Angular displacementri37rdjwxo zfj u z37 c1-7jla 4ej78a is usually express in units of

  Angular velocity is exprerdw;6h. 5uskgssed in units of

  Angular acceleration is expressed in units oft()zp6ip ooo8;gpa* s kjq-v; .f-mci

  A boy and a girl are riding on a merry-go-rounh /t:q(9xb sf 8u/sjzgd 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 dis /qzs8ux j: hgbft/s9(placement?

  A boy and a girl are riding on a merry-gwhv9tl q)knf2*9 y g;y2td:nx o-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. *9:d22fnl;yvhtw xtqg n)ky 9 Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turningh;l8( yvp p4nt at a constant rate. The boy is near the outerh(; 4y8nvt ppl edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridingtocml excne(9w86ia(fq 3/b2 a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to b(9aw6oflxc8/32(eni qtc e mthe center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merryr,d/ p(r (ixljtvhq14 -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 gx rplrd vqht1,j4(/i(reater tangential acceleration?

  Consider a rigid body thatx- /jjhrvfz 7xc1x :7z is rotating. Which of the following is an accurate sz zc7hxjx7-rxv1 / jf:tatement?

  Rolling without slippin(,m3sh v:z hhig depends on

  Two equal forces are applied to a door. The first*i .geb-lht g2 force is applied at the midpoint of the door; the second force is applti glgbe-h*2 .ied 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 the d7 v0q9qq dsck1oorknob. The first force is applied perpendicular to the door; the second force iscs0 7kq1q9qd v applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door.p k15 gk4hz2amon0d 5n The first force is twice as large as the second force. The ratio of the torque of the first to the t4nh an25m01 podk 5gzkorque of the second is

  What is the quantity used to measure an object's resiz 0m1 vaxj(p*n5af.d fstance to changes in rotatiozda . 5nvxf*jfmp(0a1 n?

  Consider two uniform solid spheres where both have the same diameter, but one (ps *zxj2nw8rfud6 hdyq85*l maln54 has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment lpy4dl8 56nnarxsj dh f2u * (*8z5mwqof inertia is

  Two uniform solid spheres have the same ;*y2t, wtiq f4y3 -obfz-i:cz- ciol mmass, but one has twice the radius of the other. The ratio of the larg i-;i4q oyo 2:tbtw,ifzf3m- *yczl-cer sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice (k voc*:le-,zwh k+ b+fvt4 eht i+w+athe diameter of 4w k h+ze+kt vcf+ela*i:- ,(+ vhwtbothe other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are ibbn49why tpkq) m;* k1ncreased to 2M and 3R, what happens to tqwhpb k14nt kmy9b;*)he sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, t)o jo2(lq-nn 452bmou jv naa5vr-*kl hat object will

  The moment of inertia pc4 w75g wg)b7j: hb8 hn:dasoof a solid 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 has a mass of 10 kg ab08n ncr4l4kf nd a radius of 30 cm. Whcln4kn4b0rf 8 at is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphe;ise0cidv/( ch/:x*n8nb2 px .spbj tre of mass M and radius R rolls without slipping down an inclined plane starting from 20i/j*8c/ti sh x(. ;cnpbpbnev xs:drest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius Re 6)qo )ix,okj rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depen) oe6qoi)j,xkds on

  "The total angular momentum of a systaitu l+ c/;puqs7+ec8 em of particles changes when a net external force ac7c+us 8qi/+;peal utc ts on the system." This statement is

  In what circumstances can the angular velocity of system oft*6qfe 8,j8 a2ucitrm particles change without any change in the system's angular momentum6fmc 82ti*t,ra8je uq?

  The Earth orbits the Sun icw6z(grz4i 7u n an elliptical orbit. Ignore any friction which may be present. What happens over time ig6 z7zcu(r4 wto the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical n i31xav2.uqvfflq;)08u nx l6ncmo;orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sucnoal ;v03 nu 2nxxlf im;q6fv8)qu 1.n?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstr7 nqc.si.o+k ,q c2tmrvo;wyt5q3*fcetched vq2ticwtcf5 .y o.r sc kmqq7o*;,n+ 3arms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by puli6o vxxy +hz3*)rju/x3 q3vlg ez8 o)dling in his outstretched arms close to his body. What happens to his rotational ki zox/z)di +hxeu x 8rj3o) qv*33g6vlynetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fe8+ 3ccg3.sh4en5e f. rz pcpeim2qr:ast spin) by pulling in his outstretched arms close to his body. What happens to h ic c5qmer3+s. hre efcz .24e8:pn3gpis moment of inertia about the axis of rotation?

State the law of conservation ofdcpl ts ebak0. , 9wif-1k5js- angular momentum.

  What arc length does the Earth traveli s6r2lu 800 so2brbti in a three month period in its nearly circular orbit about the Sun with a radius 20s 2urbl0itrsbio8 6of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dv);me4ebxqk/ istance does the tip of the second hand sweep through in 3 minutes abv)e4e; xkm/q nd 45 seconds?

  How many rad/s is 25 revolutions pe 8x+bb ,)anngsr minute equivalent to?

  A bicycle wheel rotates uniformhb cg)ed9f 8xv95 k8ctly through 2.0 revolutions in 4.0 s. What is the frequency of the 8xb h8ev)9kt9d fg5ccwheel's rotation?

  A pulsar (a rotating neutron star) emits pulri esa5p +.3epses at a frequency of 0.40 kHz. The period of its e+e35.a prpis rotation is

  A phonograph record rotate av15 cisy21hk+is eyd*wv6 c75up3uxs at 45 rpm. Through what angle does it turn in 0.20 s?h1c2v1wuy5iidu 7+ vk5ss6*y3p cx ea

  A wheel of diameter 26 cm turns at 1500 rpm., ;p 8)nhn1 ism3nfyaw How far will a point on the outer 8awm; i)1h fnnyn,s p3rim move in 2.1 s?

  A bicycle wheel rotates uniformly mr jgf37krk9) through 2.0 revolutions in 4.0 s. What is the average angular speed of the whek3)mjg9 rr7kf el?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 460l(y vwk4*1lshxu m i.0 s. What is the linear speed of a point 0.10 (lws 146h0li vxmuk *ym from the center of the wheel?

  A cable car at a ski resort cci, tb)ca8-gr, yobq )arries skiers 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 fasibb)r yg,q)co- ct ,8at 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 2.0 rad3smy9fwmk.tk c,:.-xp4 f btn/s. What is the linear speed of a point onmpt-4w.y skn:x.,km 9tc3bf f the wheel's rim?

  The cutting cord on a gas-powered wee dg50ia f9ysel*gu/bap6tm -m:9y +fad cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of teyay-am t9 fs509+l*/p:ai 6mdbuggf he end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angulqd9, mctl qb-wrrb,w: lm(-s vp9 (d:var speed of 2.0 rad/s. What is the centripe9tw( :-v , vrmcllpdrd:sw-qb9(m bq,tal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimelor)5zfj2t1 vvi/v, z ter of a bicycle wheel of diameter 70.0 cm2jo zzvvtfv ) 5lr/,i1 when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a,:g *n t9an9q2cymhq7zf( *y mhwla3m circular, rotating space station (r = 1000 m) rota3nh7w 9atzy cq2*,(m lg9amq yhm:fn*te to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat qs;* sxrauw5v 2zfun )a0wy/ -lxv9o+circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal o2- squwfya u9r;0+x/w nva5s*zlx )v force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat4jibyv,)*uxv eri37f circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (pi7y ,x) 4i*efvuvj r3brovided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end wfp* 4yi4k8df 6nstej5f ev.1o6cl 5n of a 0.750-m string, is whirled around in a smooth 6vjf45ln4 i6w .cstp dfn yeoke5*f81 level table. If the maximum tension that the string can withstand 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 clyn (w-yf:b/b m rolls without slipping 10 m down a lane :(ynf b/w byl-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 acceleratd /2 rx099ne kt0kvbp w9ql1ca6ulcx )ion 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 angular cjldjto;)3.+(zftw -cd + m ueacceleration 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 t9y,4y,6cn0m ei5 h ebn rxmc9lire rotate after starting from rest and accelerating at a constant angular,,5 0r lbien9yemxc4h9y 6 cnm acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acc /64s tnoag1yieleration 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 angular ac(f +(ugatoow+ celeration ofo t(afu+ (wog+ $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an n*;mq-h gapr ijiqfx1(3 *jupv4:7c9 k )yoqwangular speed of 6.0 rad/s while turning throuu9ciyrwgfq3 pkqmx7* oav1j)j4i -q:(phn* ;gh 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly fromf h3+c ;9eiqh2.z zw v)mn;vmw 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the)mn32q c.; m+9z z hevwhiwv;f wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s0gdb9y ;xqt a5 to rest over a distanceq abyx;g95 dt0 of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformlyikdo3 7); teh0( /t.rupel erf from 8.40 m/s to rest over a distance of 115 m. How long dku3oi0 ee hp.t;r7()ftle/ rd oes it take for the wheel to come to the stop?

  A centrifuge in a medical l1)mp ul4 b3nowaboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to 1w)ul3n4bm oprest.
(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 5khvjld (tyffoydb06zk 9(. -require tightening to a torque of 90 Nm. If a 30 cm long l (jkkb6hf(d vzy 9oy-5fd.t 0wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel requ.oghu1p4t e*o9 h-kw dire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude u.d*hho4-1 wk9 epgotof the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia 5u douagn5xv;y(9x2 q $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as fo)nl tw b(rvp,/b 2af3lllows: mass m is at the origin, mass 2m is at x = a,vbbfpl2a ln/ )(3tr ,w and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is ;dpt 1o2,(z-)cd2b(q:dgsh n so6bc yg 6e iqbpivoted about a frictionless axis thought the center O.od(bc ep; t ys dh),(z-6bqg6 idqbc1g22 o:ns 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 frictio+( ng938eis5 c8nld fg fx3zvmnless axis thought the centeg8 cnlxn(vfsd z3mif9g58+ 3 er O. 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) 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 62sf /d.pw 0iwrst dsjn,;y*w the 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 inerti s6j2dd rwy f*int0w/p s.s,w;a of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ringjex7 ef:bedji 3b , 0eo6ms6d-4uo6jb 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 withoutbjd7de me, 64ijosoe -u:b6 6 x3jbfe0 slipping?

  A 1.53-kg mass hangs on a rope wr yy*rwtd/2+nr:i,v* dv az;vtapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratitzdt;/n:d*vwv* yv y+2,arr ion of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk )5dok) ;w k7qe jntw(ypulley of mass 7.07 kg and radius 66.0 cm. What is the accelerati( doy w);7e5 tw)nkkjqon of the mass?

  A rotating flywheel can be u :0-ezi uceq)psed 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 inertia of qpkdt jm248swc)w) c, $5.00 \; kgm^{2}$ 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 from rest and rolls with/d d5eyj7 (xd9 em-s0lfjezv30im z, cout slipping down a 1.0-m h mivdesf m7jj0zx3( dd,e509z-c/ely igh 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 m0 ai, 5cs zfgpaacl4;c 5p,xn6wb0ds / rolls with a speed of 10 m/s. How high upb4 wgzicl f, a5sc;600,a a dpcx5sn/p an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 vw tqxklcq ny8i) 76.)k).kgz:4duje hr . 9ykm and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a ve.)t4q d9 iyh) ynx.rkck67lk8wu.g jz: vekq)rtical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls withou :*nqc28fvkoez+3e*u-rszmc5fngw 1 t slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The m1 fumw2vsce*8c*kr+ zq 5z: -e3nfngooment 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 c b:;kr (yiyuw;hanges 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 ory 5 tc8aq3((oi8kxtug8zm0 ef 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 mom9a*fj w4rnq 6s;gjw z:ent of inertia jrwfs;wjgq 9z:64 n*a 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?