A bicycle odometer (which .gq k)vfkxe *7j0t6xy measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheelsyjkxt6fx)q *0.vke7 g?

Suppose a disk rotates at cons airrc .;k fmqf84q-6stant 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 casefisr-;a.4r8fcq q 6m ks would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describny;; ;eqk zl4vw44cp eed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger cckz61 qb (2jq*n4ym sforce? 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 with your(dtr lkvlso6 ,y dn4*/ hands behind your head than when your s (k,lvy/6d*nl4t dor arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and s2ut m7o b 9(*rtfzz4jthree at the pedal cranks. In which gear is it harder to pedal 4ztosjm(2rtz79*ubf , a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to/fh- m1c dc( q:zdtozvg k4u4fm( 15xo run fast have slender lower legs with flesh and muscle concentrated high, close to the bodmdox f11zt(-gcod(/fvm 5h ck uq:z44y (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) ci93 ho y.ckbw4arry a long, narrow beam?

If the net force on a sys.l 3q1 )rdeb)l00q3sr) ki0 vefbwa fjtem is zero, is the net torque also zero? If the net torque o k1e3i fl3)qd)0qr wrfbb 0l 0a).sevjn a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontal.vh00 06j cra8.a:grgvr (xdc x The same steel ball is cvc gd0v0.r6xgxa 0r( rah8j:rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres sitc4o0 w5ah780q d*m; myiamlw multaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the ota5dhw7lm;*8ci mma wqy0o4 t0 her. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have t w,w9ngm scdf0b(nf,1he 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 bottom? Which has the greater r f 0dw(s,g bw,nmcf9n1otational KE?

We claim that moment 4 j2fijg(+ qyim*kes9um and angular momentum are conserved. Yet most moving or rotating objects eventua+fqg 2*4 k9jiisjym(elly slow down and stop. Explain.

If there were a great migration of people toia pajng5*7a1,n uw;lward the Earth’s equator, how would this affect the n5aj; wga p ilua,*71nlength of the day?

Can the diver of Fig. 8–29 do a sowz+x+p 6;ft,eghhvu4 mersault without having any initial rotation when she leaves the board?6px, t+ufvg+h4 hzwe;

The moment of inertia of a rotating solid disk about an axis ji e)g+dryel9ljt7194w7a)wi3s 39gs hsfqw through its center os l 4je7hia +w9)swj3 9fgilg)3e9 r dqw1tsy7f 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 ac-:bf -1 zj.ipywm m gl2om3-k rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masb-2wkjylmp f-c3omi. :mg1 -zses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and ns2 )src2lk3t have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine whi3 s2crns2ktl) ch is which.

The angular velocity of a wheel rotating on a horizontal axle points sbm7m1 bt50sfwest. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed inbt0ms 7s5f b1mcreasing or decreasing?

Suppose you are standing on the edge of a large freely rotating t2)rb ptfp9e-zdgc6l(6 ff 4pturntable. What happens if you walk toward the cente6b(pdz frff294 egt-lpc6)tpr?

A shortstop may leap into the air to catch a ball and thro-b p9yvkdw s3x1 74covw 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 rotat cwxps 97 db-4yvk1ov3e in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservationvg z8u:ja qyd50. )t oeqrsm41 of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter st t1ya.szve5j4omd q ugq80r:)able.

  Express the following anglezbzvhuo8xz(0x +0hkot;,m 5 hs 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. Calculate,y:c*42 xoeoixi 2n/)a3uzqy- ,zyds h using the information inside the Front Cover, the angular diameters ou hn y*xy2)oyixcz,:3edaz q2-is 4/ (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 bdtzd h6on 1t).eam diverges at an angdoht 1n zd.t)6le $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blendegkb2jw.v7fh 4 r rotate at a rate of 6500 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 down?7bvwg j k2hf4.    $rad/s^2$

  A child rolls a ball on a level flpom /fdzs ww6gb by+(;p/6,gl oor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diamw 6ws bm,l;+y(obfz dp6/pgg/eter?    m

  A bicycle with tires 68 cm in diameter travels 8.0ae -t97*a gf77w6nz3sgg pwxp km. How many revolutions do the wheels 7-9s7g*az7fggwe p a pw3xtn6 make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at-zevcpd gc l.o;o( c.(;8qqrr 2500 rpm. Calculate its angular velocity inclcgo.qr (prevzo-d. c ( q;8; $rad/s$ $\omega$ =    $rad/sec$
(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-ro 9yqurvd3 dnt47 ,m9 .s9apjahund makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is t7s3a upa99dtnjmv9h4 .d yr,qhe linear speed 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 veloci;ys1d 1p u w:wqzs,c ym;)v(nhty 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 s5 ka /qpe/.a*me* tpc13lfwws peed 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) must qj(ewmhn6/n.j;d xhqe, *q,e a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience ,/ q*hhx;q j(,6eqdnj n. mewean acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel ac mpyeiy2vo,(/: vntotl 47g.fcelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 /yv4 f(e.o2p vomyt:ig,n7lts. 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 radiu0eh4jnmg0sg jj6 1 (sl;)aca js $R_1$ 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 a t*q9mbc8*odnfx( *wMoon, 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 revolua9xco*q *d( 8mbnft w*tion 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 unifor:,+b j- w ofodzbh/s,w5l6upd mly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this timbw+wb,d5u6 -fd ph,oj: os/l ze?    $rev$

  An automobile engine sl,p gs2er2d 7zklxg2b1 +kg 8ihows down from 4500 rpm to 1200 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 of flying highspeed jets in a whirling “k2 i+tcb9*,zt0neiue,c izi +human centrifuge,” which takes 1.0 min to turn through 20 complete revolutz,++t nctcz*k2i u 09eibi ,eiions 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 acceogxk j 5xs)2w8lerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in th2 jgkxxw85)so is time?    m

  A cooling fan is turned off when it is running at 850rev/min It tu-caxzly 8 ixi*(p2no kis90w(t)t.ftrns 1500 revolutions before it comes(f isl(8op*nx z9) tw0x.ii2- taky tc 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 unifoqm4i( hniz )5p,. zvaurmly from 95k,v 5u.hipz mn(a )z4qim/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 reduc ,r2(r6s ak3k n6gfbtces its speed uniformly from 95km/h to 45km/h The tires have 2nksb6 3rkr (gtf,6ca 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 z:fj5g uk.dqtzr+igv4h y w 73(,t vz3each pedal when climbing a hill. Theq73 k ,:iz +tgg3rzftj zyw5d(.uvv4h pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a forcyqb ak-cx5ce8 92s4;xji t +lhe of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force istsa 2;lcq i9bxe+k-84x y5 jch exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fi dgf;j(:mg 9*y0o lnxwg. 8–39. Assume that a frmoxgl*d :g0 j ;(y9fwniction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attou, r l6hq.nl.u*l-jxached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculatero u..ln,j q *6uxh-ll the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torq,i+t oi6twvr. m2n te6ue of 38 t.t+ emoit r6,2iv6n w$m \cdot N$ 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 w fv6t4jy,tkw,h 9udc0 ;d(rrdhen the axis o 0, tdfr(rk6yj9,cu;4 dd vhtwf rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 1 bb:macyzb -3cm in diameter. The rim and tire have a c:yba1c3 -zmbb ombined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on to5 2eouy 9 sbw*na5fp1he end of a thin, light rod is rotated in a horizontal*1wy9sa bf5 2opneo5 u circle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a cs(-ddyjgg /2kl q5 p)potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction for y/)s5d 2pqkjgld-( gcce 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 objecm 3 j/wx2,p/oh3uu2pkv8tbiz ts shown in Fig. 8–43 abouttv2 hx8 ouw/m3/jp2,b3 kuipz
(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 totay,; *kdr -97cfgmp9dvyui /sc l 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 a2azq4gt( m*dvooaoh ,11 v1tsatellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass oqvaa moo z1h2otdtg(a1 *4,1 vf 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius xp4o0*wns dk ui3q 89de1fn 1mof 8.50 cm and a mass of 0.51n9pnd3 1mqsew0* udix8fo4k 80 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 from rest to 3 7)frle bw8z w ckv) 6kp38i(yo$rev/s$ 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 tanglsa(+n 0wj mr1entially on a small 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 mass of 25 kg) sit opposite each other on the edge. Calculate the torque requirns r0j+(m1 wlaed to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10bh 3w(i chu:f1-ueh* n,300 rpm is shut off and is eventually brought uniformly to rest bwbiuh-(n* h: f1u3hecy a frictional 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 crmr+1)oh 1trka, 4do 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 solely by the acti0v*-lls/a i1hj4bkybb/ +bavon of the forearm, which rotates about the elbow joint under the action of the triceps musclilyv0s-j vbhlb//b*41b a+k ae, 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 thin rod, astka2 pgr1 70,licpyrp p93.ok shown in Fig. 8–4, .a312y790o iglptpcr kk prp6.
(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 tc)ttl1 fkypo:1 tqa 26wo 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 from rest witgn lmib1-rh k. w-/3ijn:gn8uhin four full turns (revolutiong- 8nhj n/k:l1im 3-bng uwr.is) and releases 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 inertimltvd9*x 9 s +fpv2d82 ueung0a 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 enginezt.w k- 76 482igu3snewfhmi0sct w*h develops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls witqm b1lole6aslfw(fs7 ,ecqr6 03o.j 6hout slipping down a lan761fbe6l flcq aw,s (.m30el6rqjoose at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic enet*n0qw9u fwlt0omv 5u( .5*t9 nph voirgy of the Earth with respect to the Sun as the sum of tnlfuun 9 ioo*tw 9p tvq0v05.5t h(w*mwo 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. Hoe.k) cjsw-wn/w much net work is required to accelerate it from rest to a rotation rate of 1.0s. n/e-)kcww j0 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from retk.-4wq za+r2is, zzj st and rolls without slippikz,w-4.ji +rzt 2a sqzng down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It s*j.k.me* z9keyd+g4qgsjfy sk y1 2o2 tarts to fall and its lower e*gj+j f*g2 k.4es eyyys29 ok.q1dzkmnd 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 energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball roi od,16jk2i8fhn mej9tating on the end of a thin stri,8ef6k hno mj2 d1iij9ng 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 omc+atvv b4r:gxz p:6,f a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm w+v64v:,cp xab:rzgtmhen 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 r7da.xku b:ah, fyu37,5 pxcql otating at a rate of x 3 d:,hq7bupafl5,yu a.7x kc1.3rev/s 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 reduce her moment of inertimj l *-9z4iqkq4( llbpa by 4lzmil 49*j-pqkl b q(a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can (fkvn ,n;4/ f:m ef+ ewcv-hreincrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final;k f/mwv:vh+ ne(f re,fc-en4 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 center at a fr t.ccz3oxy6 89 erzccg593cso equency of 1.5rccoc .83g5y o9e9xzcsr6c t 3zev/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 fig:,ml x zzd(yo5v8m0.esh :v xmure 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 angularh7df )m-rrdp/ 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 inertia I is dropped hw1a eq;/ h4h8zspbd3onto an identical disk rotating ate1q8hb3z ; h4s/dpah w angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2dd-r3-q zp:yj 3tqli,.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round pl8htpw*2w4um rqj +;suj:p.fj atform of radius 3.0 m and m+upph; 8j*uw j:s.fwrqt2j 4moment 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 rotat4em1gm :xgu +b-v9;qcv u/fq0;ftare ing freely with an angular velocity of 0-v 0x;mefqr1fc / t+v:umaue;gg4b q9.8 $rad/s$ 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 into a white dwarf, losing about hak, e-:pwx+yncvbvg+ lo-rtrr h,5- u;lf 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-+ ;tpb - ,-+yvk,hv5: c enrglxrwuro?(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 inw(f4(0xeo hfb excess 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 dpy vip/(;k i t;vhad:6w3 (pv$ 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, tha6:, psgbz0dz6 pj7rnht can rotate freely without friction. The momen:ph,66zn zs7g r0dpbj t of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-round tu3+kd7sfup .ze rntable tp+3. uz e7kdfshat is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on8+l nnsx)ii4r 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 8ii)4rn xlsn+ unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earema 1;4cfq7m .dkx7wpth. Determine the ratio of the Moon’s spin angulax1 4e7 p;fmac w.qmk7dr momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/kxc b4o: :r+6.csmxgj $s^2$ 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.j4fvfm jfe h54bb1 e;e.g3io shape of a uniform cylinder of radius 0.20 m acquires a rotatif.fb;f eb vh5e4 goj.4i j1m3eonal rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical dx01)6 5j .kz8dw sf ihrjcpb1qisks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.cfiz1 )r1p5q0s86 kwdbxh j .j0050 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 speees; -d0p5v kykd 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 j+ o(9sbd7crq times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process7r(o9dc + jqbs, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to ujqolk,z /1gttr/, o l/se energy stored in a heavy rotating flywheel. Suppose sq,o l ,o/j1/tlk rg/tzuch a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratesuyzq 5 --rhk5. kuz)tj 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 rollingtzh 9zqq/ .3cmg3uwh2 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 an*/j ) fxeas2pf9)f zopd length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assfeppf*f)a2jx zs9 )/o ume 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 radiusy tj83i 50 c73vqbeymtgvu b*0 R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has heim 3837u e 5*gq0 0bvvjbttyycight h, where h

  A bicyclist traveling with spee4 pz3f5qiszw,6 i7,y fn: t yu)4mxxahd v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the noryn7f6t,3 5 smquiz,h)xyfz w4 4x:pa imal 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 aoon, quuy 0hb +0x.th,)ca8dr sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, t.ycxhqudn0h,ab )0 r,o+ ou8accelerating 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 her arms as thi ,x8he(ntx 6xmy ifd,cp1c71xqy6g v 9n rods, making reasonable estimates for the dimensions. Then calculate the ratio of thxpmxf17in q y(1vd, ,8x6 h6eg9cxytce angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly wxvff(8cbg dm;pmpsj.5h e2y9(/pj -x hich consists of two cylindrical plates, of mass mpfv.x( p5/yh (fs2b;9gm-d 8pecxj j$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rollzr5+zdqk3 *bx*3sa lcum-9um s along the looped rough track of Fig. 8–58. What is the minimum value of the vertical heightruxm- m3*zl* ba59qkducz 3s+ 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, bu fjk ue3.ex:a7t do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduc,v7h5yg82mynkf 3cs7 d ewj k3m+fqk; es its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. hfy; dk m 3kym 5vgf+ cw278kqne37,js(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