A bicycle odometer (which measuryd g gv+,c0j :cyp3ma)es distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens i,vyj3+y c ggdam0c: p)f you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular v7mct xys1 *u kt*-lp;ql3iz,velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angq,zl kicu31-pm7 v lyxstt; **ular 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 the angular vel exw.x:0xzht9b lc5(l ocity $\omega$ Explain.

Can a small force ever exert a greate 7yp 3df*tbk:fr 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 behind your head th*uo+tt. oe +e sp7fn9han when your arms are stretched out in front of you? A diagram may hot.eo*u 9+s pfnt+he 7elp you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedanwe02w2 a1k0afaj cj.l 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 we2a00wc jk1 j2fn.aa sprocket? Why?

Mammals that depend on being;l, l80 g/gnnuns qa6e 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 w nlsa/l0qg8n; ,ug6 nehy this distribution of mass is advantageous.

Why do tightrope walkers (Fig. tic4kh:x9s + 2jscy7 x8–35) carry a long, narrow beam?

If the net force on a sysuh e*pjdl4+67 l 1wo/l1zqhb utem is zero, is the net torque also zero? If the net torque on a system is zero, isuuelloz6wd+p*4/1j 7b 1hhql the net force zero?

Two inclines have the same height but make different angles w;l- 5pl+ad utwith the horizontal. The same ldl wa+ u5;-ptsteel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously starv : 7aik ,e yiwj02thr-i,ua1at rolling (from rest) down an incline. One sphere has twice the radius and twice the mashaajwu t:rik e2 y-7,, 10aiivs of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius rrup9.b h/s4hl x n fx* -ue97jzfg.6nand 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 bot96.ushr/nj pr f eh9*7g.xbfnxz- 4lutom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet mostk6n60oggh 1;::oijy4dyf fkv moving or rotating objects eventually slow down and sny:y4jkdki:vf6ogf1; 0 ohg6top. Explain.

If there were a great mm egm w6,tj;/7 boggj )y-u)9umd9dwsigration of people toward the Earth’s equator, how would this affect the length of the;ume-)wjwg 9m9og jd )sd/, tub 7g6my day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotati my/s+t:w laeqn1,y :dqh c4,mon wheqwmeh sm1q,dycn,/ +4 l::atyn she leaves the board?

The moment of inertia of a rotating solid disk about an ud(ewze 2 n.lt rkqx l64*7zvr jz3:7saxis through its center of mass is.7rrl*z ve7s6wq 4ke:lz z3ut(2n xjd $\frac{1}{2}WR^2$ (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 rotat/qf1xombw 8l:ing stool holding a 2-kg mass in each outstretc qf81m:wo/xlbhed hand. If you suddenly 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 andmn0 9.evjk47 )u1wwcd0rmztg the other is solid. Describe an experiment to determine which is whic47r9c.gwwu1k njz00evm )mt dh.

The angular velocity of a wheel rotating on a horizo:vpz; )fhfmi3djs kpdcmr. pb -68n cp,p1 g+2ntal 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 tangential linear accelercp. p+hfpdrzv6 jp isfm -2c3m8,bpg1 d):nk; ation of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing onmr)xkn33b,ea the edge of a large freely rotating turntable. What hxr), 3nk3amb eappens if you walk toward the center?

A shortstop may leap into the m0v0x/lb-g qtair to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Exlbm/v0 gxt-q0plain.

On the basis of the la3p qf;il9d*yqus m3:q w of conservation of angular momentum, discuss why a helicopt*qd;u 3: sy3fqimqpl9er must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles:de,1 i *bivgdff q(yb yv8a*3 in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of a5j*he s ,kuf sott( io0p*,l)vn amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of thes*vofu (pjsoi)tk*5,l t0,e h Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 k)6ouivi +q *yfi( cl(qm from Earth. The beam diverges at an ifiq+i (ql6()vc *yuo 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 blenden,oxxdw j c 0x5h*l31fr rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the a03xjf wlx*1,hxcnod 5ngular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on498nmny*4f j s.:kzq wpqva x3 a level floor 3.5 m to another child. If the ball makes 15.0 r n.p* 9nxyq8z3j44aqv kwfs:m evolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions y1jd74 t1jm4 wjfze:.thh7 wrdo t. fmjhw7 414ejh1:ywtr zj7td he wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates j +rlf25 ,bcuz.:bddc at 2500 rpm. Calculate its angular bz25 , b+udf rl:cdcj.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. 8–38dq lzvu+6pelz )/ w1j*). (a) What is the linear speed of a child seated 1.2 m fr)ldz*z q6 1wl/j v+eupom 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 naazqm ked+ 2k20,u)rthe 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 o 9snx ojddy51o-j06 bff a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge ro vypb3+4r zqvh6u60i1c(twb mtate if a particle 7.0 cm from the axis of rotation is to experizi 6bq+utbvmc6p hwvr1 y(43 0ence an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130khlwy;2t(, d y rpm to 280ydk2 w, (lthy; rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiush(*vokaho-/4c ks;rm w 3 r7ae $R_1$ 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 p+ 0opptbxk3*put themselves into a slow rotation o*3pt+kpbxp 0 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 cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,0 z( izeir8r,c*vb 9hmqy0 h-s,00 rpm in 220 s. Through how ma ,8b zscm(hqz9ih* 0vy-irr ,eny revolutions did it turn in this time?    $rev$

  An automobile engine slows u v7z/j7x*/k ctnbjz5down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “hu)pg(ucx0moid av w0;1 man centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its fina x(;uc0vwa p0i 1)mdogl 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 diamete(-x q3kz)v s(jvg +qimr accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this gv )( q+v-sizkx(q3 jmtime?    m

  A cooling fan is turned off when it is running at 85yhy 2c6bbdm7; 3 a-tys0rev/min It turns 1500 revolutions before it comes to a stobb t-3 amy;d6yhc y2s7p.
(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 rew tm+x; b0lp8iwhs5q:c)g :eevolutions as the car reduces its speed uniformly from 95km/h to 45km/h The twi +;:)qmp8hlw t0bsx:ge5c eires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 xmf5pqpo: q;+fncmbh v8 97r,revolutions as the car reduces its speed uniformly from 95km/h to 45km/h Thexobmrpm 7+ 9qfv8pnh 5:,c ;fq tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when *s thg8(bmi0vclimbing a hill. The pedalsm8g t0*vs( bih 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 end ofm s2;k*qf,u iab 56pdfhc./zuhqt 74n a door 74 cm wide. What is the magnitude of the b*. zftnd m5p7c;/4fkhqauiu6 sq 2,htorque 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 tdx+( 35by5hlde 3rrq8u 4tfl7vb x+fvhe wheel shown in Fig. 8–39. Assume that a friction torque tlfeu5373d (8brxbdv xvhfly +5q+ r4of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of massp 4l9yq-r e7dqac ago :55d)mr m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on t7gy 9oe-mc q4dd)r aq5:ralp5his system.

  The bolts on the cylinder head of an engine require tightening to a t8)be5z afri(lu 1r va3orque of 38 bva8 5)rfz1e 3u il(ra$m \cdot N$ 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 p 6a3+byzo(qta 10.8-kg sphere of radius 0.648 m when the axis 6qpt3z(ba+ yo of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of iny ug8a2gi-c u)ertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be igna-)gig82u uc yored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the cmyn ,/ 5glk;po-o14wtd9r m blt io8de09x.tend of a thin, light rod is rotated in a horizontal circle of radius 1.2 m.4 o tk dxtb9mtmel- 1oidn8 p ,0grw/l9c.;oy5 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 aih,y e a0q5ss(ti.7 yz bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay ,si (. syeaith0q5 7yzis 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown i,w 9 79lczwv w-bjw;ldn Fig. 8–43 dljww-v9bwl ,w7zc 9;about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose l y6d:5z1(vogzvb9qq r+f*uq total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, n zk9hori sf9d*h1-8,y:gdfr engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steadfnr1z ,d o9si*rgk9hyd:-8 hfy 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 czht7r83b 5wrjm and a mass of 0.580 kg. Ca 3zbj rt57wh8rlculate
(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, accel;k 04aphdlt k*5m,onserating 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 tangentially on a small hand-driven merry7 ig89(r(l5wu clkqzj -go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required towz9 cqg( i(r8ull5k7 j 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 rpzs uy89g0 x-eji v;h0wm is shut off and is eventually brought uniformly to rest ws 0ihy-9vujz ;xe8g0by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at 7 0r)fggor45xin6 o fp b(i/dt -$m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which mi*a0pyf6fob i,;8y krotates about the elbow joint under the action of the triceps oibpm 6i*f0f8 aky y;,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 th)rg)umz bfl3 4p g-3mgo,7 cjxin rod, as shown in Fig. 8–46fjrg pg) -c4omx)l ,mbuzg733.
(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 b:m9os c8i, d/p.sd orconsists 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 from rest within r-ipy+q3m8vk7.m yh xm8ad+gfour full turns (revolutions) and releases it at a speed ofmy7x-i3y8qard + +k.mg8hpm v 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 of72zy*ubm: 5hu7o;le(84vb tdfjld wt $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a tor+ *nrcpsq6;gs queu08n r;.xlque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls withouai0v 7r7gzsq l5x b) ofa4q0(,n a.qlct slipping down a lane at )q47s rl5canq, qo .0fazlg(bx iv0a7 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sdpi ik6-upzfl.oj4wcqhc* l.q. (9r* un as the sum of two ter(.* o.c6z* r.9iqkfl cpuh i wqdjl-4pms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net wo 5 gjltve( .x0 nl8no1nw xx7vxtp-28vrk is required to accelerate it frov875- .n8tvpxlt x2n0 ne1go(wxjlvx m 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 b b4n7g y4nk)c1.80 kg starts from rest and rolls without slipp bn74kyngb)4c ing down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fabtz+q wh5,qaf) 6 zze-pqjb64ll 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 cons 5 zh),ej6z4z awq-6qbqbpf +tervation of energy.]    $m/s$

  What is the angular momentum of a 03( qyhsq dn8o3qq 4m(y.210-kg ball rotating on the end of a thin string in a circle of(8 onhd s3qq4y(q3yq m radius 1.10 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 uniform cylindric9c./ p-uce1iy4no;f so* w5.iscfovxal grinding wheel of radius 18 cm when rotating aw c/s *c9ife.x5 f v 1;sn-4yuoopoc.it 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 sid ( 3brmhu0t eyi4)8xd;y qncg5e, on a platform that is rotating at a rate of 1.3rev/s If he raises hisi80q 5y ce;r(yu4 mnt3b)xgdh arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce hery 0gx xipz+6uhi) b j,mbt.90k moment of inertia by a factor of about 3.5 when changing from the straight positi0xptiih buyk0 .9g6, zb+jxm)on 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 yk 1f3pv5 raduzh glwlxn7+ s,/40s+tjgav69 her spin rotation rate from an initial rate of 1.0 rev every 2.0 s s1dvu tj ,xfnsa/7 0alh5g + +z ygw39k6r4lpvto 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 center at a fm.p(lli ko h5*u2ge 48+s cznerequency 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 clay stic8l .ulk +5s(mezo42 cphien* gks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.5rh( aj htc)aly(cy-6v-/)b in $rev/s$ 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 n uceuybl8)+e 2;uz85 8qsfug 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 ofzxa ullf5. (0 xf1bfn-v7zbe6amr.a 5 inertia I is dropped onto an identical disk rotatin(xb 5me-xaf fbr516 7ln.a0vfza. z lug at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsc(nkx pyr7 , ;;(jdadv*xryh( at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating m dg5f :0rdu3;dftsb -berry-go-round platform of rt ud35 d0fd-gbb:;r sfadius 3.0 m and 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 velon:6fyxwyll alb 7ca vj;9a64e 9 p sr:19/pcxpcity of 0.xylsec 4 9faal7yaxlnp 6 996 vw:p/jc1bp;:r8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half i8k3a1m; 6vco xvay kcj/b8rv3b8dc -t ts mass in the process, and winding up with a rad1 v -o8a cjx v;3r8kbd/atk68cby3cmvius 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 winds in excess ;i/ofy,b-qk.*axm w pof 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 (fs(elv v6zj9$ 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 5.fc )gq, - 3hx4 zzp9td ,gjn7czhwkqrotate freely without friction. The moment of inertia of the persgqtd z9gwn,kzjc7h f5z)qxch.-34,pon 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 pers o85fn nrk zzh)7*dg1v9 j)swuon stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 8o9)1zukwj*r)shndn zgv5f 7 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 wityzyvepaf o 0:h6fk,epl *l(6(e:aht 1 h the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds f1phel(v:eafk z0*6 h6lp:ye,afto(y rom 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 Earthq:k oe -e43j.pq:mngs . Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon.q: -k3gj4n eep :oqms as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at av1hxjxtmu 2 9;dv(s3iqtcg2 3 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 0.20t w1l :+5veqiin6ol1k m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. tvn1+1l ilwo:qek6 i5Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of 97)yg:ltfud jwh nq:).z3 hcumass 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 offdg ulw :tuyh):3j7qz)h. c9n energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angularwk;r6qxk :vm.)r+q)azqx 6 sy0p d qd- speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our6 it;f.j4qdtd *rc2vo Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniformjdot rv*q. cdt62f4 ;i 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 ikg/ . cfd2tw wgt92u3kt to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “fd2 ck3k.tu 9 2wgwt/gspinup.”
(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 illustratlg5iqvud62z; 7 jfi.,:ga twtes 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) bxm5ciiw 3g /38b dow8is rolling 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 p) 4itsiws(8mhex z6;hivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, det6i) tze;x4(hwi8 smhs ermine (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 vertically onog;d)pg(;klc the floor, and we want to exert a horizontal fdlg );ocg;(kporce 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.:hb,kwr ja;h /xj,+g x2m/s on a flat road is making a turn with a radius The forces acting o+:krh;jw/bg,h xj,axn the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of lee:sb( ibz -u8-bvx7 dsngth 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a ratv7bidxz -bes s-b :(u8e 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 cylinde*r; )j7/elfotfx u nvzj)qs/33yo9 wbr and her arms as thin rods, making reasonable estimates for the dimensions. Then e/3uzsb n;v*/jq wjx ) 9)7rfy3ofltocalculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly zwyvod3 s26f(es rdix2 /ox 84which consists of two cylindrical plates, ofs6 fow/ezo8 sdi2(x rx yvd324 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 track of Fig. 8–58 fvg47 bu(jeczb.a76 r. 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? .fu4jar7z7b( ve6gb c Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do njit 20;:ea myiot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed u f9ip+;nk 8 l8(dokuvbdh3me gf zpk,k2 *e58sniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of gl3onf8z kde;s, *2p88( be kh9fi dk+p uv5mkeach 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