A bicycle odometer (myp*-h d .8 z51areu4my8 ps v1j5zacewhich measures distance traveled) is attached near the wheel r5z8m s1mp8av 41y .p yjc*zeh5a-udehub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates 2.lk5z2e h(t(dklo en k7eup6at constant angular velocity. Does a point on the rim have ruo2de5t nl(kzk e(h 76ple2. kadial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value onh/w2i e0uz fjbkidsj8 48,s0f the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torqulyxt 9o x/,e w08k.gnge than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head than ag)9gr8l7fmf bd4 i;ivmid61 when your arms are stretched out in front of you? A diagram may help you to anf67 lafd 8bvrmg;g)d4miii 1 9swer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the6osh1* kyt :dh pedal cranks. In which gear is it harder to pedal, t kh1ys*6hd o: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 being2 jzrh0,.yxe h elv*jgyl2xd8z; g)j 9 able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageh gd)l;e x2 ,jyvr 8ze2g ljj0y*.x9hzous.

Why do tightrope walkers (*cfbi :,hyi d4bw w5u;Fig. 8–35) carry a long, narrow beam?

If the net force on a system is 35vstf1m .- *mtxdkuo zero, is the net torque also zero? If the net torque on a system is zero, mx.tu tk3 -1dmsv5 *ofis the net force zero?

Two inclines have the same height but ma uc93-fhuhe9x 5ot*vyke different angles with the horizontal. The same steel ball is rolled eu9-yh f v3txuc59ho*down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneouq g-2 jxio.rbl-w- 4hqsly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed r.jbi xow2h-qql-4g-there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder havv 7(/1(jvherz( h0x*ilacmzz h7vyn 2e the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rota/z0(lzj1v( 2(a7cznh hxh7myi ev* vrtional KE?

We claim that momentum and angular momentum -ik:ln+jbb 0o +sohg1 are conserved. Yet most moving or rotating objects eventually slow down and sto +obs1oj0+hl:g-ink bp. Explain.

If there were a great migration of people toward the Earth’s equator, how would a/)u50nrz nviu.1 rhxthis affect the length of the uv ir50u.nzr/an1) xhday?

Can the diver of Fig. 8–29 do a somersault without having anuzlb6 09xm-dny initial rotation when sheum96n-d0b lzx leaves the board?

The moment of inertia*mqpufr*y-m, jm c o7an( a(/t of a rotating solid disk about an axis through its center o,mo (7y ajqt/ruc*fmnpm* (a-f mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg xbo55p* 7fw viwjja*: mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay **5iof x:vjap 57jwbw the same? Explain.

Two spheres look identical and have the same mass. Howeveryxb+t*4kpo93d pu.h e , one is hollow and the other+pohe dt .k94pbux3y* is solid. Describe an experiment to determine which is which.

The angular velocity of a 0hdcs 7 fr8q2emd84s8lc ug p,wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tanges80ucs4pc8mlfe7 h2rq8dd g,ntial linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating svy;y.fq sw3. turntable. What happens if you walk toward the ce3yv.yssq;f. wnter?

A shortstop may leap into the air tq l91 hpzea7dz2w l02to catch a ball and throw it quickly. As he thr29l0 zwhlzpd2 e q17atows 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 acwa)dbewt ,h e s2jq +2hw ,k3.8fakz/ngular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keef b2+ c/qzwkjas,aewe3,wt28h dh ).k p the helicopter stable.

  Express the following angles in radia9owsoc 4vl3h0ns: (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 amazinge w y.kl.t.d7b coincidence. Calculate, using the information inside the Front Cover,y.ed..lkb tw7 the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directeda.boe2 q3hbl 9 bnjd6: at the Moon, 380,000 km from Earth. The beam diverges at an angb: .n2qob3 edlab6 j9hle $\theta$ (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 65bg7l.(0z; k;j ydx l dd./cprj00 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as t.b7jrxyg0 d ;kd;/p(j lzcl. dhe blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball 6aya.s n +5.5 icflzkfmakes 1a fcs. knil65a.zy5 f+5.0 revolutions, what is its diameter?    m

  A bicycle with tires 680 pcyvi(9vi)n cm in diameter travels 8.0 km. How many revolutions do the wheels y) vivpi(c0n9 make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 ra*(o 3nqpty4w c0brkvmqm4fdc9e) 79iw 5h*w pm. Calculate its angular veloci*5wefac4*90(pb )q y dwk7cnohw4t3 miq mr9 vty 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 on-1a no:3w gxlgfsj-cpg* k h/2f0c z;ce complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from cw:2*fx f0 gso3;kg-/1- gcnz cjlpahthe center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angularsg.)sfffhknqj + /n pk*5 8:ki velocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pouw2k+) l0rgn9r jkk (tint
(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 particle 7.0 cm from the t:r13il,/ z5f lneoffaxis of rotation is to experience an acfzr1 3fi/5lt:n,ol f eceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelera/ojz1chpfq; ob/ :n ( hp8gfh(tes uniformly about its center from 130 rpm to 280 rpm in 4.0 sfc8jhhp:hpgfob ( oq//zn( ;1. 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 radiu4u 0zhi,9w1.axscko8y9rr 5a yjzn o;s $R_1$ 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 Apod 2 db udcp8zjt, kkp1.ruq41/llo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 1cjuk2dpp q814ru.b /d, k1td z2-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 h4b qpw70xg )*woprcd .)pm(zbt3i8 g 15,000 rpm in 220 s. Through how many revb po)h(wzmg8.xbd r3*qtgp w 4i)p70colutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm inpp5 hue ksr34*. ,my g9;imkpc 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 flyingi m32zs hf7co/ (gw.lv highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachin.f3m /c2zwolig sh7 (vg 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 0s8 qmub zzkfao. i00;uniformly from 240 rpm to 360 rpm in 6.5 s. How far will 0 oafibkz80.;qus m0za point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned ofw1odw(+e so c+f when it is running at 850rev/min It turns 1500 revolutions before it comes we +ows1do c(+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 reducesu2:jcb6vk qyix. )j) nkn*0 iv its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0bux62vk. q*y v)ic0nji )jn:k .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 revolut-5kbx. 1 hjsrcions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamete51h.b rkjs-c xr 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 :(pd s15;m.lhfrrs z hbike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 1sh(zf5: pr.s d;hmrl cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end itpubo 94en:g7tei3* of a door 74 cm wide. What is the magnitude of tu o9b43ign7t pe:ite*he torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the w7a2d hu d-tkl 5vdsgpvtbj/0l9a*75yheel shown in Fig. 8–39. Assume that a 7ltk-adb u/vy9gth5sv*d5j 0d2l7ap friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attacewfhr zhrc;/e71 5 yb7 hh/7qhhed to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in ther /hh7q1r /hc7y7ewfh bh5;ze horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylix 8jdshe+wbv99x40i q nder head of an engine require tightening to a torque of 380 9h49 ix+djsbqexw 8v $m \cdot N$ 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 qyfmt.a v7:e3when the axis of rotation is through its ctq3f :vm7e .ayenter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim s3, mjao;yk k,jjf6lzee ,2h/9ow8 x zand tire have a combined mass of ,j,w6sy2lx z/feoajk,jzek3 m 9 ;ho81.25 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 ro5 9bswz l(1zdmld +: trq-(rxftated in a horizontal c:d xzsfbz(mll5-9r1 d r(q+wtircle 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 potter’s wheel rotating at constant angulau;lq3my ls6w2k -m,srr speed (Fig. 8–4 2yq-mslr3lwum k6,; s2). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects showmc68kgouxkssj. 1r ) s 6y-0tqn in Fig. 8–43 -.6jsx8su rgs ) kck0mqo1y6tabout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mass is m3 f dscw+34 w11d,g:x+nz pi/hx liol$5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the jfbhux.xtm a( 3c :bb6p5(wy (correct rate, engineers fire four tangential rockpa(j3:twbh5y(bux 6. mcfxb (ets 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 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cqw5,pig ;yxaa4l 1wg. m and a mass of 0.580 kg. Calculatxq1g5ail.agp yw , ;4we
(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 vji5zm*ek. z: from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is able2(uyp 1n7cu9ye is,a . ndxo6i to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a unifo i62nn(7i eyxac9yd,u ps1. ourm 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 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 evewndi8 sq3d uhf59 pj5(,l yw7untually brought uni ,f8iu 5u(57yjlwqh93pd nd wsformly to 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 acceleratesq94 f6e i-lnshvkb0r/ 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;ty;kbj rw8: a of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45ba;r j :;wy8tk. 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 thinxb:hes7gxd4xg0h dfz :k2 w tx-2* 9yu rod, as shown in Fig. 8–464 *st hwhexxb:7 2zxk:y 9gdufx2 0-dg.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masse-w5chejc; ;lv s, $m_1$ 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 hamp7w j2mr 39+0;r vjsu 4hzxsiemer from rest within four full turns (revo40ehur m +vrs 29p jz;j3xw7silutions) 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 okc48kab3+eqpc ea uq8*3f yh/f 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 torque o yvd.h)u23j+- msv ebof 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 5 )awrfgl3n1hslipping down a lane a 3 5r1awghfl)nt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to l2x*8 ra br+ eu2y3omhthe Sun as the sum of two termshreal8oxyrmb3 +2 u2*,
(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 164i9mr4gmd zl-zfs(+2 bethl)l 1z (l. h0 kg and a radius of 7.50 m. How much net work is required to .gl l2z+-lhzmdsl1mf) e4zbht(r9 (iaccelerate it from rest to a rotation 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 from rest and rolls withouc:m6cr 7 1jtukt slipping down a 30.6c 1 jurtm:7kc0 $^{\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 verticab/5/ qmv p qwj4uoy 1hre2e.zdq1up0s* nx9: slly on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use csoze. /sqb0um hy:1/x2p q p r9n54ud eq1wv*jonservation of energy.]    $m/s$

  What is the angular m-s5gdpb( a oz7omentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an agbzo d-p7sa5(ngular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrictwn il.dev +og:( 3pd3jo-, 0f6 wq0 7lwndklzal grinding wheel of radius 18 cm when rotating at 150:3w , 7 p+kd 0d qfwewn3ij-tlldn g6z0o.(vlo0 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 rotating at aawu/h/9hlq1 b 8ij1azkc 0fh i- gx*2a rate of 1.3r1fub 1 0-k j/ a2iag/cai*9zqlhw8xh hev/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 i:jm c 1:j yn;csp5reg3n Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tucsy m53gr1 jce j;::ncpk position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can incrs c2do g1mlp1s3cnx- 8ease her spin rotation rate from an initial rate of 1.0 rev every n8csxcpd 12s om-3lg 12.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axio;9xd 7 ah 1w)rgcu4pvs through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clayw ax9; or4)d7 gh1vpcu sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinninkr 3,dkbq +ig4g 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 mome+.l++3nu0took 4rwb pqp 6nn dntum 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 diss0lak .*/jxzfbr 1 4,c4 yfg0qjm,sbjk of moment of inertia I is dropped onto an identical disfbjj40s 14. gfl/z brcs,q,*y0a j kmxk 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 hiw6 i f onu-448x*zvlduss.8.4 $rev/s$ 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 g 81lppa+wmx5x : pxv h:/avv-com;9pa rotating merry-go-round platform of radius 3.0 m and c58 vphxm9;g::1apam+ woxp vxvl p /-moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angulare v58/fb qwwj, velocity of 0.8 ,jwb/vqf58ew $rad/s$ 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 whyj r+qg 7( umtrvk2onvd8uf3c a d6l;8(f, ex2ite dwarf, losing about half its mass in the process, and winding uru o 6t7cq+kdveln(fmr, d3f8av2(yu8 2;jxgp 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?(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 windsv3y614 ohcpk t 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 7uw bw63j oej,lkh pfx*:(z2 s$ 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 ro/ +rde*(p lwbw o2vxvz.pgo (8tate freely without friction. The moment wb( o.v/wxpg2( eor+z 8*pl dvof 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 st vhflf-xqs9bu8 ,;z 9oands at the edge of a 6.5-m diameter merry-go-round turntable that b 89lu-;zofs9 h,x qfvis 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 on urp 4 ks:d2 0rx)0ieqwthe top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. xp )dkrq ur20 s04:ewiThe 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 Earextg 0qca)y, * ibq;h.)atv68nwpm- fo/j)esth. Determine the ratio of the Moon’s spin angular momentum ( gsvf* a nh-qmp)xact)) . jey,eq6o/bw;t0i8about 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 rat wxph5s8x95ri .rddz6ce*r0za * inp3e 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 gv..0s+q w +pbz 7z-azf rox3suniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torqu..r+ s3 bx0w+vz poqzzf7-ag se delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each;xt *xfzqy 1 t;:tl1ur of 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 the end of its t; ;xlx1ztf:1 u*try q1.0-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 2rq edz*j 2:v9po *nlld6 *jonthe 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 m3 g fun)pyx-o 4/,x(e 5 qmpiikvn;*pgreat, were rotating at a speed of 1.0 revolution every 12 days.pxgm*;e)v n ipp k-i4xn5m,qou(fy/3 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 automo3d8jq p9 o5trsbile is for it to use energy stored in a heavy rotating flywheel. Su 9ro3tjds8 5pqppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a 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 illustrate*rmt/1 e6 zytxs an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at sp3wid7 (so5o4w7dkwy peed 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 (i.e., we ignznt0 znw0h9c ,ore 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.z h0 t0c,w9znn 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 vertica n6:aiec r,:*yfsgd i.lly on the floor, and we want to exert a horizontal force F at its axle s:f.sy6,agi*d nrc : eio 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 flat road is maj)8 m* p -cljt*svmjsy8u,y.iking a turn with a *t * ,s yl88ui.y jcsm)pv-jjmradius 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 oak.0 0k,ki8rv22rj gg7y84dmbykl9 cus l z -xf length 1.5 m and begins whirling the rock in a nearly horizontal circle above his l9j8.sxk7,u r l r- yg8dgk kk4ivcbya2mz020head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, makrd08w, q;o*q) b hslxhing reasonable estimates for the dimensions. Then calculate the ratio of the angular sxq,s)d80;ow h lb hqr*peeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

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

  A marble of mass m and radius r rolls along the looped rough trat 3e3u7i5izecs iq+:uz )l0y dck 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 tu)+i y7s5e0dzqz ulec3t i:i 3he track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do nuhoem 3bn.bk835-nbou;nq4l ot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uni,f3j hza5cv8rqp2g2k.i k0 o hformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was 2j0ho2k3 hrfa,pvc kzg 5. i8qthe 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