Angular displacement is usually exyej 76 0fadof8press in units of

  Angular velocity is exp /iqu; 2thzaoztmc f:.;fetv9lt4 ./j-gc+d rressed in units of

  Angular acceleration is )r0qk,gvpe cs401 y;c )owbobexpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning aati6x1 in,a- at a constant rate. The boy is near the outer edge, and the girl is closer to the center. n6-ata1ia,i x Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which y utdy6)h3 1t+lja4y5rxex7vf 4+59s kpciw i is turning at a constant rat 3t)5w4hrdlx49+7 piai1ctxvk5 jsy y6 fyu+ ee. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round whichqf jeam:e(. 44c3 emqtuc x5 sp:),msrk3)cux is turning at a constant rate. The boy is near the outer edge, and.kae f)x5cj4mpc3q 3e: ) s,( c4m:xeuqrmuts 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 cons)z(c,rp5uqw,9iskrc w)z b o6 tant rate. The bw )z,,orcwb i6zuqk cp)9sr5(oy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constagljsl899 rmk -nt rate. The boy is near the outer edge, while the girl is closer to the center. Who 89-sglr jml9k has the greater tangential acceleration?

  Consider a rigid body t8ppqj4zqm(h5cfc: + ihat is rotating. Which of the following is an accurate stateme5imp j8:+(z qc 4hpcqfnt?

  Rolling without slipping depends zm 1men bdvt ot0+-3e3on

  Two equal forces are applied b(tles*3d (n.90ftqha6 yfi o7ikku 3to a door. The first force is applied at the midpoint of the door; theloshk t6b3(yn ift 739ki fqad.u e0(* 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 the doorknob. The first force is app3:a,uqk *z iq zi183qb-i cyeplied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater to:3 bu- a ,3iz qe*ci1kqi8yqzprque?

  Two forces are applied to a doorknob, perpendicular to the()jgyb +89 vndgati) n door. The first force is twice as large as the second force. The ratio of the torque of the first to th)aginvny t8d9(bg) +j e torque of the second is

  What is the quantity used to measure an object's resistanzj19 4in)uhy9g 0aw flx8wy *qce to changes in rotation* 9zw14xa9gw0 y8jy)hl u fqni?

  Consider two uniform solid spheres where both have the same diameter, butdxqq k7i8pt.gu*l96x ps ,j9u one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment ji.,g xusqkl9tp8 p* 9ud6xq7of inertia is

  Two uniform solid spheres have the same mass, but one has twbz j ,7xn;s 6eddk-/rf6su7jg ice the radius of the other. The ratio of th f /76nr s6 xe7b,gs-ujd;dzkje larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid sph/aome b2vpi:3 eres 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 vb mep: ao2i/3of inertia is

  A uniform solid sphere has mass M and radius R. If these are kir/x4e;.ote9: dj 48iw mf frrqo:xdgy(2-qincreased to 2M and 3R, what h( g fdo t- kfi9:eyrr8:jr2q xxqi;de /.m4w4oappens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to hfk 1ev6/yza*s/yc0ran object, that object will

  The moment of inertia of a solid cylinder about ikb;9q jmstt1k*/16o i oexf/zts axis is given by 0.5 MR2. If this cylinder rolls without slipping, f 1 ztt*9;ij6/e oks/qok1xmbthe ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel vkt1bjyq8 /kh)ar3oo/s e8 )sof which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? As so8tys 3jh)ro 8b1q e/)vkka/sume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls with 2qn.llkv0*f;wy p) 3 r1uhebpout slipping down an inclined plane starting from rye1 lu2bn k.l* 0h3wp vqfpr;)est. The linear velocity 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 incu+ i9,pjrj b68hxsd x4lin9+x8xsjup h6 ijb4 rd,ed plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net extefz,270u+oy vgica/y*d7 iu k5em mou1rnal force acts on the system." This statement k foy +egmu 2*uimdz,/uyav10i75 c7o is

  In what circumstances can the angular velo9)+0t)ozatufuwh g /fcity of system of particles change without anyu/ ow9zh0t)fu+af g) t change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction wh,leg/y t0rn a,tp- /nm-ri p4rl2ejypa+7tq; ich may be present. What happens over time to the Earth's angular momentum about the Sun;,ta- l t/r, 0g2yqlet/a yj7nr4pn+ppmi re -?

  The Earth moves about the Sun in an elliptical orbit. As tkxw;.hd e1fu:w6t h2 qhe Earth moves close to the Sun, then which of the following best describes the orbiting sh6w.efk qxwd:1h2u ;tpeed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast zz3 jp4xy:tf1k hkgv75wbm52spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axiswpm4vg 1jfx5k z:5kthb yz237 of rotation?

  An ice skater performs a pirouette (a fast spint3cavt s u08m 6p8mz0by; rd:t) by pulling in his outstretched arms close to his body. What happens to his rop z06ty;m v 8tda8 u30tsmb:rctational kinetic energy about the axis of rotation?

  An ice skater perfor,my9b0sh vo 5kbxq i16ms a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia abox5q, ymikb 0b hos9v16ut the axis of rotation?

State the law of conservation of angular momentum.9xo,9 r9slw bqwistsev6 44adrxe,2 /

  What arc length does the Earth travel in a three month period in its nearly ci ha3ycfc8/cgt 70;q9dmu hs-zrcular orbit about the Sun with d hfms;aqt-h9/3cz0c uygc87 a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distancez-f6fiecc .ang ,pd,7/0*ccdig k+ il does the tip of the dez glpci0i,i6 kc-7. f n+c/dgca*f ,second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minuty3d 6c2uq.rtwnh u)kbf.f d,+e equivalent to?

  A bicycle wheel rotates xvlz)ce /mk,nc/e 7, vuniformly through 2.0 revolutions in 4.0 s. What is the frequency ), k/v, nez7xcvl/emcof the wheel's rotation?

  A pulsar (a rotating neutron starmrj o2, sly2jo6t +1xl) emits pulses at a frequency of 0.40 kHz. The jrmoyo1+ls,6xl 2jt 2period of its rotation is

  A phonograph record rotates amg(gv3d6 0 +mzlogmk2t 45 rpm. Through what angle does it turn in 0.20 sz6mk +g0d3 lmg(2vg mo?

  A wheel of diameter 26 cm turns at 1509 / d.:oxdnrh:dknvz/0 rpm. How far will a point on the outer rim movohdd:n9 k// xn.:rvzde in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4p,v l/9m,jkf p2 k(*7pksbysb .0 s. What is the* k7 p2 9pb,sv/s,kjpyf(blk m average angular speed of the wheel?

  A bicycle wheel rotates uniformly th 6m +.;2bx3gw kbsraojrough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from t;wkb6b ox aj 2+.3rmgshe center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The ca;jf 5 3mqef*svble which moves the car i f3q5vs*fmj ;es 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 anaa-lq0 d)ttd + , ju--rxtxej2gular speed of 2.0 rad/s. What is the linear speed- e-t dqduj2)r taa0lj- tx+x, of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter isx kys73b,hc ;n 0.16 m in length. If the motor rotates at thenb;k3 ,cys7 hx 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;d n(bfj a ew ea3n;kjapq3dw:*9.2 af of 2.0 rad/s. What is the centripetal accelerajkq(p3febn.f;2a3 ; 9 wd*djae:aan wtion of a point on the wheel's rim?

  What is the centripetal acce c2pwj0uq5 8xqleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike isw jcq580uq px2 moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circulamzlc)g9*4epy r, rotating space station (r = *p)4lzy9 ecmg1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 l)- t510 gfxq9) cgldtxaibm( m with a speed of 20 m/s. The maximum centripetal force (ptaqt xxc 5l1)-)l0gm(bi fg 9drovided 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 cy fnp+)u ( kys+ldm-1y tf6j6fv u:kr;urve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (pry:6l fty+ kn6upd -u1y) j; v+(sfmfrkovided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachedi6xh0e27, 5 l4fgw7gjo tem2scuej *s 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 withstand is 250 N, then what maximum liwtsx67 l5eojg2ejmfigs72 ,*h cue 40near speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 .apjxzd) vptzi3 ih-e x 7r.f ,.utw+xop843 ckg and radius 9.0 cm rolls without slipping 10 m down c ri8zpj7d,px. ttp)uie .-zv 43 owh.+x3xaf a lane 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 accelerationj2z ;ocnkivf+kzq 42. 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 accel9 wru2 q 2zr*kq-b*loaeration 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 rotate after starting fa+g+k1t.klx9ws q m +drom rest and accelerating9l sgx mq+.1 kwda++kt at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angq:8ohvk8 q 12whr1jb aular 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 angular 30a-yhl :3h toz.xejwgf gq +1acceleratiooeg +x f w133qj0y-l:.tzhagh n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reachrx+ iz a(8dl p;khkn9ri;( o;hes an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular ;;kr ;xdiok z89nail( h(hpr+acceleration of the wheel?

  A wheel of diameter of 68.0 cm slof.jt/b7 z0f/l3t jtsbws down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to refft.7jzs/b 03lbt/ jtst?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/sv :uo,okn5 4js to rest over a distance of 115 m. W s5ovnku4:o, jhat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s y46 e6a/i3u* vhb7q );wtrvdgp )dwnlto rest over a e3gi)rw; 66lv qb t4vdyd a/u*)pw7hndistance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at acl 3fo57cxgfa22 i 7fd rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular7lcf2x7fo a i5gd3c f2 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 torqudd:av -3mg0 .hm 7kpiue of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requirvdm03m :.padgh ku -7ied when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 3bktkiil) -0 -odb.o2 o0 cm long wrench is used, what is the magnitude of the force requir-i-.bkkiooo 2 bd lt0)ed when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inero2h;ede9-mhe w+b58amw3.2 1 / lta hcxmteedtia $3.00 \; kgm^{2}$ 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 or js 5s5aiaiy,esn/* (rigin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the oa( s*,i5 rsy ejsna5/irigin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought th om)d n+kxu-f qz5ulop3;64jl e 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 wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What isp 6u4jndo 5fl)o-ux; kl3zq+m the angular acceleration of the cylinder?

  A solid cylinder of m*sculwn j:+yv1pak/ 5ass 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 force F1 = 5.0 N tos*yj5c+1wl :kpv a /nu 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 ina::pig-bo+ 9ne3g g gv h.t;ph 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 inertia of a rod about one ;. goihgeghbv :pgn+:93pt a- end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 c a6 8hjpu(t/o+obmkdpo vq014 )mj*ynm and mass 1.5 kg. Neglect the mass mh4/j*6om+tn1dp(80jo bo aukvp )yq 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionleszmoa)ox+s0t9nt*i4 1q 5 uyfzs disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of theamuqy z 19t x+)f*ont ziso054 pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk i(p,8fhp ,hg ppulley of mass 7.07 kg and radius 66.0 cm. What is the accelerationppiph , (gf,8h of the mass?

  A rotating flywheel can be usex:9lc ,.zysmn jv*5wr6+,cey ohd. tsd 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 inerow ga 9+ 6lz0am1c6kyetia 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 mh 3jj5 hqt c:i4mz(lsp ;9 f*koh:wby2 starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is tw j5f9syi:hh2k *b4c :h;o(3tqjzpmlhe speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.v.)5pc urd* dds j-+jq td;9qdp(*( pbviwqx-0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb(pw+d ;dpx 5)*-ji .jqdqdu-bv pd 9 *v(qrtcs before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rmop . * est2 fchsr5*ef1pslshh/) ro,)sd9a3est and allowed to roll down an inclined plane. How s3h l 1do *f. ,)arshsm chps*os/52)tpre9effast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a tl,;rgnyzb1 .zg4zk3jj*s0z35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a spherezzszngby4t; , *jkjg3z0rl.1 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 chl9g mhd3rc fj2;+;tbyanges 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 inertia 90fp *o bmvx i/3t(udgj86lgbof $5.0 \; kgm^{2}$ 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 5.0sp73ju.yic-oeyy8tkh 0n tr t(j 7+-o0 rad/s with arms extended has a moment of inertia ofj3y-su y pio8 7+k- j0c hoynte(tt7r.
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?