Angular displacement is usually expde88 r+d(e;ocad wm 1rress in units of

  Angular velocity is expressed in ugx2 cet80sgiaa6ig7mf 6r 93 jnits of

  Angular acceleration is expre5ui+jz dkyzrzo .8in;rma)je -h*r03ssed in units of

  A boy and a girl are h-uee7(jpv8 z7rrt ;c riding on a merry-go-round which is turning at a constant rate. The boyepr7 jet7(cru;-h 8zv 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 on yg*59 u:b3awfp7qnx sa merry-go-round which is turning at a constant rate. The boy is near the outer edge, and gyw3n 5xa* p f7sq9b:uthe girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constantx0 /hyy w mi( m0ausqt5*4rbr( rate. The yyw* r4uaq(( imxbrh 0t/ms05 boy is near 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 constantsslto r5n 99j9 rate. The boy is near the outer edge, while the girl is closer to the cj9rs ns9 5t9loenter. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a const9mruy24 -q)k etcvd8x ant rate. The boy is near the outer edge, whileq2kuydvme t4 cx8)9-r the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid bod5/p1j vir r:pgy that is rotating. Which of the following is an accurate star p1:r5p vjig/tement?

  Rolling without slippinnqap v5 pg*0sqay48+pes,7 f zg depends on

  Two equal forces are applied to a doorfv3qb p7 ihy3)9gw ,to. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied oiv9b3fq7 hg 3 )pywt,perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is5q-q-65qw l;xbp5igf ut (fcz applied perpendicular to the door; the second force is applied at 30e to the plane of thebq(zg5;5ftquq - x5fi c 6-pwl door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendiq8id 76b,j bhbcular to the door. The first force is twice as large as the second force. Thebbi8bd,7 6qh j ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes i*sq5tvqtd +:- kskq h)n rotatio)v-qq5kt +: k stdq*shn?

  Consider two uniform solid spheres where both have the same d3 7qahwr,6idy iameter, but one has twice the mass of the other. The ratio of the larger moment o6q7ariyd,h w3f inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but oni)1nbh, df dfcp19k)w e has twice the radius of the other. The ratio of the larger sphere's moment of inertia to h))fnkd1f 1wi 9cpd b,that of the smaller sphere is

  Consider two uniform solid sphenb4yv 21d t2nnkvb6e;kl gjz3j 9 9p:tres 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 mome:d6 ;jk9 tb9 2zjbvetn1ln24kyv p3ngnt of inertia is

  A uniform solid sphere has mass M and radius R.rf)gfv 7mu7b) If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a centr7 7 )vg)fmbrfual axis?

  If a constant net torque is applied to an object, that object wc7qnd6us* / o hatol64ill

  The moment of inertia of a solid cylinder about its axis is giveq84 kvc g*e3pq5 9kzuwn by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translationqz4*8p kwgu qc59ke3v al kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 1x7 jjrn;lvy* z-; ,a .hfsof7w0 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energyr .l-jf;h;,fwv ja x ns7ozy7* of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls w9c gln*f6b7d4kv yevs*iz17 eithout slipping down an inclined plane starting from rest. The linear vv7be6 14vez*s9dfkn *cy7lig elocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere k 1zcd5 d;wce;ko9qd1 of mass M and radius R rolls without slipping down an inclined plane starting from rest. The k1;1o 9edcwq; cd5dzkangular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes 4p,eb2,bidp d ncli145 rq0 wewhen a net external force acts on the system.1dpi,n542bel,rd wi0p 4 qb ce" This statement is

  In what circumstances can the angular velocity of system of particlpq5k fxi(*p5n 9szy +wes change without *p win+s k(x5y5p9zqfany change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore anakbp*ql bokh19+y6 xo8 w:o0 iy friction which may be present. What happens over time to the Earth's angular momentum a*+8k 0i69akw :o oyo 1qblpxhbbout the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movq*.xtdm)pb 6i xm. 2fnes close to the Sun, then which of tn)bm2 xd mf.6i .tq*xphe following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a piroue9v3hc 8l.oyzcauct./5xjg( myi3 n1ltte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of tcz5y/ihvl l 3(. o13m j.xyc9cnaug8rotation?

  An ice skater performs a pirouette (a +7 kpo2h /ryy 30aay-w6ws nqwfast spin) by pulling in his outstretched aq3 /yw6o0- a hkyw2py+swa7 rnrms close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a piron (rpp(r.b0 :p-qq nxdbwzt82s2dv. muette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inerti8.2(-q rnn d.drp(z2sqvxbm :tbp p0wa about the axis of rotation?

State the law of conservation of angulbq n a44bzf1+yar momentum.

  What arc length does the Earth travel in a three month period in its nearly circ lpk +v/(. uo.7 x)m3x wbgzg9q8osuilular orbit about the Sun with a radbs)wmk7 v8pg.3(9izx ll/ouxogu. q + ius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has .mczny4,j0,cfd temgy sp+)+hsds38 a length of 0.30 m. What distance does the tip of d03.,fjntph 8s,csy+dmzg c+4 )yms e the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutt ;jib:o t 8:31fbtrytions per minute equivalent to?

  A bicycle wheel rotates uy/ce8ht4- a9e 9r.ra df6knn cu-dh k.niformly through 2.0 revolutions in 4.0 s. What is the frequ8ncda 9dr/ta-k6rh4.ne-9c .hy fkeuency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 l7qejov mu 6 jyw)zl3 xzc)x5144g q5gkHz. The periw1v4 gq4olc65m)3lgye)5jq uz z7x jxod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle doebkcvp3j4mt any:h( u 7 m,r.z*s it turn in 0.20 szpv mk thnj4c,*(y.:3ba7urm ?

  A wheel of diameter 26bx;fg y7.7 qlpb b m(11lk:: cbpxay;x cm turns at 1500 rpm. How far will a point on the outer rim movecm pq.xflg(1xbbb7a :;yk: y1x ;lp7b in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 6n95p l:goupskhs;;is. What is the average angular p l;o ginspu695hs:;k speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 k:4yhi3 rjj3p revolutions in 4.0 s. What is the linear speed of a point 0.10 m from t:jk ijp3 3yr4hhe center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cabpos kw6ai;* rz*rct*y-4o+ m jle which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast musycprsk*4-jwoz;raom* t 6 *+it the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatc;y 9n.xqgsvtvj4))( / xb6ic,wxdl king with a constant angular speed of 2.0 rad/s. What is the linear spek46 xw)jbc/)qxin,s c.gl9v v;tdx ( yed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If thev0yb.uxph) r3ikk8k k9h) fl2 motor rotates at the rate of 2i2k9h pk 8k.f x3)ubrly 0kh)v0 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 anwlgz di+ou7v5ejoh t4 o*7 .u(gular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's riuo7vlto(z u4 w57ji *+de.gh om?

  What is the centripet q3x6cdv j72l1vg-ebgal acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike 71dv -lgvexqjgcb326is moving 8.00 m/s?

  How many revolutions per min8- h6l*htvt+z xdbs 4s:obx 7bk w .a(uf/xx*hute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artifikxs*(/ w a -87x:+hvbb* xs d.z4ft6lbh htuxocial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat clhn/ 0t096e 4dhtckod ircular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by staticte 4k /l0ddh6otn0c h9 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 radiu.) w)u.0,by7 jee:n(h-lhyzdnjt fips 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fricu y jj-,e.ehifh0.n y 7t:)nzwld)(bption) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the o8.;nlk+rxnq,.c: 6oe9um qvw fx1y ,xwmza8 end of a 0.750-m string, is whirled around in a smooth level tab 1zlq+xrm qx;cxy.9 mokuv8,86.no f:a,nww ele. 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 m0 p.to zt6s-svi:dl ckk0;e17.5 kg and radius 9.0 cm rolls without slipping 10 m down a lat0i kozvkm0-; :ce1d ts 6.slpne 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 accelerat uw-i3,ivlar5(b lz*t 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 egjr9tynjcr7v (7)yt7hp )sh; )c4w langular 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 rotatevhjtv;:c b l2-0xlla( after starting from rest and accelerating at a constant angular a vav- ljl(clxb:20ht;cceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acct3tx. .xt(3puxh9 vag eleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 209him1vv +fqe: rad/s decelerates with a constant angular acceleration+9v efvi1h:qm of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angulcz 5fq zeu -w:yv2h(,lar speed of 6.0 rad/s while turning through 2.0 revolutions. What is the lc :z,hz25-(yufwqveaverage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unifoe0vn6 s- ) nxq e/ l:vhu.6mxx 7-i0awjpihkw9rmly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revle/ 9p u-xemvhi q0 n. kh-wj66n:a0wxx7)sivolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly ,na -,f vh7prhfrom 8.40 m/s to rest over a distance of 115 m. pfa7 h,vn h,r- What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest o )3ubq 0ir:zyzh0 .rjh44iiuhver a distance of 115 m. How long does it take for the wheel to come to the stb hz z:rhiu3q)riiy04hu4 0.jop?

  A centrifuge in a medical laboratory rotates at a1wfe0t 2d2( njofz*w0+dnzgt rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a cons( * gnjtod d20 t12fnewf+z0wztant angular 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 reqt62xsjw e*(/ty fw o) zk7u3ulmgh *2luire 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 tokj eygw2(7)m/f6lzuu* *sw3 2xt lhis perpendicular to the wrench?

  The bolts on a car wheel require tightening to auc9:dbx/q k9l torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the forlx/9:d9b qk cuce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia( iww6nmwi75v $3.00 \; kgm^{2}$ 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 origin, mazz 58ws7 xnap(76cw y,i.vrv zss 2m is at(6yz7crnxvpsa .,i5w wv7z8 z x = 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 x iifx+ vuk3:4frictionless axis thought the center O+:fv4uixk3 ix. 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. (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 thoughth,b z.b+6. yennyr ,1j/ncjog the 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 wrap e/j+.bny6nz by,j,c1orn.g h ped 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 tvt ld9ja , m 8cs3ahfd29ebhbw5mo38 0he horizontal position, and thw98hb5hca0j3st,8 a3edd bfl ovm9m2en 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 one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. Neg77ehs tn;)i ;3kdb6fp poesr8y5l l5 hlect 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, ahnrylpf7) o ls 5ed;bs hk8p ei6753;tssuming it rolls without slipping?

  A 1.53-kg mass hangs on a r*o3 vxo)n7)jnp/zv x uope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratinxoo /z vnx3vuj7)p)*on of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of maa:xglz - *n3yqq 4r;exss 7.07 kg and radius 66. n xqz*4;:aerqlygx-3 0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it q ;fnov4l.t4v(e1pw xis 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 o yfe8g4pqtsib+w q /2,f $5.00 \; kgm^{2}$ 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 fev;76a vux9 o iswx(d3d-c,b wrom rest and rolls without slipping down a 1.0-m higc(3v;6sd7vw-ueio9 axbx w ,d h 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 rolls -58ivqpi g)en fsjd7 2with a speed of 10 m/s. How high up an inclined plane can it climb before coming to reg5njsf7peq- 2i) 8ivdst?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowehs .4 7(rc(by:el+plz6prq vrd to roll down an inclined plane. How fast is it moving after dropping a vertical dista(+p. eplqbr:4rs7(y6clhzrv nce of 3.0 m?

A solid sphere of mass 1.5i v. wnp;/ x/0k /xsqsq:bgs7m kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The mpq;v /q:swss0n// xg ikbm7.xoment 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 mom4 f*ie mobd,1fa26p g7 kmsvf3vx*3vjentum 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 momentnp)rys v157w:r0rux6bo go -mowvzp*, 6 8boj 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 5.03+feou.t ,x k9 lst*kn0 rad/s with arms extended has a moment of inertia9lueto*nx tfk.3sk,+ 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?