Angular displacement is usually express in un35 1;cwqmdn f w9ft(o8c sjs 36usgf-yits of

  Angular velocity is expryazx y+ab1i33 g*x p2vessed in units of

  Angular acceleration is expressed in unia *; fnjn8f: zr55,m.vxbc wxlts of

  A boy and a girl are riding on a merry-go-round w45+wo4 fap9qewd/ lyp 3zg( ykhich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who apz w5k9(yo wqlyf p/ 3d4+4eghas the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a co ,q6 we2fqf rajv-uv,as+n( o0 :qa9xlnstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the l qaq+2sq-a,uvrfxev9j6a,: n0 w( fogreater angular speed?

  A boy and a girl are riding on a merry-go-round whichqc1q6vnezs 6b31do .b/p0 omd 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 lin q 6zsnqdc16oo/v01mbd3bp .eear speed?

  A boy and a girl are riding a mls hq,22 j6gh7av.xprerry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the grqgjlvr 2 s6,ha7 p.hx2eater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is ta ltduktt*e1tr - 689 e/qpjm5cr0.v wurning at a constant rate. The boy is near the outer edge, while the girl is closer to the ce91- trrl/6qwv 0m*t5 ecupt8jtd ke.anter. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatingxt8du:u.0mamy z8-p j . Which of the following is an accurate stata yj0p mx:- mt.du8z8uement?

  Rolling without slippinstj(3; :9 z2lv1(npznk hrinxg depends on

  Two equal forces are applied to a svi,p1 nqob +0,ax mb7door. The first force is applied at the midpoint of the door; the second force is applied at t1, +savnbxpi0m q,b o7he doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. T ck/u 4lim;hp,he first force is applied perpendicular to th/,hip m4c l;kue door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, pe ol;;a-l8cmub.x7fkqe fs c)6rpendicular to the door. The first force is twice as large as the second force. The ratio oo;-xcfu ml7f 6bqe.s);kcal8 f the torque of the first to the torque of the second is

  What is the quantity used to measure anhaiwat( 0pm7uhy+ h9d fd(t0) object's resistance to changes in rotationm+(y9h 0 i0 h7tptuadaw()hd f?

  Consider two uniformc;ue q6.g zzc8 solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of. u6 zecczq8g; the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one haswnx*nlhvd7c8:l( t*u twice the radius of the other. The ratio of the larger sphere's moment of inerti ntl7*wun:*dh vl(c 8xa to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice tls:s f sl l+jr:v(.i4whe diameter of the other. The ratio of the lar s.sli : (s+4r:lwfjlvger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. Ifq:1x vx30tui9(s a pst these are increased to 2M and 3R, whatxpv:(t ui9xa0 tq1 s3s happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is appliry: mejax l:;)m /,a5lgu9pogte+m5 hed to an object, that object will

  The moment of inertia of a solid cylinder about its axis is givq+dnum90x o3zen 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 has a mass of 10 kg and o8mjlzc50+gcn. x0dn a radius of 30 cm. What is the ratio of the rotational kinetic enerlm z 5jnd+c oc.0gxn08gy 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 radiusxm7k 7/, ff6kc7p rdb (ng-ud7wdz bn6 R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bk7z6 bdd6dnxnc p ,-w b7r7gkf(mfu7/ottom of the incline depends on

  Suppose a solid sphere of mass M and radius*x: o7nbfcq27f g ry gaxt552w R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphew7 go*f5xra 2:2ygt5cq7bxnf re at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a nb 4jgo r+s95)f3 pwe:herym ,n*vi)ge et external force acts on ti +ejy 5mn,r)of:9 4bw vhegg3pe s*r)he system." This statement is

  In what circumstances can the angular velocity of system of partic 6no qr4iapotbi//2j-les change without any chang/oi rb4o6naq/2 i-jp te in the system's angular momentum?

  The Earth orbits the Sun in an 2l1k5lz)lpwqzr ee *)hm9c6o 2v w72g4yu ful elliptical orbit. Ignore any friction which may be present. What happ)ge16ve m4l7p2)f2wz*u ql9lol crh zky5w2u ens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves)agvy d;a6hecl2 sd 7+ close to the Sun, then which of the following becydv d7 ;h2ge +a)lsa6st describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in h6 sb:s fiqrg8v+dbei2v m /2y+is outstretched arms close to his body. What happens to his angular momentum about the axis of rotation+f8e s:6iyb v/vgdim+22bsq r?

  An ice skater performs a pirouette (a fast spin) by pulling in his outso9nk*+s(lftl (v 4dwitretched arms close to his body. What happens to his rotational kiv i4+*tw ( lnf(oskdl9netic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast fczr-tp53jl)l32f jy*by l h;spin) by pulling in his outstretched arms closbrl)2yjh;t* j3zyfp-fc3 5l le to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservationa 5rvcfr.xj5 + pr.fg* of angular momentum.

  What arc length does the Earth travel in a three month period in its nea5gu8f;o )ysc/- tzjzcw.j vjy -j9o4vrly circul ;oo ygw 4j- t59/.z uvvsjcj-8)ycjfzar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. -c+kyjqp i1e,ux+ ig4 What distance does the tip of the second hand sweep through in 3 minutes and 45+pxgi+jyc4q1u- e k,i seconds?

  How many rad/s is 25 revolutions per minute equivalent to-6i /ntwhl fm; *gyx+x?

  A bicycle wheel rotates uniformly through 2.0 revolut / .t/bky)cz61lnisjd ions in 4.0 s. What is the frj kz/1.sbnltd /) y6ciequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. neq 7kq)c8v v4 hf91heThe period of its rotation nqh)k7 9h8 e41cfqevvis

  A phonograph record rotates at 45 rpm. Throu eh )9veyp93xegh what angle does it turn in 0.20 yee xh9 )3v9pes?

  A wheel of diameter 26 cm turns at 1500 rpm. How far willxngv cdz)/arz 3x*5a uncgr2,.fr7i 7a9+ g do a point on the outer rim move in 2.r7gf.5 x/nigr,7 o zr ag+*auna23c 9x)cz vdd1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions sqk -1hq39 ;bi ap8 7vr/bexsein 4.0 s. What is the average angular speed of the wheeliqrb-s;v s kbq a89e 3hx71p/e?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatd wqc((;t 4h s7(pymkb is the linear speed of a 4yt( (khpdscw m ;bq7(point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a dik5ewi7 oz3wt 3vw4,lustance of 6.8 km. The cable which moves the cartiz3,4 woe3k w7ul wv5 is driven by a pulley with 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 angulajdqo wol;9r* 9hq5k0tr speed of 2.0 rad/s. What is the linear speed of a9 hkoqq* 5rwdj;0tlo9 point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the4);ytlpx6p v5 ve)rbv motor rotates at t5v y )e6t)vvblx4;rp phe rate of 20 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 t2lvuv5;kn+u z gvd*,y sc73;f8gwpq2.0 rad/s. What is the centripetal acceleration 7* td2f5cg knvz;q;w v3yupls8u,gv+of a point on the wheel's rim?

  What is the centripetal accelerati9fbvc284 df3t ui3:+s cu/b db bw(sgmon of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is (tvusdsib bcf8 4dbmu+3g:b23f /cw9 moving 8.00 m/s?

  How many revolutions pc tuynz zf.l *)(ay(d8 /-kkcger minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity /cuk(c*tyz nk( a l)z.g 8-dyfof $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/cza)bh dle1fih+ 12p/s. The maximum centripetal force (provided by static frictib ehp1dfz2+ 1ia)c h/lon) 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 speed of 20r-lbk8 z:+9 vrtob(x m m/s. The maximum centripetal force (provided by static fr+vk:t(rxbom-lrb z8 9iction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachetb otqv0;11 gd 32kdiwd 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 wiv3t o12k01 wibdq;gtd thstand 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 slipping 1 j)fvl:m;iv7+ :gdlkj0 m down a lane at 4.3 m/fdjg+ 7 k)jliv: l;vm: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 wcmjcqx2:fq.19z)s 0( c vmgzkith 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 constantfep/qn m)3hjn)4l-jl 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 rotate7up;ngw ywu 4+ after starting from rest and accelerating at a couwgy 47 w;+unpnstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular a:eimr)/4y 3nhrp hu* occeleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at;tph* 6fq3d dn 20 rad/s decelerates with a constant angular acceleration of tdd3;6 * nqfhp$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/rdvp znmb 0w i0k1;:s6+4vs dis while turning through 2.0 revolutions. What is the average angui s0;bk4m0 w+v z6:sp1dvni rdlar acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest o 14fi3*q+ ; n1q dq7xis9mde*pygvsy/d nt2jxver a distance of 115 m. What is the total nums 4 eiy7 1g*+12yq;jfqqip3 nxddd mxnv/*s9 tber of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unifor.9cvak (e; nb2n0f83vur jon cmly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelerati0f8 v.n2nv; (o39uecarcnjkb on?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tomrgi r0)u5u x3 rest over a distance of 115 m.u)x 0ir5urmg3 How long does it take for the wheel to come to the stop?

  A centrifuge in a medic18un3g , ;k pwjjw;cuz d3rc.ial laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angularj1rd; p czu wn.jc,i8;33uwkg acceleration before 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 wheel require tightening to a torque of 90 Nm. If a 30 cm lod,l(c/1bf9 ls.auzqn ng wrench is use(zq,dla.lnbc/ 91fusd, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90hs6k;c4c;cmxiwa8y v zb yc6.4 /q/bs Nm. If a 30 cm long wrench is u/b vkbs;icc44mc8 wx acqz.yh s6; 6/ysed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerhuz ( * (57qbovthk6g.cv8r gwtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: md8*xw:farujw *d 4-hfass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the momentw4d8rfw*ud*hafj:x - of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the h)xl z* )zk:xwqk*73n x -lva;wwse8s center O. A rope wrz3 x z):x-sq8v 7xsnk)*w lk*ahw ;lweapped 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 frictiyjoff:f 3xl 4k50c qp)onless axis thought the center O. A rope wrapped apojq lx k ff54yf:3)0cround 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. The rod is initially held in the horizo,j0 t) i/e 8nqkslu9:xspi 8yuntal 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 a rod about oneq:88s i/s 9,p ltkuyu xji0en) end is ML2/3.)

  Consider a bicycle wheel to be a ringa+4gnpz*+e *eegyu v0 of radius 30 cm and mass 1.5 kg. Neglect 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, assuming it rolls without slipp +4ep*azu+gnee * g0vying?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of masru v4e,gmgy*+)4m fw js 7.07 kg and radius 66.0 cm. What is the w+4f)*eumgy vg4mr ,jangular acceleration of the pulley?

  A 1.53-kg mass hangs on a et6 ez4i a5x5grope wrapped around a frictionless disk pulley of mass 7.07 kg and radiuez4x55 iteg a6s 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used*pr vf6b:9 gg1zr0s ke to store energy. 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 in/widwz-8 oa ,* fp9wqdertia 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 starts fr+nu5 fa3(e/jp l7 wwbmom rest and rolls without slipping down a 1.a 3pfwuw7 lj +n(eb5m/0-m 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 ra *igizsw:x-c *fipvbow.*z .*(fsr0k dius 0.010 m rolls with a speed of 10 m/s. How high s :gfs*zziw vx .*-k*r.w*0pfi( cobiup an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20suxd 7ne7z5y: kg is released from rest and allowed to roll down an inclined plane. How fast is it moving57szxed7yn :u after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kk.w:5iaodk h0 g and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere kh:i 5d0wok.ais 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 changes 7 l4wqjzh7dc wxb.a.9yz z7q8 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 iepp.v70 : hja qj(vx-fnertia 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 withjhq fn0 dnw+g1t;b p3, arms extended has a moment of inertia tnwbhpq1+jg30;n,d fof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?