A bicycle odometer (which measures distance traveled) is attached near thea*s/ lpfzoj d-*dz -djsx43h - wheel hub and is designed for 27-inch wheels. What happens if y-3x*lpzf4d -sjh-dsj zdo/*aou use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim : v+ wot9u1dduhave radial and/or tangential acceleration? It9 1+o:vud uwdf 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 of thu;3t:4acvh3)f dk)bn xpxl q:e angular velocity $\omega$ Explain.

Can a small force ever exert pjx0hl y ru304a greater torque 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 be0t xf;nf mzdyup/7 ).xhind your head than when your arms are stretched out in front of you? A diagrdtfyufn 7 p0z.;/)xmxam may help you to answer this.

A 21-speed bicycle has seven sprockets at thato)td zl..63 /mxeohe rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rearaoold e/ .m6tt).x3 hz 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 being2re -z00ev6au es r7hz( 4ikce 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 dynac k6 -r72ae0rez0(4z huseive mics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow g2n a xkivhkp5h.0) 2kog+1aabeam?

If the net force on a system is zero, is the net torque also zero? sk q2 c0*9i(v6-slqb oft1 3pqyqce5uIf the net torque on a s90 csyeqi b-uoqf16q5csq t3v2 kl *p(ystem is zero, is the net force zero?

Two inclines have the same height but make different angles with the hor0/mr 5mkpcre*izontal. The same steel ball is rolled down each incline. On which incline mpre m5r*k /c0will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (fh n;e0zr, tjq0-w:xfdrom 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 kinetdthq;jz:0n 0wfe ,-xric energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They statz c*3j-z/ . cxe,tupwrt from rest at t zcuce3*/jw,. -tx tzphe top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most mov.qx ) yhjnhqo5vp( :c8ing or rotahqq j :h8y ox(v)c5.npting objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equade apz -p(pi8n nx,46ntor, how would th8i 6paxen(z- 4n,ppd nis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without hajb9tzgp, y k3/ving any initial rotation when she letg, 3/kbjy 9zpaves the board?

The moment of inertia of a rotat;/.1oxll tdgc ing solid disk about an axis through its center of t;d/lgcox. l1mass 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 hoyom k(0d sv:;olding a 2-kg mass in each outstretched hand. If you suddenl: 0y ;(oomdkvsy drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow axg2ryt/tba i +*1*m3: tft yw) ljsr0gnd the other is solid. Describe an experiment to determi2 t*gfr1+ t rxyi/lt)3by*amw:jgt0 sne which is which.

The angular velocity of a wheel rotating on a horizontal axle points westf l :fb5 4j(sx(tza(rh. In what direction is the lineaah 4 (s:tl5jfxz( fb(rr velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable l5ck la4z2n:q79, l, dmdfwzr. What happens if you walk toward the cd l4zm:f, 2ln9k,5 dql7cr wazenter?

A shortstop may leap into the air to catch a baw 4ih *ke- :r(gzzta.vjlwr1,b35h zoll and throw it quickly. As he throws the ball, the upper part of h4z v 5.weorw(lzz*1rbt3 ikjha,h - :gis 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 angulayjm +ni9ql -;su/;be cr momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can oplb s-mce9;y;i/q + jnuerate to keep the helicopter stable.

  Express the following angles in radians: (a) 30 m:55h w/x ccv h5ap,bp$^{\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 coincidencm)7r gfxg +j/zpdkez1 i7uj)9e. Calculate, using the information inside the Front Cover, the angula7i+)zf9x/ m7d)zk1 ugregjpjr diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earslkf.yweuhzck )8i2 7b+5t a8 fl,fp- th. The beam diverges at a weffp. l8k27c5a + sfhb,8z)-i ytulkn 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 th;j l;rddlg;c.t le59 xe motor is turned off lg5c;t9. d jl;lrex; dduring 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 makesh m(5mr10r/5,ffwb u3gsrx k b 55fku1r , w rxs3(/fbbmg0mrh15.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many fc-( y0d3orz*c f qni9revolutions do the wheels9icnq*zy o0rcf(fd- 3 make?    $rev$

  (a) A grinding wheel 0.35 b1+d 4 ga)6f)y8 vntclact 7usm in diameter rotates at 2500 rpm. Calculate its angulara)8b)gndycf41lt+cs6t7u a v velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8.xa(;: 6. vjy.vd nsuc,ygttq –38). (a) What is the linear speed of 6..n(,ut vx;c yy.tvagdqs :j 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 thi3/ r .ckeao* q5fvbp5zx-iidbj.( r*e 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 pointvk:zckuv/ nwm+9) tu 4
(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 axisei 3 e* 3dt-whl/qkv,cg *ln1j of rotation is to experience an accdl*i1e,wq v gl3j/k -3ch*tn eeleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceleratescu;l6n/ kte-w ra-3zq uniformly about its center from 130 rpm to 280 rpm in 4.qu/awl tkzn--e3rc6;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 radiuu iq jx**5ziq+ (7v,6 pwpowkss $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft pus+ jmng kd0v0g++a l ds;7.rblt 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 vdks m.++lg+ 0 jsan0d;gb 7lrof 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 accelerates3u x rido4ixe+ -dqo+9/y4plar+v(y e uniformly from rest to 15,000 rpm in 220 s. Through how many ovr -a9q 3r+4xx4eiiydd pel/ (uy++ orevolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calci bv--t(z fjokvbx9hd9an5z+s*/u0l 3fu 2 nl ulate
(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 hig4 o-t83,ff8 foaqpisjhspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions befof38 f8pjs oiq,o fa4-tre 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 rp 6f9 *c3q pml+9kf:hqbk6nxfcm to 360 rpm in 6.5 s. :phxk mk+c3*qbff99n66 fqlc How 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 runmax5a u36aee/ ning at 850rev/min It turns 1500 revolutions before ite 65ae3um axa/ comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly q 9 p1iou:5v/me9krj cd8gleqmj6j7( from 95km/h to 45km/h The tires have a diameter of 0.80 m. r gd9qieqjuk8 69v71lp:jmm o/(ce j5
(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:6ii -q+g evaq as the car reduces its speed uniformly from 95km/-qqi:+g6vae i 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 all1d) ;)ecq k*da,pugxl her weight on each pedal when climbing a hill.al cqxukp;dde *)g) ,1 The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the enc2 c2j2e /y/ioo:w dmvd of a door 74 cm wide. What is the magnitude of the torque if the force isowmcd2e2vy/ 2 ijo:/c 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.wybj3)9p3h50zy xdkg 8–39. Assume that a friction torque of9y3wkgzb3h) pydx0j 5 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mcq b,tn hb(yv/*x; ml/ass m, are attached to the ends of a massless rod which pivots as shown in Fig. qnl hmx(cb bv,*/;/yt 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engr2 4meyc-pkb- ;m1sejc4 xc3ub) omz/ine require tightening to a torque of 383c4b4b ;sy uje -e-mpc 1mm/)xzrok2c $m \cdot N$ 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 q5iq :g/+tn( gk6rsjt m when the axis of rotation is g t+tk65:(jq n/sirgqthrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in vzfnoir4377km 33gw g diameter. The rim and tire have a combined mzmiwn 7vf37g r3gk3o4ass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizon 6i/-zyrceytfhv+5 0k tal cve0-6yi/hkty c z 5rf+ircle 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 atc9 yw4 zawz8mtep4() potter’s wheel rotating at constant angular speed (Fig. 8–)wcw9zepm t a4(y84tz42). 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 gdec +x0zpdet d92n,x 50bz (lshown in Fig. 8–43 zdd,dp nx l9 e5+0bet0x(zcg2about
(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 iz 4)whu p,oyg a7o up0 zssc;c,q5v2j+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 corrd b:sh;uh hgn97no6l7r0/pwhect 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 iss hrb 7hw /h6g7nd ;:hl0n9uop 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 wijgegpadexi7e+r 2/4 7ja:++ mugllm553llc bth a radius of 8.50 cm and a mass of 0.580 kg. Calculate u7a525 eg +m dggpj4m lb7aex+3ir:ll+/ cj el
(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, ach; b cyzh7pp 9rh6gx)*celerating it 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 tangentialo*; xdg*s 6c +e pf0d)f;dnvd80.sd p0pbwfvfly on a small hand-driven merry-go-round and is able to accelerate 0dwcsf)p 0+d;vg x. s p* 8bfdo*p e;ddvn06ffit from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque 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 r cfm*zj.3ub) mt (t sk. *tj7qau*le+kpm is shut off and is eventually brought uniformly to rest byft e*c(jl 7su.3b tk) qmj*kzat* m+.u 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. 8–45cwf u92od 9e69rv25j kvsnld5 accelerates 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-k r4gv a:xo5y5r4oxb 5gg ball is thrown solely by the action of the forearm, which rotates about the elbow j:45v4ogagb o 5x5rx ryoint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig..ro 1q7 ;qa u,f8r,lr 4mwtpfg 8–46.upo q,.,;q7 r 8lrgfa4r1mtfw
(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 masz *em76bnrf)nrfjua. 3; -g7-+xny j ,ik dtbxses, $m_1$ 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 6amen4t)4sgys -r*r ythe hammer from rest within four full turns (revolutions) at4m 6nrsy4a s-* g)yernd 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 hy:nwgd(ul - k;(c9 yw)blr1z uas a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque 5xxr/d:w3c cg3 l.s6la b dd7wmd 66bkof 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 slipping down ienul84nq -t( a lane at 3.(i n-8etlu q4n3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kineticm4g1ekk( 4 kvs energy of the Earth with respect to the Sun as the sum of two te( g44mk 1vkkserms,
(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 radkg 03z 5vjv x/ksn9qp8ius of 7.50 m. How much net work is required to accelerate it from rest z 3pvkjnq /9kg0v5sx8to 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 froso1o5*f99h lvo nh zhzlq-+;tm rest and rolls without slipping + o9z9lh h;5n1f*qoo -ts vlhzdown 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 verticallyroe *yrwi pizhn0/6t ph/r 0;. on its tip. It starts to fall and its lower end does not slip. What will b6irpnw. */ yi0e0 zo;p/r hhtre the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-krme*3 m2rxc)sd0s(d 1 pl h2yow; uzn7g ball rotating on the end of a thin string in a circle of radius 1.10 m at an angula2 0zdxn r sc1ed7o)ps*y wm 2hm3u;(rlr speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular bw u3q osfzn e jq()pd;rl+372momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm zufb sqq)lnd po( 3r327ewj+;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 platfh3kbb0 7 g6y2h i)seuiorm that is rotating at a rate of 1.3rev/s If he raises his arms to a shg u2y)6 370hikeib bhorizontal 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.n cew aqe-d1tu21w fcbhj3; h:0mx8 :m 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 tuck position, what is her angular speede :1wb j21;c0qfhwx :3mmnhecda-8 ut ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from a*q- -f.jg75j :/lw +habhq vsqo ebj/vn initial rate of 1.0 rev evflv v-h7/j 5+j .qewbabh/ jo -qs*gq:ery 2.0 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 axis through its cent s,;uo1p cu de-2hdtj6 mo:ye0er at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg anh odte6uu p0mjdey,;c1o:-2s d diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momenj4;jycvus o*e50 pj0e/n-l hftum 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 momentu: oa2k (krxb6yily.2 s tccmbz0hbs(j /z+b)7m 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 cylindribroga)3a srd c4qm133cal disk of moment of inertia I is dropped onto an identical disk rotating at angular spe)a brq31cr3omg4da s3ed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4irl,;2y ,l8svd t cr-l $rev/s$ 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 ste :rnu** mwq:bands at the center of a rotating merry-go-round platform of radius 3.0 m and q* e:r*m:wubn 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 angular xf-ljcsg7rm4p+-0 tkvelocity of 0. 7jmr40+clfx-sg-k p t8 $rad/s$ 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 eventuallywtk,2- f*spuxaw0 r *f collapses into a white dwarf, losing about half its mass in the process, and windin-wf2r pxw ,autf0sk **g 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 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 wv/, wzfb5xzr l*d p**4cp6:dfgi1 yloinds 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 x4xsev udd)lz /*gz)27/gv nmcr5zu7$ 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 rjae2hd q 1 ,/c(mefsdx5jh4d)est, that can rotate freely without friction. The moment of inertia of the person plusd( f,dcsm52d jxjq 1 4heahe/) 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 6.5nncxi eq;y 2(4 ksii ka-hn805-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment o(c4n eki nn8h-;s 2xkq5 iaiy0f 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 ta:bm604p cup/ds0lk p8;mhq-vs- p u che top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How farv-6s p-bud;p cq8 uc4p kas0 :l/mmh0p does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always l) xxvmi7pf4e; zk6. sfaces the Earth. Determine the ratio of the Moon’s spin angular momentum (about 47fl6iz. kp;xme)svx 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 fm0c0l tre3itpdw1 2 ;drom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acqud s .vs0fmpego71g*p 0ires a rotational rate of from rest over a 6.0-s if*psdoep10m v 0g7 s.gnterval 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, ea59t3prb7.snmqs 3i/wpp 0j tx ch 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 1.0-m-lon5r 3/twnpsq3i 70pjmp.ts bx9g 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 rear whe,byscqg so0i.k v16isc. z6;pel ($\omega_R$) 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 tujh utmvt5d xy:s 115-imes 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 sp -v5 xhtsy:mjutu 1d51eed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for itd rp-h/. *mhkbi: osa3 to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylino.dha/ p-*mh 3bi:ks rdrical 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 an1i7wwds3r8 1 hd2qp wdgq4orq9qqi 85 $H_2O$ 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 rolly);2 , vm-tugi8oeto( ukgp- fing on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e.9g tz6rmyi-:l8a+ d p+ro0dhq , we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, : ahdm0dg++8r 6 li-zto9ryqpas shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. Ir;l w0k.n*fs st is standing vertically on the floor, and we want to exert a horizontal forcek r w*l.sf;n0s F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a aykvo.mq /a+(d cu 9.rnnh)i7tt m+v*enk-d1turn with a radius The forces acting on the cyclist aqnhdacd 7i1kmk)+a+v o9.et u v/mr.*ytn(- nnd 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 slin*mc4pno 5 2ey7t)+ v o0ejv*vi(qy.e3qe kxy tg 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 after 5.0 s. What is the torque required to achieve this feat, and where doesyqyenpv yoeivmx*0 +c*3vto52t4(je ek 7 q.) the torque come from?    $m \cdot N$

  Model a figure skater’s body l),nul*(8pyr r(vies ejk w/4as a solid 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 wit*rli( nvrs/kyl 4,)e 8w ju(eph arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plazg( kcel-*jz ,xvb *7utes, of mass *7,lkc -v bze*g(ju zx$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 track of Fig. 8–58.c35f fhq qpamj :.bj+.f5 )yqi What is the minimum value of the vertical height h that the marble must drop if i+). bji ff3qp5f qhamc y.:q5jt 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, but do not alnw7 ./h wzwq2ssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unle hpji/cie0 ;(9e,b tiformly from 90he0j tb eci,il/e ;p(9km/h to 60km/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