A bicycle odometer ( 90e rfzb-qme(which measures distance traveled) is attached near the wheel hub and is designed for 27-inf 0-erqzbe9 (mch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the r8k zis6p3m2ypwrm(gi8x t-7 eim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration chxe2pkpi 3riw s8gmt86m- (y7 zange?

Could a nonrigid body be describecdbj,wcr;x/jn/ 5 r+ 52s yejsd by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain;pke1etn2 1a,md tnhbk-r0 4n.

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 diffice4 lm2zg4mchv cl9 -ddbx2-g ssi8w62ult to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram maw4- dci9 2cxgv-em2z 8g264s bdhms lly help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three a)fs0)4 u+pkjtnfl)jl t the pedal cranks. In which gear is it harder to pedalkj ljn ) s)f+l)p4tu0f, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slende2m7 r(1shsnzjr lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of ss(2jm rh1z7nmass is advantageous.

Why do tightrope walkers (F4lowxx+c*u9x,j9ef: dni ei 6ig. 8–35) carry a long, narrow beam?

If the net force on a system is z k 0ymajy75dki f;75s.bnyz/wero, is the net torque also zero? If the net torque on a k zy5a f/wnyykmd 0b57;7si.j system is zero, is the net force zero?

Two inclines have the same height but make differentp8) re;/usjhab/lo3a4,eoc5 /pbvr l angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explai,a; se l/bpjouo3 av e)/rr8l/4hp5bcn.

Two solid spheres simultaneously x*k3d) r :amw6ysomuj- ehj-* 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 y- swm6j-: 3h*jouk* )xdar emincline 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 aahwqnh/4 ne- 5nd the same mass. They start from rest at the top of an incline. Which reahe/ n4nh5wa- qches 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 con p fo2ujgav4b.dt 39ct5*7n reserved. Yet most moving or rotatinof3 e 4b*2cg pnrujt 957.advtg objects eventually slow down and stop. Explain.

If there were a great mut3 */y2t thlfigration of people toward the Earth’s equator, how would thht t/2uft *l3yis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rot /.wqzp/er0h)6uk rcgation wh/.eckhpq0g/wu rr 6z)en she leaves the board?

The moment of inertia of a- :y0r nee2cug rotating solid disk about an axis through its center of mass igrc e:2u0-nye s $\frac{1}{2}WR^2$ (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 sto28j7a;- :ci /nln 5fjzezfnxo ol holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, dec:jfn-e cxlnz oa z /f785n2;jirease, or stay the same? Explain.

Two spheres look identzo0m21d1 0hsiks hja5ical and have the same mass. However, one is hollow and the other ishi1mk 1j2h0zdsao5 0s solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizon-nd(l ay u x*pgac6n20tal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angularuald2a p0n- 6n gxc*y( 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 rodc j.i22ch9hur:bt)7 0wfv fptating turntable. What happenb22:u0cv7.wch f hd9r )pfijt s if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it tq gp30 )o:;q*jav0pj9c phemquickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notim *hp9cgaqj 0pvq)tp: 3je;0o ce that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservav kffa 2pj zp/lcp v.g.wk;:,9tion of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller ac:wpk / p.,kgf;vzflj 9p .2vcan operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3x mdi. ej1fg-0x-hm u30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, using the-vy7sk6lg 4h7p3km mq information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, l7s v kqp3hy7m64 k-mgas seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The b82;f((f 6r1asou gaiyht2smsw.f/v seam diverges at an angu .(fa22s6moafsh8 tgvs fiyr(w;/ 1 sle $\theta$ (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 pgp/ zn xoy6v ( h:k;k2oxql;0rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is th2z(/no lky0oxpg ;vq6p ;:xhke 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 0xu4*etsx)p mzwx4;2o 0eiyx makes 15.0 revolutions x w0p2o 0xsm*yz4; ti4)uxexe, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do ug z9 bja2x2r7theub 92g2z 7jxra wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate itt0tlk2 q0 6wyf8l)jv os angular vel0tly 2qwlo )k f086tvjocity 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. 8mb*eq3 ych2 l9–38). (a) What i*m yhbc2 elq39s the linear speed 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) inq8sl evopkte- /h2 277te c;lm its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spexh9ao y4y 8d/h7).g ttalv/.we(po byed of 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 cenk*11cm5hk jg eipws: m 2y7cg.trifuge rotate if a particle 7.0 cm from the axis of rotation is to exm mg 7w*se1gc pci.:j 5hky12kperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acce702qd-ck op fflerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. De0q f27dfcop k-termine
(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 t cqn o qpcqs)2i 5gcg6cpo*:c9 kb1.)$R_1$ 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 9 4m xli, 4dc+lf-lbekjr w8.cthe 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 cyl4lfb9x-.rk m+jl8c dwl4c, eiinder 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 lir4* aa4,awj.q;z j uto 15,000 rpm in 220 s. Through how many revolutions did it tu;qz ui*4j j.aa,arw4lrn in this time?    $rev$

  An automobile engine slows down from 45 wet9o6+isp8o y/3w rg00 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 jets8 iih ac6xz;v m abg48a*bc;:v in a whirling “human centrifuge,” which takes 1.0 min to tuvgb4za a:i 6hc*;mxb;88 vacirn 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 diameterumy o6lm 4 vrbe;v,q dd.6:kf+ accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of.ov udv,dr4 femmy66:qb; kl+ the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revolo5;w :gfdq p2/4p b 9;t(4dbt:bwapa *lwtpntuw;4dppb(df gl;45tt:2b9wtqt awp*b/:oapn tions before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car rj lm5 dkgk*d/,educes its speed uniformly from 95km/h to 45km/h The tires have j5g ,*dmdkl k/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 revolutions as the car redtdzz,. nt49bduces its speed uniformly from 95km/h tt d4z.z dbn,9to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when cl6 tm02v2naj)hszf b(yimbing a hill. The pedals rotate in a circle of r(6 b n20zhy)satfmj2vadius 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 of6/)fliv++ h(7dhnm(mdqtpq u 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exertehm/+qmnl(7id ( upthd6f) qv+d
(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 w/iuees9.e r:4py3hqim4r)o wheel shown in Fig. 8–39. Assume that a fricsh:priu/ 3me w94q.) eoyri 4etion 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 bedp;/9bi r ft:8v st+massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in th:bitf+epv9s/8b ; trd e 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 engindi0q/6cts:lrbt u 83m e require tightening to a torque of 38 0t lbs8q ti:rmdu6/c3$m \cdot N$ 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 ofxp pjs-t (j6p2.o r7b.hsc9zf a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its cent cpho.rb 2zpft(9.jx-ssj p 76er.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rimff4.x4j vs.+ls:.7,namz4pisqf j wp and tire have a combined mass of 1.25 kg. The mass of the hub can be ignoredm.snf:.wa f q47 s 4sf.4ippx,j +ljvz (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a s-j2 emth*v;z.r 6by) jso5ye horizontal circle of radius 1.2 m. Cj- th.vyj5 ;zsmy26ees)bo* ralculate
(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 pott( vllr 72l;tzher’s wheel rotating at constant angular speed (Fig. l lv2zl;7thr( 8–42). 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 inyj g/l htjj3) xjx9-x/c a0vw;ertia of the array of point objects shown in Fig. 8–43 abowaxthg93j/ljyvx)x c0 - j/;jut
(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 try/*rz 6 j.m od.cs:whwo oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satell7,u,ql7d o2c yni mu)iite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satec,quilnu7 7yo2i d),mllite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform w,b g8/mg( qbbry20fzcylinder with a radius of 8.50 cm and a mass of 0.580 kg.2bgqb(mf8rg/ , 0ywzb Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swikhjd g fp0fn4h)6q3y, ngs a bat, accelerating 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 okvcih7z7.)m :2mc4 t((ts iy3kch qv 6zk,cismall hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a unif723 o)k hc7csvyzv i,k4ii(c mtzc6mqtk(. h:orm 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 )v1ruz6m7 4 +ms(jhrwd e hed*eventually brought uj) dh7mzev1d*erwmr(4su+6 hniformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at 7 et+-ktr6ge i.si 92ki8i w1k,5nuktv $m/s^2$ 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 th5hon e)ln 3+0wln2py ,gh e3gwrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifonlengngh2 ,y 33l0oepw w+5)hrmly 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, aam;/h eepgg3 5s shown in Fig. 8–4e game/5g;h 3p6.
(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 consi vfrz2ur-lm qv 71d:m45vtu 2usts 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 four full turns (yicgpkq hzd (/ p6q:x o4 za,iv0.s43qrevolx pp4qg3q ica kszdo4i.z:y06q hv,/ (utions) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a ,d1q ozu wln1jgqy/9z 6ij o,: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 of 280qi h l53 oz(bp3dwbbsn 24am8. $m \cdot N$ 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 slij9h;c w:k vs* g5o4g nsau8 ufhmk,,.zpping down a lane at 3hkuj, ;sa8f n:v cwk* g,.h9zsom54gu.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun asu.9j,24ogt/bv rwi7u aods dz1 ) lpu, the sum of two termsgrpsoo 4.9tuva u i ldd/jbw71)z,u2, ,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net wx6:-sgyab+(povp6 f i ,hj: lnork is required to accelerate it from rest to a rotation rate of 1.00 revolutia-b +:6 opjhp,v(y6s:gnlfx ion per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg star, jq eor (etlob1wc+*)ts from rest and rolls without slipping down q,+bw oe1le)c (jtor* 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 iiukmz1wt )34hbeflh s-*23bwuf 0(lvertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hitsu 4)e *3h-sbw f2m1 kb(liuf3zwht0li the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg 0d4 r eqq*2qheball rotating on the end of a thin string in a circle of radius 1.10 m at an angue04e* hd2qqqrlar speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-1fj0xnx pi-2m3 tnbcr, e;1oc kg uniform cylindrical grinding wheel of radius 18 -pr1xfcb n ot3ex2;m,jc0 1incm 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 platformtb2kw )n0 -cot that is rotating at a rate of 1.3rev/s If he raises his k to-tn0 )2wcbarms 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 4kawaj.*h m pkj wkq5;*4v3uzher 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 54k*wa4akuhzk*3;q .pm jwjv1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial raten3dtgey/ljl8 4l8 2yr of 1.0 rev every e lylrl 238g 4tdj/yn82.0 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 center at (gso+) jw*0rmfwt j;ba frequency of 1.5rev/s The wheel can be considered a uniform disk o*ojj +f0g)rwmtsb ; w(f 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 sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spin 4u-mhuwz9z6bning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of t-o58w gmio 1q cgooer4a8hkg5s7f )f+z.p wm,he 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 inertia I is dropped onto yt4-- vph,yv65h:a cru oqaa6an identical disk rotating at acyaa v566:-p,t- y hquh4orvangular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atyr/ v.8s merd; 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 rotatin. v. ooco w, o(te5pf0rkd:m)bg merry-go-round platform of okbo)oc5w(,fp.o:0tv dr.e mradius 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 velocity ofv *i3y:kz; ljfi:x 2li 0.8 : zy2ilvif :kj3;lix*$rad/s$ 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 aw/i gps dn9+ke(. w+wl 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 integek +w gdepi(wl.nw /+s9r)$\approx$    $rad/s$ (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 excesz.:e-y wdxmj 5d7vqc ;7c-z4bielq. ys 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 bx/e-l1 s f00 xqox0dj$ 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 p( ke ppgdao-. (t-3dqwlatform, initially at rest, that can rotate freely without friction. The mp p(k3-tdea-q.d og(w oment 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 st j9mhgi/nf 34r k u4u+/kqwdg*ands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inehqri9+ g34dj/ukn uwmfk /* g4rtia 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 7h+ck f1.bx iqtuf1t)kfkw5 / the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of bft1 u7/+)kq5fxitk1 c. khfwrope 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. Dpb: mb8 (x)jflw/4xou-5 .gb2bmesuq etermine jo. f)m/( x bbu gpbs5:ewbq-84m2uxlthe ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from 4f1nw 5s aqh/orest 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 acqun qk.;x3 rnz1j3ux (+a*uqnedires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculater nzq +1eu*(3knaxx jdqn;.u 3 the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricayrgpx zul /h-ks8/ n52l disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindricalp58/lyuh2s rx g /kn-z 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-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 spe 29sp8:cldw)hqy(vz v * .oiuged 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 our Sun, but with mass 8.0 times as great, were rotat2o lw 1xc i)jq5cko.k3ing 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 uniform sphere at all times, and that the lost mass carries off no angular moo3j )ciklowk2.1 5xq cmentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to 0:wx4vf c gi/ruse energy stored in avgc/rfw i: 0x4 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 “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. ympd8tw vk66 l*jg/gchn64y 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 (h zhi( 9t40letv4bgq c;oop) is 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 a:c vw-v ;d zqg3-3qqqjnd length L 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 release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume thadqw- :q;3c qqjv -g3zvt 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 on the floo1 ) pg2k7cktcr6nv7 58mdzgxdr, and we want to exert a horizontal forcck1)5tkg7c g7 r62v8mdpdzx ne 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 travelinaqbog8 89ua* ag with speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normalaaao *9u8q8gb 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 zsd14sng cxu *0uea2i 5zwg7/.50-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 after 5.0 s. What is the torque cw z ues d*5zx0g 7/nugas142irequired to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’qbbpyd,)(t(z s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculabq y(t(),d zpbte 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 which consists oq,/ni b7 xh)1g5vgdiuf two cylindrical plates, of mass hini7x ),d1 guvq/gb5 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. i06gy(nv wm.e wp y21l8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highes0mvlp6 w w(i.e n1yyg2t point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do n.c8vhm;bndcw:-3r xw 0cl d/cot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85/p pw.pm-.l:ozmh3auiu8e x; revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelerationm p;leu/ ohawpui-. x 8zp.3m: 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