Angular displacement is usually express in unitgbh*u hg+f0*.i4h p7:a)t z oi(jm + oia)uluqs of

  Angular velocity is expressed in units of5 5nr n1 nxb1aqf hwly664f8nk

  Angular acceleration is expressed in ue1)e jrtyx17. bc5j nvnits of

  A boy and a girl are riding on a merry-go-round which is turning at a c2y uvm1ac+f sk3d-:q sonstant rate. The boy is near the outer edge, an-+maycsf u1qs :v2d3 kd the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ridit469,jqa zeqf 1p mq2j+grg 3ing on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. qj1m4,g2f e zg3ijt p+rq9q6aWho has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constant rtt8))lf4a k)* dmcaor ate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linearo *)ck)am f)8ttl adr4 speed?

  A boy and a girl are ridingk5q*qevior1mes0a- . a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Wmvqasr10 iokq.*5ee-ho has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at g etmj/du2dj3i/62ezp (r whsq4)fi2a constant rate. The boy is near the outer edge, while qzwf3 (emrps2)ige/ u h6d i /24jj2tdthe girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating od0ri ;p jy(clv r3;ui(0kwa+. Which of the following is an accurate statemen3(;r00up jday;(+l rw ikocvit?

  Rolling without slipping depeny4;g3m s4xm hdds on

  Two equal forces are appliez z2oj)yk7 6:yl5y qyzd to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Why z 2ozj6y l5:7yzyqk)ich force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first fo00)l5al,m ywfk4mkl*dzf)w; omtv4k rce is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which for4zdwo0 fl vw)ktf,y0lm;m lam5k*4k) ce exerts the greater torque?

  Two forces are applied to a doorknob, perpendigchf *,x, 2viicular to the door. The first force ih*,gix icf,v2s twice as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resi:p5t,l a(jvpthw 6d1bstance to changes in rotation? (wjbt ,h t1d:5v6alpp

  Consider two uniform solid spheres where both have the same diameter, but one ham jpkrri t.1h /1il0.bs twice tb1.r1.mi h itjl0/p rkhe mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the rad xy11azx h1.0tgdo 7lt zi(.ovius of the v(xxdzy1 tzito.0 oag.71h l1other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mas; mbdui7 -*mtas and twice the diameter of the other. The ratio of the larger moment of inertia to tha7 bi*-mad;mtut of the smaller moment of inertia is

  A uniform solid sphe 6lx tf4jyne qn8o98(vre has mass M and radius R. If these are increased to 2M and q tj 6 8lv8fyxnoe94n(3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wb:m pnum j5-uq8p9 ds5ill

  The moment of inertia of a solid cylinder about its xz8s z,x*x 5imaxis is given by 0.5 MR2. If this cylinder rolls w5*ix,z xx msz8ithout slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of *j+bwo znw-, tj ;+ ,s6ug4pivc hhb5zmass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total transla5 j4z,+u +bp*w6nzvoiscg,t hb-j; hwtional kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M ea+b21x + p1sd-yoob rand radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere atb2spyo-+e+xb d1a1or the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withoutq( 6y hw/;iigz slipping down an inclineg;(w iq6yi/ zhd plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net etv,i rv 0)qon a/fv/ppz w8a w))iq2h4xternal force acts on the system." Thi2 8qit/vrv)vpa0fwnipha)q /o )z, w 4s statement is

  In what circumstances can the angular velocb(juqjc g f4c36r gn()ity of system of particles change without any chanb(ucq(crgg)46f 3jjnge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore anb a 2qe1hgl:au2b /ed2y friction which may be u122alh2qebagde b:/ present. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptqa0zt *1l 7 gw:g-lvcwical orbit. As the Earth moves close to the Sun, then which of the following bestgwlt 7v0-q gz 1:*alwc describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pu0gkkm- a2o u;glling in his outstretched arms close to his body. What happens to his angular momeokkug 20-gm ;antum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hisklt0 y7mmm, m, outstretched arms close to his body. What happens to his rotational kinetic m7m0,ly,ktmm energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling ingxo p, 9;(8ua o4irmy,sepm r, his outstretched arms close to his body. What happens to hi, (og e8ao x,,9;iy4psmupmrrs moment of inertia about the axis of rotation?

State the law of conservation of angular mo -my nami35)q3 zjoe/,lwa;w /c.fqnementum.

  What arc length does the Earth trm 2dd:w5w65g,6rv,qgpl akqh avel in a three month period in its nearly circular orbit about the Sun wi,rqgwmg:wpdqv65lk62h ,ad5 th a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What d0csghc1uy 4 / e5b56d.-eenacv:wnkdistance does the tip of the second hand sweeea 4k:vngu.6n h eccs5c/0ew y-1d5bdp through in 3 minutes and 45 seconds?

  How many rad/s is 25 revoln . 7u3-pvvq//atg jsbutions per minute equivalent to?

  A bicycle wheel rotates un4o d g3ywgmxj d 9(elml80cog7)h)7 yniformly through 2.0 revolutions in 4.0 s. What is the frequency onyw7m )8co4xo9d(h ydjl) 0eg7 3lgg mf the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a f77tswm1 kridt2be8a)requency of 0.40 kHz. The perioddwm ask7t28r7 )1tie b of its rotation is

  A phonograph record rotates at 4 -/k60sb ikb6d6ca1gc gqmfn)5 rpm. Through what angle does it turn in 0.20 s?q ba- f6bm6 kg61g0cd/n)csk i

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a qt: a)xjs(thtk )5rc*sj d :0bpoint on the outer rim move in 2.1 s?tj )s 0dr)cjt:*(sa5 bqkx h:t

  A bicycle wheel rotates uniformly through 2.0 revolutions li4lanehyz7-q5h ya t4e2e :6 in 4.0 s. What is the average angular speed of the wheel?h 6ea2 q-i4 :e45lyh yez7taln

  A bicycle wheel rotates uniformly through 2.0 revolutiojil wbd7k6; ukp0+b. tns in 4.0 s. What is the linbjulkb6 +dtki07 .p w;ear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distancexjf w* ykr.w 0xr7.3vc of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate fv.rywxx fcrj .*3wk70or the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.07xr/ jvrut8j(dok8 s+ rad/s. What is the linear speed of a point o(/ 8+xrjrto8d kvsu j7n the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in l69x;oftb 3r npjm, 7rooke . 9c1ihe1cength. If the motor rotates at the rate of 20 rev/s7p t6 c fe1.crnhj9; xoeo 1,bokrm3i9, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating w6cud7bi/ gck)g k0 575e7c allsrk-kvith a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a ps7vigcbkuc5 al )r/ce05gdkk7k76l- oint on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle wh p:p,)*rym exw+*zstheel of diameter 70.0 cm when the bike is moving sp +)wt*er*hypmz:,x8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotat3kgq+ dub q cho*8ilva4p.. f9ing space station (r = 1000 m) rotate to produce an artifihab4.l.q3uf+9*kv qpi ocdg8cial gravity of $9.80 \; m/s^2$?

  A car is negotiating a l0r8x k7pxe*2wogig* flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction)ge 8pw*og* i7lxrx02k is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve o19r(c7 wfb-gno9fj q hf radius 50 m with a speed of 20 m/s. The maximum chb-ofrf9jqg 9(71c nwentripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to thmlcmnr;) zb/txiutb5;-q1n6j eu7 )e e end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linelbqx 1imnu;m6b5ejuet ;7r c))z t-/ nar speed can the mass have if the string is not to break?

  A bowling ball of mass 7.hi/ :tq ,etrjm0y0u,z 5 kg and radius 9.0 cm rolls without slipping 10 m down a t0 qtjme: , ,/zuhir0ylane at 4.3 m/s.
(a) Calculate the angular displacement of the bowling ball.   rad ( fill in numbers only)
(b) Calculate the angular velocity of the bowling ball   rad/s ( fill in numbers only)
(c) Calculate the radial acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)
(d) Calculate the tangential acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)

  A wheel accelerates with a constant angular a*2 0j:l5cq v lik6nbzccceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?

  A wheel accelerates with a constant redhwi *g ).4hangular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does a 0.300-m radius automobile tire rotate after star4zd.*r1)sf6/ qy- qysb icdlmting from rest and accel z64 s-l )sq/iq m1cf.ydybd*rerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelera ov1d8 / x)kee+ms 15my1vbuxstion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatingimr0n71vedn6cz( 9hxw o/qo, at 20 rad/s decelerates with a constant angular acceleratio vwqxz,79cr/1n(ieomn h06don of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of+tr a*yk2m b6/ts qxv0dv+8 f+dh*lot 6.0 rad/s while turning through 2.0 revolutions. What is the average af 82+ddl0*tvb*+t v +a6rkx/qth ymsongular acceleration of the wheel?

  A wheel of diameter e,w8 a o46/ qsphi glfpuc0b/6of 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions /6gpceha8ou i4lsqp w,06/fb the wheel rotates in coming to rest?

  A wheel of diameter of 68c3ackp dpx.2rif(,tnu 9o p;r4 4r.vw.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular urvr4 pf4.p.ct(din; aor9 wx,p3ck2 acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly frzziexc)9f, h(xx* u ;pom 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to cuh9 x,i(xz;x cp f)*zeome to the stop?

  A centrifuge in a medical laboratory rotates at a rotational sqg orj8dr5 ,lxsv7j8+peed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to xj+j5 ,8l7rrdqg 8svorest.
(a) Determine the initial angular speed of the centrifuge.    $rad/s$
(b) Determine the angle (in radians) through which the centrifuge rotates before coming to rest.    $rad$
(c) Calculate the constant angular acceleration of the centrifuge.    $rad/s^2$
(d) Calculate the time necessary for the centrifuge to come to rest.    $s$

  The bolts on a car wheel require tightening to a torque of 90w u3ians +o 8 5yv/vnkzsqv5h/qd/z;4 Nm. If a 30 cm long wrench is used, what is the magnitude of the forc//s;/vwh4vszunqiakd5 +zqn o3v5 y 8e required when the force is perpendicular to the wrench?

  The bolts on a car wheel require cn8.r*(eb umg ;bqkw. ;oe(pw w/o.uwtightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force applied.r mwkub;* /b.cqo8eoe.w(;pwgun w( at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiissoj kxks1o76 weo r(/1w-a5nb y70n a $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass m is at the orx,ri+ 6,k wyqm-),/ trsxavgiigin, mass 2m is at x,a,g t+/sqkx,6ir riv)m -ywx = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought thi61 6ott43 w ,svv74lg jv:rba7jt0nsfh-axle center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = ittas4bfwhjsv:03v6,la7xl7tv o 16n-grj 4 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought tmyb d5n ( zti ,/x0b)eu;mrz5ahe center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does miexd;tnz y ( az),0/ubrb 55mthe cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in thed mnj 89l8n esk,5em6r horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The moment of inertia of ard88ekn6j5 eslmn9,m rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. Neglect ds+4eri6er 0p4c xg-n0i jct ,the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuminjec4ix0e i p-r0td,4gr6nc+ sg it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pi0s4tk8 eb*h0*vn wv xulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the 0*n itkvw4vshxb0e8 * pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frryf8)ilia29yw* q.hvictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the 82ivh9yy*laiw qr .)facceleration of the mass?

  A rotating flywheel can be used to store energy. 0ubn2)gkprc 7 If it is required to store $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of ine 7yslz)k.h yux,ne(czy ,1v6drtia of $5.00 \; kgm^{2}$ starts from rest and accelerates under a constant torque of 3.00 Nm for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

  A solid sphere of mass 1.0 kg and rad-g e0tb *d-fi7 hgy/5pj.yxf eius 0.010 m starts from rest and rolls without slipping down a 1.0-p0t-7bfyf /g d yei-.gxh5*ejm high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m kv pv:3a czl; 1cu)umu+x1*vwrolls with a speed of 10 m/s. How high up an inclined plane can it climb before)v* axz:; v1p wm3 v1cck+uluu coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed)0q xy.ptqe6,z; dg ot2gwr l. to roll down an inclined plane. How fast is it mov2.dyx, t6wqrot q;z e.g)gpl 0ing after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without 9yqka6srz d( y:ay.)b slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment r:szyd(6k) ba.y yq9a of inertia of a sphere is given by $I = (2/5)MR^2$.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

  An object's angular moment6lcs39w aquy1s ,okb,um changes by $20 \; kgm^{2}/s$ in 4.0 s. What magnitude average torque acted on this object?

  A proton of mass $1.67 \times 10^{-27} \; kg$ rotates with an angular speed of 2 x 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton?

  An ice skater has a moment of inertiu eq(v6 vmni5u)zyo4 /a of $5.0 \; kgm^{2}$ when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to $2.0 \; kgm^{2}$, how fast will she be spinning?

  A figure skater rotapce7e;tged2ka j ,*-iting at 5.00 rad/s with arms extended has a moment of inertia oe,i7e2;tj p *gcedka- f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?