A bicycle odometer (which measures pl4i35m6j6k q. ekxx bdistance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicy4b lp6mx qe.kji36xk5cle with 24-inch wheels?

Suppose a disk rotates at constant*/pr-hmn2c zm 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 tangenti mm-npz *h2/cral acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angu rversx.vq 4e+zza 5q+r0p/ ;tlar velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger wjl5l7dag,9bw :07y e.i ziueforce? 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 behq/rh0 3b )cdr2ilgv 2find your head than when your arms are stretched out in front of you? A diagram may her 2/)c 0f3gd2rhli vqblp you to answer this.

A 21-speed bicycle has seven sprockets at the rear wh*e ,mettj+( jjeel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprotjjje m,e t+*(cket? Why?

Mammals that depend on being able to run fast have slender lower legs with fleshmi.s*ha/ws4g x *axx 4ok*3ne and muscle concentrated higx4a4as *w/ngh.om e3*k* ixsxh, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beamdhylzhuri j ts.w9, g8u2+u4 2?

If the net force on a system ip4fdj1qf mmv rhqz5876p s1s t.o3yq-s zero, is the net torque also zero? If the net torque on a system is zero, is the net fq3mq shfjs1v8oyt4 1 -qpfz6r .75mpd orce zero?

Two inclines have the same height but makei*6vcn 0iup9gi j .ph; jr/sc7 different angles with the horizontal. The same steel b6i p;70 .9nu/vcpijr js ghci*all is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simulta:k :w)-qlqi z zxzqi9 ghdr5:5neously 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 there? Which has the greater total kinetic energy at the bottir5q-:l 9 q:id:gh5k zzqz )wxom?

A sphere and a cylinder have tv nl 6df.)bo-o(s/yad he same radius and the same mass. They start from rest at the top of an incline.6)vs ofa nb.d(yo/-dl Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet mos+ ( okm+rgjr ppy5-a:ht moving or rotating objects eve+ (5gok-ahm:j+yp rrp ntually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how would0 7vrspg z oqb0(t(ibu++ds3r this affectus3drz po g(+0 0q+vr(stbi b7 the length of the day?

Can the diver of Fig. 8–29 do a somersault without havihe0l3(u.jqzo 9 w jzc;ng any initial rotation when she leavec o 0z(w;l9hzjqj3u. es the board?

The moment of inertia ofmeng5(t fo8 w+ a rotating solid disk about an axis through its center 8 (eg+m wo5ntfof 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 2k/gj)jgy s8; g2dv czlib )32k-kg mass in each outstretched hand. If you suddenly drop thydg;2 b)k2 8g3c)l/zjvkisj ge masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and ha rx/uva+xl;*uk 8h iw5v8p4jjve the same mass. However, one is hollow and the other is solid. Describe an experimeki xp vvw8x8 j5/4+uu*ah;rl jnt to determine which is which.

The angular velocity of a whnnjbqne( l c-0 )uv9u41lsf)b eel 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 angf)se-ublb 0n49nvlq) 1n (cuj ular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a largeyn*x5*um60cb mp-ck/y 4xmfv freely rotating turntable. What happens i4yuvmc6n /p y *5xb0-xfmm*c kf you walk toward the center?

A shortstop may leap into the air to cahhoq7 , m 7;pydb/sqk;b)f 9vstch a ball and throw it quickly. As he throws the ball, the uppebys s)pmbo7;f;hqhd9, q7 v/ kr part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentumnnxb c+ok1o )1, discuss why a helicopter must have more than one rotor (or propeller).) 1o1nxkcbno+ Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: ey o67vq0/brt (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. Calculmbjbd7 6uy u l6g4l;2xate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and t6bluj6 m2lb; y7g4duxhe Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges 68rio,v0;bbplb4rob at obrl;r 4,0bv ibbo68p an 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 6508dav i4dwch(x/s gx 250 rpm. When the motor is turned off during operaxvis8 / 4xwcd5a gh2(dtion, 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 makes 8p(* nof.v fvsoelrj:61e q-u15.0 revol.e-rv8f oof*:jnue q6 p1v(slutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 kmz,0 5 uqyz(n jhi/mu9y. How many revolutions do the wheels make?zmy9yj q05i/,(z nuuh    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcumm-.m4ar zmcl*4 65y39 qfy gm *ydswllate its angular velocity in mwl*yf *-964rs y.5damm qmmyc43g zl $rad/s$ $\omega$ =    $rad/sec$
(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 ri-s2u//omzm zevolution in 4.0 s (Fig. 8–38). (a) What is the linear 2s/zmo/mz -iuspeed 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 velocity of the Earth (a)up-tj6, uwb7c,sh /fi6 2stlltps3k 5 in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of gy d3azhyc*+a4v j si)3)7ql la 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 rotathrh7p:rz) mhfn594j1l9vx yy8 es r3 ze if a particle 7.0 cm from the axis of rotation is to experience an am57rhlfj:vp34y e8n9 yxr s1 zh9hzr )cceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unifortp3vpjvo7x:7 j12ui k( b7ynau0 w ikev:xh;8mly about its center from 130 rpm to 280 rpm in 4.3kuht:bxaw kpj 7vpx :o20 7niv1e8(;uvy7ij0 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 radius fitz,yyju/8g cl u-1bls 5s;:$R_1$ 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 t uetul9xa /9w7he Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinde/u7xe 9au9wl tr 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 acceleratle iu0 cb;9o8v0*x nw6*ad:vt3mny m kes uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it t uki;na l9enwm6: *b00xyv*com vd 83turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm ia.re s 4z2/9(. ob .wnwepvyknn 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 whir ob(tysha,7zm6hbm; g45l;o i ling “human centrifuge,” whichzim asthb5,o;m(6y7h bo;l4 g 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 from 240 rpm to 36 qh6wmd43y rw*0 rpm in 6.5 s. How far will a point on the edge of the wq6mwwd y3*4 hrheel have traveled in this time?    m

  A cooling fan is turned off when i/5 q.t8a zqoxmt is running at 850rev/min It turns 1500 revolutions before it comes toa x.t5zo 8mq/q 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 6,rytauxr8f 69 .,qe bu5 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.u6xu8q9a, r ert,f.by
(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 amp iqc )3+3pf pfzi(u6jtb+ jy deg,:(s the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 )que3+t((yp :ijbgc3ff+p mi d6,jpzm.
(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 al o/qxx-w76x:6na a+ kwvx tse4q70sp fl her weight on each pedal when climbing a hill. The pedals rotate in a circle ofxwnsa ep7oa:f- vtx/x6s6k7 +40qwqx 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 force of 55 N on the end of a door 74 cm wide. W6 txj;myz (yt+hat is the magnitude of the torque if the6z;y x( +tmyjt 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 Fcp :2-z(0jg2 c lsflbrig. 8–39. Assume that a frictionzp2c (g-jl2:b s0cr lf torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod uei kw*xw(9b0- iycj6akq d: :which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this sys(c9jw -:0qbud*w6 :e iakxiyk tem.

  The bolts on the cylinder head of an engine require tightening p)k;2:o nvyod to a torque of 38dono2; yv k:)p $m \cdot N$ 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.eti* fk 9;2e-rj r1vgy648 m when the axis of rrf-ij;e eyg 91v2*tkr otation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim g8)hknry 3ib,( + zbtpand tire have a combined mass of 1.25 kg. The mass of the hub can be igno3npr+zb)(hg y8ti k b,red (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontal n/b*5jnu-to8 s6* ocr b/xxiy circle of radius 1.2 m. C/5*us nxo6onr/8ibj-*xctb yalculate
(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 poyhgzpu; ;(c7o icb6, cwayz(g(ef15c5zf9l o tter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5wgczc(b ;,c9fc;eoypziyzo6(7 5 f (ga5hu1l 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 osy2b ,iz ;52etth,b d na52tcbbjects shown in Fig. 8–43 at,2ibzsbb5 dceat, 2hty;2 5 nbout
(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 i2 sah;u m1ep u+ 1cxxnxrfxek*2f42k: s $5.3 \times10^{ -26}$ 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 correct r 9:7litw sq+1oid wdqol))6gg ate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and l) qst7lig6id gwq)d9w oo +1: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 wigt lplhc *31*6trr9qxth a radius of 8.50 cm and a mass of 0.580 kg. Calc*p3c 96gxtl1 trqr*l hulate
(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 a6ri ;oh1 mjs-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 a,enq8lfs g2q 6ble to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a un 2lf,qge8 n6sqiform 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 eventually bcc6sgwk r-s m ,*+u.adqeyx p). 3em7frought uniformly to rest by a frictio-a)c6m*u3gsdcqm .sfe,w yr.pk 7e +xnal 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 3.6-u,;t2v) (xryztlul h jg0w7(*8ap) c oixjek8kg 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 - *1vf 3hqx9*qbh wbn)5zsn oqaction of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig -)ozb3 51nfqvwqx*hs*qn9bh . 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, as shown in Fig. 8–vziv p2 j*d-m74vv7 m2 jpid*-z6.
(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 consiswz9l*usjidi;bk b +x +u2w-u7spih 1(ts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer frn,6k v qvodb3jy;y s79om rest within four full turns (revolutions) and releases it at a sp7nq jv9kod3 b6,vyy ;seed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of e028dj(k;k udpi k8vn$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torzggj 1i7x -8s+ prr6qaque 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 andf m9 :q 0ijn:opccx+fv19n6gb radius 9.0 cm rolls without slipping down a lane 9 m vcb gffoqp ::9nc1n60+jixat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wio 1bhb(+4 ac g.c.; )f u0yttllicx-ywth respect to the Sun as the sum of two)hylc- gyaw.u4+cf;t1b0 ti .xo c(bl 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 ruk8q )+ 1q*qfs2mh +zkmss1vm. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cs q8sh1qf*1q vsuk + m+zrmk)2ylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest jga fy2gcv( :+ y*ua5band rolls without slipping down a 3y :g cua*a52g( +bfjvy0.0 $^{\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. I)j(kv)ck3xfau sf al +de(-u6t 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 conservation(s cxakua6 fdue+j kl-v))3 (f of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin stuu xd0fit5o.-ring in a circle of radius 1.1x5fu0.o u-dt i0 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniformy(*kup p.u(d h cylindrical grinding wheel of radius 18 cm when rotat*dkpp .hu yu((ing 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, f8un*goj;0wr l4 -ho atf (mxcdz2h54.v vy 2ion a platform that is rotating at a rate of 1.3rev/s If he raises his arm vj4 hx(8.2m -2hot5odc vyf0nwrzi4 afu;g*ls 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 s rdtcpznz1t 9rg* s*be2s:3 lad*2x :her moment of inertia by a factor of about 3.5 wesn :rbsz293l*1ztgas2 *dd c p rtx*:hen 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 increase her spin rotation rate from ak ke5y6 (lp 6sir,l2iun initial rate of 1.0 rev every 2.0 s to pk66 rk2sii e,luy(5la 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 axis through its uqer / 9+j66dy sn2cu(jgz- ujcenter 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 6e c9(d/jq6j yng2+zjusur u-clay sticks to it?    $rev/s$

  (a) What is the angular momen 5),cbik im6hn)ln 1at*7d sjd (lpq);1rtucntum 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/7q eea*z njs, 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 inertot i3frjb3i )dhd:wl )rp8v*3ia I is dropped onto an identical disk rotating at *wf v3idlr8:b oh3d3ipt)rj)angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4bpx: e-(r1x xo* d9zrg $rev/s$ 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 platfor xjpz la39zfsa 8:4c0um of radius 3.0 m asz zaj8c:94 ap x3u0lfnd 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-rounditi igu8 5x-5py4h5rd is rotating freely with an angular velocity of 0.8d-r 54ig5uiipt h58xy $rad/s$ 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 in8xc n-d9, jgflto a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integerd8 ,9xg- cfjnl)$\approx$    $rad/s$ (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 winba .ua-gu;b4tiekz 0(ds 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 n8d+o v.s(ja4j k,hqx$ 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, initirmcy /kudv(0ic0.y 2x+ r2rddally at rest, that can rotate freely without friction. The v d2m(rc+c.0i/uky2r y0xdr d moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the h;51n due4j da vjhi6ek:5qsfsj1 +f;edge of a 6.5-m diameter merry-go-round turntable that is mounteu1s; aenj 4k15s+ffq: j5e;h6 ihj dvdd 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 the9 dqvsqs 3fz9brj y917 rope lying on the top v3b 9sr9 qy 1dqj7s9fzedge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. De-8ibucmi5 sfe3 bb w4i5.t,uutermine the ratio of the Moon’s spin angular momentum (about its own axis) to s5uiuit5i3bu.wecbm 8 -f 4 b,its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fromv6hbygqy32 g3:oh(m z rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the sha)y ff (s+ymc6zpe of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration6z m c)fs+yfy(. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solanl6-t19 pvwctjp/+kjdhs55 id cylindrical disks, each 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 ttcdlj/5-9wkjs p tpa5v 6 1+hno 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 rej(. 60firq8szgqpx (lar 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 timivwu( w5b;zo yb5k u1/q:5tm ces 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 process, what would its rotation speed be? Assume that the star is a uncb/(v:z5; 5 t q5uio1wmkywb uiform 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 use energy stored :5;r nsgx.jlar1nh6 bin a heavy rotati x6sa rj:l;ngrbn .15hng flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a 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 ana 7rylt;45*w*vin yan $H_2O$ 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 horizonskm b+sik7m7w4n3 8cr tal 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 L3g o3z;xojo o/ 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 oxo3j /oo;g3z 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 verticallyktlu63 * rn7mnq,1pgq*lcy.cr9y sl1 on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against 17lr3 mn,ynkqlcc l u1g yr9* stp*6.qwhich 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 h,9t 2razms- nis making a turn with a radius The forces acting oamznhts,29 -rn 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 0.50o*brad6+p( pk-kg rock into a sling of length 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 aftk*6a r+b(dpop er 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 pci /(buk .7wzp2fam0 thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstra 2k u0cfp7bim zp./w(etched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists umj.6u.zju j/e bux2,-pu4ooof two cylindrical plates, of mub.xm2zj.uj4p ouu- j6/o, ueass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rougha6h8k0 cbk+qzu(xc; f track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assuk8(0 ufax qbchz c;k+6me $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do notsy r8jl43pdg -x/w5m+c(aj y t assume $r\ll R$ h =    (R-r)

  The tires of a car mi/wv nthz)c *(ake 85 revolutions as the car reduces its speed uniformly from 90km/h to 60k/wv)z*ct(hn i m/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s