A bicycle odometer (which measures distance travele(ej otvmby48rr,q* c; d) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle wiqe vrt8mcob*(,j;yr4th 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does n2 1bvd3bl8oh p:s, gxj9j( cda 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 abncvj8h1gb3 ds 2 (,xpj:9 dlocceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body befjh2zau g 980i sn72ww described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force7/ypi)0kbhwh0.-ywe am q o4v? 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* nj8/kna- f6cjmq1gn c/etq; to do a sit-up with your hands behind your head than when your ag1e na/jj8mkn-qq ctnfc;6/ * rms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at thezw+o8 u-olf kj;4x i4i rear 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 o z4;u-48kif xjwo+li small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run i 02g kw1u2f3w qc*owq6 ,uj/nsk v+fkfast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–3 / 3, js wkukc+f w2fg1vqio2nk*0q6wu4). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carrctbq(p7 d:rm 1 e/xov;y a long, narrow beam?

If the net force on a system is zero, is the lp7k1vw z,fg+net torque also zero? If the net torque on a system is zero, is the net force zero?kfz pvw+,1 lg7

Two inclines have the same height bc16l+ay/uv h4u(c i oiut make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at th4v1aliou i ch(+/ 6cuye bottom be greater? Explain.

Two solid spheres simu 5zium0sgwp qq70.ac5 ltaneously start rolling (from rest) down an incline. One sphere has w0mu5izc5ps7q . gq0atwice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. 5w gw 3fg07,g yo+vxzbThey start from rest at the top of an incline. Which reavgx3+0w7y ,go5zfb wgches 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 co o65z6ul3a ofcnserved. Yet most moving or rotating objects eventually slz f coa653lou6ow down and stop. Explain.

If there were a great migration ooptbrjo +g:0z6ur6j l, .64voft z s8of people toward the Earth’s equator, how would this affect th4 r ,pgzts6tojbou6 o:l0+fjzo.86v re length of the day?

Can the diver of Fig. 8–29 do a somersault without having any ini9e xp )q9lh4p e4wbqa9fpax2.tial rotation when s lfb 4xq9ewaqa.hp 92)9e4x pphe leaves the board?

The moment of inertia of a rotating solid disk about an adqs , dxii986oxis through its center os d6 dq9ix,8oif 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 sittz0 6x+dl5/f aa,ayipding on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angulaai/5paa 0l6y +d fdz,xr velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one ) di-yg 4r609sykookw is hollow and the othe kiw46yk)oo dgsy 0-r9r is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal afrogm pgj 35sf, c5py6+o(y r7xle 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 whe,(3s6focg+grp55r p f7yyj omel. Is the angular speed increasing or decreasing?

Suppose you are standing on t8d6ytqkoaw9 7 9tp,xk he edge of a large freely rotating turntable. What happens if you walk towarda6, y9k 9xtqd78t wokp the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he0o;5mz/d acme throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direcma /med; c05oztion (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss wh p.mnms .-tuk3 c45djhy a helicopter must have more than one rotor (or propeller). Discuss one or more ways the secknd .3.cjspumh 4 m5t-ond propeller can operate to keep the helicopter stable.

  Express the following angles i; jl+ied og,f-oi.ux0n 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, usiv.r /;tg7+ aaroust; 2daphl1ng the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as see1a d27aul.tv/o rga;r p;+sthn on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beamzaq3le2jg r* 5ol1 c3g diverges at a31qgz logj 3eca5r2*ln 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 6500 rpm. When the motor is turnex dsr/jfk462u+l: fes l1-bmln5b4 j wd of2:bj sfx+ejk6u/ l- r514l4sl wnfbmdf during operation, 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 level floor 3.5 m to another child. If the ball oi8o 2she ryz e9wv83(makes 1e se8y r9viz3o(o82hw5.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How sj6 cwj6l:lpg7 v y;;zmany revolutions do the whegc p;yj v:zs;ll6j 67wels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Cal .:yw8i,yaqnvculate its angular velocity iyi8 vqn,y aw.:n $rad/s$ $\omega$ =    $rad/sec$
(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 (Fig. 8i qchwg9wy3aqd3:te)lx ;g18 –38). (a) What is the linear speed of a child seated 1.2 m gw;iqh9c3qx83ew )1y:t adl gfrom 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 ic.s b)f4wt3 cbts orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of(pw/ekhr/gv 3:3 qgcez 1xj.-ugk/t v 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 a centrifuge rotbi72kt*gb1 xkate if a particle 7.0 cm from the axis of rotation is to experiek1 x i7*bbgkt2nce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter whe7u v;ljijh/ht4t1 *d bel accelerates uniformly about its center from 130 rpm to 280 rpm in jh /v7h*b1tl dujti4;4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu8b g5oui-bw 9r+3moons $R_1$ 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/ef- z-x gd-2-hqzbl z 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 rotati2f bzx-qzge -- zd/-lhon 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 15,000 rpm in 220 ek ;tp4y c/eo0s. Through how many revolutions did it turn in this p;e0k4yct/oe time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5- jk rcd-d8u(zk2v -p5o28 0c oikdjec 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 :hozx)uf60e(kt ivi5of flying highspeed jets in a whirling “human centrifuge,” whichz)(o:0fthk xi65ueiv takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly fro( 18+da jdnsiqm 240 rpm to 360 rpm in 6.5 s. Ho ijd1q+sa(8n dw far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runningc sgj73hjmrgtl v26 3) at 850rev/min It turns 1500 revolutions beforemgsr23clg3vhtj)j67 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 revolutvcw:yjg b7j ,zf vc-) pg(v(f9ions as the car reduces its speed uniformly from 95km/h to 45km/h Thc ( z:7fjg-(v9,cfg )wvbvj ype 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 miffrew 8pj;sch0, o ,gxzoafn )2)8* revolutions as the car reduces its speed uniformly from 95km/2ag x*8o8f0swfi h)prnmj,fo c;ez,) 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

  A 55-kg person riding a bike puts all her weight on each f7n d)8nurs x5h30brfcywm . qnr292ipedal when climbing a hill. The pedals rotate in a circle of radius 17 cm.cr5)8 mhrd.wyif 0 39nf2bx2usrnn q 7
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What ihdncdmc-p jd/0n4.uo 1 m8 d.ds the magnitude of the torque if p-jnd 48du/c0m1ndd oc hd..mthe 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 wheel shown in Fig. 8–39by dug 6v 99f6x 8psh1ma; yjxw2ai4c/. Assume that a friction torque of 0mu81dx6 fhs9 ij2gc9pv4 x6;yyw ab/a.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass myn4l fbp2q s+ei8m0wu9(f 2 vq, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod w m+2qf ly(vs eb04i2pqn98fuis 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 head of an engine require tim*hq,g dt8 yl9e.) ablghtening to a torque of 38 q d8al )9by h,e.m*tgl$m \cdot N$ 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 1b0 omwwi;o;tvjy4r 3of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is tvy340;r1w ij ;btoomwhrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamecm; taqpewlg5zq17 54, n*bojgwy-y 2 ter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub cb a2qmjezgt 5,;5 wqy1g-7*4 pcnwyloan be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated (ol)*b:nxe1 i ehx7ihin a horizontal circle of radx) hn*hb( 7:eloieix 1ius 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 pottervtwpl *h sf1z7(oo12i ’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her wi*(phzt o7l2 1svo1fhands 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 in Fig. 8–43hv ljtxub: xyhi +*-w 6i,;mp7*t6l xubv+pixijhw:;ym7 h,- about
(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 oip - ..x1unyxg: lzj0sf 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 satellite spinning a3dq+0gjeo . ujf:e8qut 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 0.qdf jqee 8+u:j3oug is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a u*ht+u4nt vsjei2mfa,pwb97 sr) o50iniform cylinder with a radius of 8.50 cm and a mass of 0.585a*+ov0t wr9njus i 7et,fispmbh2 ) 40 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 firwag yfxqg9, j o*rxb9 6s0(dx,kg)/rom rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hanckvj .m2(aq )1 cuplt6d-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 edg j1vp6qckulc 2.at)m( e. 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 10,30uvtj38m)tujph,bg7) su7a+mlw7 jt *ca )d6i0 rpm is shut off and is eventually brought uniformly tm7w)ajt hv 77usm+ua* jg pttjbic l),683u)do rest by 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 acceleratesif3 7jo)ilcdb mz3u *( 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 solely by the action of the forearm, wh -wk1e9n;fnhhs z a))jich rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly frohnh ws)1)zfjn- ak9e;m 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, as sh uj tv0 -5(wqnm8lxa7mown in Fig. 8–46.avnt5 w qmxl-j8m0(u7
(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 ck *58v0tp iszg ;zefk(onsists 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 hamme6/g foqz3e;ci/q -mmmr from rest within four full turns (revolutions) and releases it at a speed off;3goz/ mm/6mq ci- eq 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 *is;aq.ydc*jo.k z1s 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 developc4gdd(mz 7bx 9fgyqm:;zm -t 0s 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 without slipping7um whyxc9 *u/cka-c2t up0,h down a la0 wcpyuc*k9/ ,ax7 cht 2uhu-mne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun m4 xcbwt81kimm f36b ;as the sum of tb;m3fk cmt 1b48xmw6iwo 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 radiuswoz2 a 7fzt0nr e0)wd*t3p 6ge of 7.50 m. How much net work is required to accelerate it from rest to a rota3tp)zgtw7 * 0r0ndezow a6fe2tion rate of 1.00 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 fa quy 0gxy)z/:q,g1fz .ko9k urom rest and rolls without slipping dg/ :yu)y0fzgko q.q,z kx9au1own 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 starts to fat 7obfd l3,lk(f4*axkw.axf) ll and its lower end does not slip. What will be the speed of the upper end of the pole just befor4fdt a kk)l(faowxl.b7x f3,*e it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the 3katew73 gnv7jh1-3 rpl7c fb end of a thin string in a f7e7b vlphg t-3knr31w73cj 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 y :gqu5/rxs2/ wu(0xl:c ilc oa 2.8-kg uniform cylindrical grinding wheel of radius 18 c2/rcxo(xs0 :/ uq :cyiluw5lgm 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 platfork b8ek 1k0jw(xm that is rotating at a rate of 1.3rev/s If he wxjkkk8(e1b0 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 moments 5o-i.jw*ao h of inertia by a factor of about 3.5 when changing from thoi*os 5-.wh aje straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initiala mzkm3fx+smy83 vxuqj65z2 ( rate of 1.0 rev every 2.0 s ma32u8k( v5mmzs+f6 jzqx 3 yxto 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 1 hpr),) uzyqknw3 .xirotating around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radqnuz1 ik,3rph w)yx ).ius 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 angula2-w)e,qauye( l2 ktbhopb39 hr momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of tjl (,6mish0a80 pbgs whe 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 oftm q)w7 i 5j,amhn)lyma3z45 c inertia I is dropped onto an identical disk rotat hmj)a4tyi5zam,7 )mqw5c ln3ing 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.w)+v1)v7lue vq3mrvk 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 ohp u*4eo4o5+j1 qo u/zenmnn8f a rotating merry-go-round platform of radius 3.0 m and momeh84o+o 4jzo/qe*m un5un ep1n nt 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 merm ;pok,uy*w85 veyo6yry-go-round is rotating freely with an angular velocity of 0.8 v,y m; yy8ue*wookp65$rad/s$ 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 c; 8,+q szbbudp16l lhuollapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momq1spzhl 8lb+;6, udubentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds;szhj 8kx+ngp qi .**u0mee)am ur56d in 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 s+8 vgqmh8oh 9j5o(lj$ 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 gr22 pw(ts6yp/9sbj n can rotate freely without friction. The moment of gb2(9p6yp nrs2 sjt/ winertia 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-g:z- jy2ri.m2 qeutmq4o-round turntable that is mounted on frictionless bearings and has a mou zqy :qjrm2i42.m-e tment 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 rosgq /r ifa69e.lls on 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 w gaeqi.sr6f/9 alks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the 1edo::(mz ob bEarth. Determine the ratio of the Moon’s sp(::oebm zod1 bin 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 at a rate of 1 mggujsd c) ;c.dw wu88*/$s^2$ 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 cylindewykt2836d-z otco r9kpl )e4hb iq9,rr of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval z)e,ql6h2tobpr9-y84 r9kkdt ic3wo at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.vq4p cx p k;5tcxi0eam.x04kno v84 q-050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.01k xxqvt08 4c4n5-x; 0qk eo4pmap vc.i0 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 rearv r(6-+2av 7 xuopezdu 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 r a)i8jwq1:yneotating at a speed of 1.0 revolutije)iy: 8 w1qnaon 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 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 automobil0hymyt2i c zg+f;zqpg)pr fd0p6 -1t.vv,d5 ge 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 3t,ggpfz5vvpyt g.r 6z2-h)d;d+ i p00qym1fc 50 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates a s.wnd//q bnbkuu5 :f5n $H_2O$ 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 horkakzvk y 4n5q k0+ef90izontal 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 finkjog /q- -y*reely (i.e., we ignore friction) about a hinge attac n *-goiqy-/jkhed to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing ( 3oor isxr *yp7g5p/bvertically 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 st 5rpix/ o(7bo3syr*p gep has height h, where h

  A bicyclist traveling with speed v=4.2m/s o )q1962t*pc vjv feveon a flat road is making a turn with a radiot6cvqpf2 e j)1*vv9e us The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length ztl.kuf,k* b1 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque co*zlk1 ,. utfkbme from?    $m \cdot N$

  Model a figure skater’s body as a soiho9cn kfa37g, t-.xzoh+w9 pg5ryu,uf,z j4lid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with 3 pghg,ouz5hcx, -f 9,w+ajkz ni t9fyro.47uarms held tightly against her body.   

  You are designing a clutch z i-f8 - oh -jrkte7a*fkv;f4ri) 03fprxj tg2assembly which consists of two cylindrical plates, of mf fi-3fp8k--k z vor)*i0;7trj2 4jhxfraetgass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ikqt2v;wu x+b. u9*z :6 glfkjalong the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marbl v bx+iwkg;q9 :.kz ju6ltfu*2e 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, b8yo:d x5b)uqh ut do not assume $r\ll R$ h =    (R-r)

  The tires of a car mak 6p7ismxu i)9re 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 sx7 pir6miu)9 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