency of 1.5rev/s Thegb6 guj:af3 z8 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 figure skater h*ol+tto p4/x 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 momt: p:8ptu/ hqkc76+s dqp udg8entum 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 diskr m wx*+ ylwd3f53obgzl*/),wf- irc l of moment of inertia I is dropped onto an identicbo d5rl m,*wzf/-* rc3+xwg3 w)liyl fal disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 s wqbp88z63z b$rev/s$ 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 m7cjl3rae o6v9iq9:n r) )cwiwerry-go-round platform of radius 3.0 m and moment of inej 6:o vc r9)rw39a7niwc)lqeirtia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with a 7lrbr3em: nlf)ou*e./ tsnu;n angular velocity of 0 lel;tu/3r7)*ro :bm.sfne un.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses int, e 6tu;lbcp.zt n9p;mlqv37do 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 Sun’s new rotation rate p9 u;qe6 3pcztt,;n7.dbl lvm be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120:3l zcuqg l1ciipl(2dj w,+ t9 $km/h$ 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 p 0jc7 ugvq0jcun-un z-4 ;(qw$ 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 withoubo h,:k vpt9 qx+5ctc/t friction. Tt:/vhp k+c9b,qtc x5o he 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 personi4n wlv3a4qs:.0u uku stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings andlwu:kasqu n430v 4iu. 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 i*x zs3/v y*7oft2q ak3t lx0ion the ground with 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 v ikz l3o7xs 30f2xiqya**tt/far does the spool’s center of mass move?

  The Moon orbits the Earth such that the sames 2ass i41t0ly side always faces the Earth. Determine the ratio of they tsa4si 0l21s 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 fj b3q0;r hd .n-mlc1.fvg2c rgrom 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 the shape of a uniform cylinder kgd. 6g s sr.+7wiln*yof radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant aliygw*. rs 7ndgk+.6sngular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each otfdsa6kc 7/f x.*6r0 l8v dtgjf mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches thefva.76c 8dtltdk 0 *s6gjxf/r 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 angui29:(zyq,3jyiedyh 5mt/ek i lar speed of the 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 size of our Sun, but with mass 8.0 times as great, were rk ncu x+umwe:45o)o q1otating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume ton5 c )uwqo+x:14 mkuehat the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to n go1dgi55lr* ogl,ap5wp+0y.6mmz cuse 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 need,oggwd55m*6 nlazg rcpyio 51l+p.m0ing 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 rdws gx -p kurr4a:c k (;ikfcbpc(..1fx+s)5an $H_2O$ 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 rollinc xt8( s(qou-bs vq+e-g on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely ( v (iu9 i 4d/cmwh/vzx(w9ks)yg;j;b ei.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) thew;b4xvc g/9s;u m9(/wi)z(jydevhik angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floh. /yju syxq 9m1ba5b,5er b;vor, and we wan ;b 51yy, q9vbr5mjb xhes./aut to 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=4.2m/s on a flatkybgg 9/funnkf:8ndo+v2:(p road is making a turn with a radius The forces acting on the cyclist and cycle are the normalvo2y(+ng k9kd:8pngf f: unb / 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-kg rock into a slot3v ,xm-(fhe at- x4ding of length 1.5 m and begins whirling the rock in a nearly horizontal circlx3emt d (tf,-o-hvxa4e 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.nxg0(s wtwmx8g7smmk )i b /d *a:p.7vi jc.p’s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensibw m8dsp w0a x7mgit:.spknmc)7x(*.jv/ig. ons. Then calculate 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 consists of x4nx92 .x*quzagf7y wd( mqrvby .s.1two cylindrical plates, ofns*.m9 uxq.wqgxyy.bz adf4x( 12vr7 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 alo0y4hnulaqpf*77k . h rng 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 reach the highest point of the loop without leaving the track? Assum hukr* p0fh4nla7.qy7e $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do,fu2a4q5yy ti not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speezldi)m)u0 ir mj*,gp8 d uniformly from 90km/h to 60km/h The tires have a diameter od ,) 0i 8)z*lmprgjimuf 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