Angular displacement is usuallmw6ui+p 1 89 kthrb(ajy express in units of

  Angular velocity is express :acdp23uh/z 3ngjv3a e f4o+ged in units of

  Angular acceleration is expressed in unitwh k0b(3p-d5 v/dco,9 qvk dkss of

  A boy and a girl are riding on a merry-go-round whivxzygf l+e:1p 9/vcp(ch is turning at a constant rate. The bocez x p(flgy+p/v91v: y is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding o-bh8/(2( jys2 eiy+xsazx ibh3i 5c pxn 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 c+(ha 3esxxj22 hibyi(z5x/sy p8bi- has the greater angular speed?

  A boy and a girl are 7 xhm.o: u.nymriding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and tm ymonu. h:7.xhe 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 a0jz,9dcq x6g:5y;-behrvzs3mz 4 crz constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?ry g,z4e53: sr z0b;h6-9qvzxmzj ccd

  A boy and a girl are riding a me e3vj +,s;znitrry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the cenji3zn+ tevs ,;ter. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate20xh ghs* c ,h:6seamden;p-u statesh xnde0;,e -hpu:62s ag*hmcment?

  Rolling without slipping deq0 wk9x+4vz-n/iyq;pds( yam; is9mo pends on

  Two equal forces are applied to ae,8xht 7 oab6nvp:rn) door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied p8a,:e)nt h 6 nxvb7porerpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is appo v9+bhw )yt5eop.r*plied perpendicular to the door; the second force is .* yr+)5t9ew pvbhpooapplied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to pt7dimhvu n11c a mq-a3*3i ;athe door. The first force is twice as large as the second force. The ratio of the torque of the first to the torq31 73h1 * maiqp-a ;cduanimvtue of the second is

  What is the quantity used to measure an5u34ae ums ryd(d45 e70se0ql ukfru6 object's resistance to changes in rotatimqus edd5 0a6k(u 0leu 3rs47feu45yron?

  Consider two uniform solid spheres where both have the same diameter, bui8g7a85oaz)sb. sc w qt one has twice the mass of the other. The ratio of the larger moment of inertis5.a7o ziqwca8b8 gs) a to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one ,ppd f1gm39g tw,8aylhas twice the radius of the other. The ratio of the larger sphere's moment of inertp3tdgl9 p8f, gmy1w,aia to that of the smaller sphere is

  Consider two uniformjmwu 5+f sx5;a solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of i5uaf ;+sj5xm wnertia is

  A uniform solid sphere has mav-lmyfvn17i6-- vd cgss M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment vmgd6 c 7i-1-vvfn-l yof inertia about a central axis?

  If a constant net torque jf8cz6vx (w7y2o + gyyis applied to an object, that object will

  The moment of inertia of a sol ohfq6+h 6zof(4m6novid cylinder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has6bh2w87m9+u snvbu xl a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotati2ulb+8hs9 6 m7wxubvnonal kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping dow9n hcpmsn (,)9m2cc can an inclined plane starting from rest. The linear velocity of the sphere at the bottom of th9spmc, n( cha )2ncm9ce incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an e6i xjf91s 8geinclined plane starting from rest. The angular velocity of the sphere at the bottom of6exi seg f819j the incline depends on

  "The total angular momentum of a system of b/2m2v spx*s6n rgsv* particles changes when a net external force acts on 6p vvb2*2ss*xgm/snr the system." This statement is

  In what circumstances can the ang)o fq1kg,vpx2 qg/, vyular velocity of system of particles change without any,/p,1qy g o2g)v fxvqk change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fry (x. yrwbyncooa8) j3 8svulco.i69.iction which may be present. What happens over time to the Earth's angular momencc 8x8.a(ysjoo.i9n)ybw6vr ou. 3 yltum about the Sun?

  The Earth moves about the9 u6n:zn q vnu9et1s(m Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth(9t u:1m9nvq6e u snnz about the Sun?

  An ice skater performs a pirouette (a fast 9u(mfj7 gm .-lzg 9dufspin) by pulling in his outstretched arms close to his body. What happens to his angular momentum a.lgj (9dm7m-u fzfg9 ubout the axis of rotation?

  An ice skater performs a pirouette (a,e424 qqo uu.x w-yxwr fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the ax2y eoqux.4r x 4qw,-wuis of rotation?

  An ice skater performs a pip.hjll(kg9cw d07mv*jy x(w. qbr *i+rouette (a fast spin) by pulling in his outstretched armwphj j(wry lil7+d9mcqb* . g0x* .(kvs close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation i*nhhi7emor: a1q ki1(:)mx bof angular momentum.

  What arc length does the Earth travel in a three month period in its nearly cpg c a.su.u 140v2l5uc ,5pkvebvayn9ircular orbit about the Sv,s9 v214c kba cv gu epl5u..y0a5pnuun 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 doestx 6d9x4) diaj the tip of the secodi4j xxt)6 d9and hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutionsp mvp7m:4bc5r per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the7;.cxg h,v(vbsl .(ow ya8rhi frequency of the wheel's rotatib hohx (.7a,yiv(vg. l cr;ws8on?

  A pulsar (a rotating neutron star) emits pulses at a frequen6 gb)tw.mw-zb1ne + 9j vdhxu,cy of 0.40 kHz. The period of its m+.eg,wb6)ubjwztd n-xhv91 rotation is

  A phonograph record rotates at 45 rpm. Thy3uej.l-6pozu(*f5xc: k6upbt gw o-rough what angle does it turn in 0.20 lpg -*6 t5uo e-(.p6kcoubuxjz:3yfw s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a p rc .gzof)htuuq4*3l4oint on the outer rim move in 2.1 s)*uoh 34gr. ltczq4 fu?

  A bicycle wheel rotates uniformly t1 p/ry:s*;mvgi(b ztzhrough 2.0 revolutions in 4.0 s. What is the average angular spev rpmbzst(1igy* z/ ;:ed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wha5iw7 30bb ncwpt is the linear w5ipw0bnb7 3cspeed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries sk jqkiumsy8 3- tea(:x(iers a distance 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 for the cableu-yt 3eam(iks j:8x(q car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular5jtqd4n*q 3f9 owo4f f speed of 2.0 rad/s. 54 oo9f*dwtq n43f fjqWhat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If thg: u2griwf,l:c+ :f.v. hfmzm udoh+,e motor rotates at the rate of 20 rev/s, what is the approximate linear speed of th ofg.hd 2+mf hrw mu.,z,f+lv::uic:g e end of the cord?

  A wheel of radius 1.0 m ixi+e;6p ;r 0trxqlz9g s rotating with a constant angular speed of 2.0 rad/s. What is the centripetal accelqrei96t;r zxl;0g+p xeration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter f79 r3i1f siktz,h wa6of a bicycle wheel of diameter 70.0 cm when the bike ik z,1 sfairw96htfi3 7s moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space sta0qrujs ,2,rcy t(wjh sk72vi7tion (r = 1000 m) rotate to produce an artificial g qu sthvcy ,k2( 0jrsw727rji,ravity of $9.80 \; m/s^2$?

  A car is negotiating a flatk6lv (-ntq-yp;p ial3 circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provideqap6k inpvy(l;l- 3t-d 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 curve of radius 50 m with a spe8mqy5ag xo; x,+d l8azed of 20 m/s. The maximum centripetal force (provided by stxq8oa; ,glzdm58a+y xatic friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a io:4spj+ 6 amm562snk mk 2m 4,ddsxbv0.750-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 linear speed can the mass have if txmi j4dk+ mkp2d6 m6m:2s ns5sv,ob4ahe string is not to break?

  A bowling ball of mag)*76rb-yi3 f iw baxhss 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane bi iy -*x3bwr)h a76fgat 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 wi1960zrlnk wv,zrls. fsr 4k) eth a constant 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 constan 6,+qsd7ab h8b +wfex -fc4f2zksv mol1s.m9ct angular 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 rxa bk(auylatvo zx095wdzh z(x 1;365otate after starting from rest and accelerating at a constant60h v3d 9by z5oxawkt5xa1 (lz zau;(x angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acce- d,:erz,ojy7-glle r leration 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 con a8(nrd4hiukdzg 1sa n )9v405i7t ctnstant angular acceleration 0k541 i9rn) dnignst at(z 8hu74acdvof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed oklpt2r7-pm oes r6, p+5kn, jjf 6.0 rad/s while turning through 2.0 revolutions. rkslppp je, tm 72nroj, 5k-+6 What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly f-y 6mk)xy9b o1cp +kw4vqy5pf rom 8.40 m/s to rest over a distance of 11omkbp fy6kxy1y 5cp4w- vq9+ )5 m. What is the total number of 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 lb )om8n7 zz)0ql6w-,eodc hurest over a distance of 115 m. What is the angno ze hw0o)dlu)c8,bz 6m q-l7ular acceleration?

  A wheel of diameter of 68.0 cm slows down (/vqrk oq5 eho ez6.n/uniformly from 8.40 m/s to rest over a distance of 115 m. How long 5ovrhq6 / o(qn .zee/kdoes it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates aonk-emvb6o/v6ga4 y 2t a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before comin2ba vn /ok 6v4mey6go-g 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 whem*pf;98qxsi k el 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 txk8pqmfi9;*s he force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm lqf7ua g/6n0zpd ) vkg+;sv;fyong wrench is used, what is the magnitude of the force rv s+/qp; fg 7z6fgd;kyn)a0vuequired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of +hnx -4ysx- . yopeh:cinertia $3.00 \; kgm^{2}$ 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 2 afybm) 2ujgbhz5z9+the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the orib5aby 2u )zjm+fg9h z2gin?

  A solid cylinder of mass 10 kg is pivoted about a frictiof*,6t jvlv (ugv.+bcdnless axis thought the center O..jv+ u(6, lbcdtv *fvg A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thry+o+ 1ilhp4fdhl)w ynj-q)/ ought the center O. A rope wrappe/q 4nl))ywrfp+1odhj+ -yhi l d around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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.01chz g ya+:yc:8fl diiz31ck 8o f7ck The rod is initially held in the horizontal position, and then released as the free end isg0ciak k cy7z1yc:+fo8cif3d1 z:hl 8 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.( /o2vzsuzcq jlkuk6 *7hk( a to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a foqh oa6sl 2kz kvcj(7k /u*(.zurce 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, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope s .y eo5mq)0kl6m/ 8tedsjj;qwrapped around a frictionless disk pulley of mass 7eq);oys.st56q/dm j0mje l k8 .07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless d lxr512cq8 c.k1b kdj7fu eib6isk pulley of mass 7.07 kg and radius 66.0 cm. W k6 5frxlu c1bbc 8q.27e1jkidhat is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to store ubg,d vrk1x; tw8(yb/$1.00 \times 10^{6} \; J$ 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 4at, ydw 7kvy.x d ybi3l6a3r: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 radius 0.010 m starts524qi iy nr1.k gbek1j from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bokgb k jyi5q1irn2 41e.ttom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls wik0k,, s e/ a6e0c6dl zbz:oiqbth a speed of 10 m/s. How 06/:lo, k,z6adeiqeb ksb0 zchigh up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and all wtvy.my;a*c9owed to roll down an inclined plane. How fast is it moviy yt *;.w9avcmng after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm roll amqg+hj c+d,62hw e:ys without slipping down a 35e incline that is 7.0 m lo yc2wm+ :+e,qhahjdg 6ng. Assume it started from rest. The moment 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 momeik g 4 xj6ld;qtlg 6ng:k/2lqe: v2oz0ntum 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 ihdw.0izbl91ust ds /4nertia 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 a wa7hfnk()pcs2a9olp,wy (m 1 rms extended has a moment of inerti ofp7lp y2(hs cw)a(,kma1nw 9a 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?