Angular displacement is usually express in units ofq8qovo,q; mde 3s.:ts

  Angular velocity is expres1m)m w j.n3- hymx5qqtsed in units of

  Angular acceleration is expresvi 4 x31ok:jxpsed in units of

  A boy and a girl are riding on a 3fzmd0v, +qo9 yyz b845wmmbv 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. Who has the greb 5 dmoy zz,m 4qvbf+9wvm0y38ater angular displacement?

  A boy and a girl ares b*ehz /kma9nq4i+( glt,0oo riding 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. Who has the greater angular spe eb0mq9 no*,olt i4+zhsk/a(ged?

  A boy and a girl are riding on a merry-go-round which is turnin dphtbh5v4q/9qzmn(r1 j(;wvg at a constant rate. The boy is nearrdbthh 4 vjnz1w(q9m(qp5/v ; the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant-m-sfd+ys d xl z- w7n*k10xfa/j4cuq rate. The boy is near the outer edge, while the girl is closer to the c-*qfxdd 4as-nwkx1l+0sjm z-y /u7f center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is tu(1rs8 qh5 tggvrning at a constant rate. The boy is near ghr5tqsv8 1(gthe outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid bodzja8qwql+be)d8 c) u(o 79 en ajv)d3oy that is rotating. Which of the following is an accurate stateme v)j)w9 lc8n d(a)zd q3+e8qbou 7aejont?

  Rolling without slippif+2l15 yix2x cdxl ,kcqdr r*3ng depends on

  Two equal forces are applied to a door. The first force is applied at the mi7 rbr9 gj:)vhb18tfkr9 jvyn 7dpoint of the door; ykv 1f v7bn)rjgh r7 8jb9r:9tthe second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at tvcvp(6 n/9hl a 0vpb0uhe doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which c9vpv0(p/n 0lbv au6h force exerts the greater torque?

  Two forces are appli)ms 9kqjvz egt*nnv u*;31 f7eed to a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second iz mv7nvk*g s n1e9q)tu e3j*;fs

  What is the quantity used to measure an object's resistance to ch bl,-gf2bnq/ml/ tugyl3y )4i anges in rotatin y4/qlm)-2f3b/,lg gibu tlyon?

  Consider two uniform solid spheres where both have the samfm7j7f(s -t wkt0 -- a ugr*hw8gwy*qbe diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smas0* yjw-7 *b7af8fu thg-qgrtk (mww -ller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius;v* xs5 bo5go n)xam+s of the other. The ratio of the larger sphere's moment of inertia to tga;55xm+ o)vbo *snsxhat of the smaller sphere is

  Consider two uniform solid spheres aw 2h(qbz hi56where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that h a2qw( 5zi6bhof the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If v a2puytzma c+intf;oo3b./g n9 l(6.these are increased to 2M and 3R, what ;.i23 bg .+ylmta n/ oo tc(6ufv9paznhappens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an objec *) fu;jy-asm3 wvtd6 do/qdq0t, that object will

  The moment of inertia of a solid cylinder about its axis is gi f g.4rxpf *isc1wau8.ven by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotati u.f8.xas c1wrf4*gpional kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a; 4y+xvg fq)r04bsj ac mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy rc404y;jafbq+x )gv sof the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of/os4l -zmo7 flxh11 dv mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear ve4m z7-dv1hf/ xsloo 1llocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an ;pxx ( .xyebqd4-ynw*inclined plane starting from rest. The angular velocity of the speq4n -wdbx*.x;y x(yphere at the bottom of the incline depends on

  "The total angular momentum o0f k:y 7t6b4a3t/dw tg*llpdvf a system of particles changes when a net external force acts on the system." This s6tfb tyltad7*d3 :p4l gkv/ 0wtatement is

  In what circumstances can the angular velocity of system m0v)fdy2ul0z of particles change without any change in the system's 2z vl)uf0dm0yangular momentum?

  The Earth orbits the Sun in an elliptl iuh5;thew wjs0xfkuhp6.i(6eh ,,8ical orbit. Ignore any friction which may be present. What hw pt5isi8j , ; flhkex66,ew h0hu.u(happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As t p)0n9.;rzf ax;quy et97zgi ohe Earth moves close to the Sun, then which of the following best describes the orbiting spexq t9ya o7gfrnpzu.i )0;9z;eed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretc+:ip dezng7abq27 us0h1ve : phed arms close to his b7ezbg :up0+ipe72a: 1h vq ndsody. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fastss e q7yziz3*2 spin) by pulling in his outstretched arms close to his body. What happen*s sz7ez 23iqys to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his ou5q v7f f5nlbo2lc9e.1oufa w:tstretched arms close to his body. What happ2l9ebna: .1ff o7lvq5wcf u o5ens to his moment of inertia about the axis of rotation?

State the law of conservation of angular -qklbs9 ,mc1zi, wvm:momentum.

  What arc length does the Earth2xdaxuoa8rao5,. -vjqx2(g z travel in a three month period in its nearly circular orbit about th-58 2xdjugox2v rx, zaq(oa a.e Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does bo( kj0mt5 fyljgu* gk0c() o;the tip of the second hand sweep through in 3 minutes u* mj(oo)gy0j; f5 kkltg(c0band 45 seconds?

  How many rad/s is 25 revol9c 2 zosa;y;hjutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions ia 56xm qmsopam m:tow7 r7q*58n 4.0 s. What is the frequencyx8 p5:s 7ar5m*wm6t qa7m oqmo of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. T lz op2:4jvbpt*x)wu )-m ;mvbhe period of its : )b-mpwz j)v;lt4vx2*pumb orotation is

  A phonograph record rotates at 46wyizgsdn ml 2).c 2j6pm..xf5 rpm. Through what angle does it turn in 0.20 s)mi.ycgz2 2 .npd f xw66.lmsj?

  A wheel of diameter 26 cm turnsspugl xxbp 1/5l1ux)/ at 1500 rpm. How far will a point on the outer )/upsup5/xx1bx l 1gl rim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 red+j7:xkd4 f :odh7 xgyvolutions in 4.0 s. What is the average angular speed of thx7k7fy :d+dd xohg4 j:e wheel?

  A bicycle wheel rotates uniformly through 2.0 revk,09midtfv3 y olutions in 4.0 s. What is the linear speed oft,k3dyvi 0 9mf a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a dist5xy bfie 9o2ugkc,4 o3hh1ji+ance of 6.8 km. The cable which moves the car is driven by a pulley wite19xjokc, ub hf3i h5o4i g+y2h diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for 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(w k4wd3p rxhl lsu1 2.0 rad/s. What is the linear speed of a point on (kl1upw x3h2dlrs w:4 the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in kef ;q(3j ii9ilength. If the motor rotates at the rate of qjkii; i( f9e320 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2g 1yqc.t1x01vwyx5n b .0 rad/s. What is the centripetal acceleration of a point on the wheel's riv xyx 1bt 0gqyc.1wn15m?

  What is the centripetal acceleration of a point on the perimeter of a bicyclsqh7x8dk4i+ me wheel of diameter 70.0 cm when the bike is modm i78shkx 4+qving 8.00 m/s?

  How many revolutions,0:ehqs hh8f s per minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to0qhs8 hhf: ,es produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m;d 9w76vpvpt a/s. The maximum centripetal force (prot ;p6pdv79vw avided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular bmukg9 g.i -9nbsmx -,:cl( (rwsr mv:curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fr(9 bvcx:rng.(rlw-im 9skb,mg u - :smiction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachedhip6 7e72yj3 )bj umth to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withsta7tpihmeu yhj 7 6j23b)nd is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slix6e- ,bxhzfz04:xffyt , 6hmm pping 10 m down a lane atf-t 64xezf:hh 0xym,bfx,mz 6 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 constanf(z4tv1pxo r6h mu+ )pdpxb:0 t angular acceleration 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 af hytzc.jw8n;x 2l0d:(sp- uxngular 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 rad:d-k7,v 2qj5 p no1z;atfe ctuius automobile tire rotate after starting from rest and accef5ketd-o 1j anz2; 7:t, pcvqulerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest0ue))pha-qw5 py: qv( / vykvx, and has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constant +ldxb 9 0)x;b geeeyiolv+ 5b1angular acceleration o)b el;1l9v bx++goee0xdyi 5bf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s whilevgvsk e,6c5a mkaw+(mw4q8fr 5es o5w8q)z, b turning through 2.0 revolutiaq k4 )wsgk vvsm6,weq+f 8,r55bcmza 5eow (8ons. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from t d sj--plr,2r8.40 m/s to rest over a distance of 115 m. What is the total number ofj2 rld,- s-ptr revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over a(7tp1 b9afa jk a9p1( j7tfabk distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 c1ocugha05rcx(ek wx u 0 3c,4zm slows down uniformly from 8.40 m/s to rest over a di,eux0ro1ccuxca ( zwh g4350kstance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates ckr0dy,2 ohb;-l ps h8at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration beforer;p2 sy l,b8hk h-co0d coming to rest.
(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 wheew6kccim. q:k 1js6j;m(.vbrp l require tightening 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 is perpendicular to the wrenpmbw 1vrj.j;cqk:k c.i(s m66 ch?

  The bolts on a car wheel require tightening to a torq,)ez e300ji z rigy7rque of 90 Nm. If a 30 cm long wrench is usj,0i0ge)iyerq 7 r3zz ed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment 2rqw4y6zwrkqd(wv u8 . os6d81fhg +nof inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mod 9wzp+7yu;jk celed as follows: mass m is at the origin, mass 2m is at x = a, aycw7+kz9;pj u nd, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of kp8/.4g czfmup*ra 1( gfcxd6*xm dm;mass 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a *d86 gx xca1m/;k*pmzrupmff g4( d.c 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg in g(n3ui j8e/ams7zx6s pivoted about a frictionless axis thought the center O. A rope ei( mj6 gnxu3 nsza/87wrapped 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 the 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 / j b)tsmvg,9d0qzc+l the horizontal position, and then released as the fc zm9j/,svg0 )qbtd+ lree end is allowed to fall. What is the angular acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass a2ndcyfl*.,7 q x.hnm1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket oah f*, y. nq7l2n.dcxmf radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrappeb 5qpy ,wt*9bqd around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the w y* bpbt,q59qpulley?

  A 1.53-kg mass hangs on a1zeg 4znh lre 9s0hmr81 5hz/;fndn5d rope wrapped around a frictionless disk pulley of mass 7.07 kg and ra54h5fez dsz0nhgdr lr8 n;/1zh 9emn1dius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is rwcdqot37( ld-b s5cm0equired 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 inertia of ;uallu+emd *7qh*+rzj c ;;ex $5.00 \; kgm^{2}$ 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 1.0u 9g+klb)j5om,y:yws 0c5 rmf kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plan,m5)gfrym9 yks o:w lc50jub+e. 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 rolls with a speed of j4:ov.ali .wx bvz .3y10 m/s. How high up an inclined plane can it climjwo 4abx: .lz3vvy ..ib before coming to rest?

  A hoop of radius 0.50 m and a mass of 0h ydv;b .8mpvqc(o) g6.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a; h8m.g6) pyob(vvcqd vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and ra w1etp:q)doa.dius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The momentpw1):eat od.q 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 momentum chana 3v,-6o-h2ybob eqhsges 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 +s a5:wito,b5zqoyr 5 of inertia 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 rotating at 5.00 rad/s with arms extended has a moment of in8-jt *z3.wjhmhvnvo .da7 ok4 ertia.vtako -zh.oj 3w 47dnhmjv*8 of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?