Angular displacement is usually expre)agz4+,3zfls wz,zj 2n2 si lms 9f:lwss in units of

  Angular velocity is expressed in unitscwrgxx/: mz)o 4i.v/r of

  Angular acceleration is ix na;ptl693pjt;4 krexpressed in units of

  A boy and a girl are riding on a merry-go4duy)8hwiks+z+my w0 -round which is turning at a constant rate. The boy+wu0+d4 szw ym) 8kyih 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 a merry-go 6j.chk ojle,rl5ryp1)c1-p y -round which is turning at a constant rate. The boy is near the outer edge, and the girl is closerl-k hp)5jerop1 6 cljyryc. 1, to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turniwr2/v, td 7s(6vajbp dng at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the 6bra( t7d/wv, v sdj2pgreater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at q cb/o gf*-og7ogk p03a 1bj,ia constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has th ,oigcpgg*q/fboa30 7jb o-k1e greater centripetal acceleration?

  A boy and a girl are risb 1tq9o6*1r x mo5cnm08nod vding a merry-go-round which is turning at a constant ratetovsn c b o*n58d19m6r1 qoxm0. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate(d kakz7rq) phnrsc o;q3/6k7 stateme7rk (3/kq h7cp)a6qkosd rz; nnt?

  Rolling without slipping dependsef :j1fao ywseru) ,7: on

  Two equal forces are applied to a door.-z6( slidsb fdd4jd2 4 npr8)u The first force is applied at the midpoint of the door; the seco bujris4dn8s4l-zp dfd62)d(nd 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 zoyk) k3jn0g;nhnjy0o+o9 w 2 doorknob. The first force is applied perpendicular to the door; the second force i+29kj o0w)yo0; knyonz j n3hgs applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to thof.,nlcfm)m:;. y ycbz (4dcxe door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of 4,; (lfcfy:b) .ycmcdm.z xnothe second is

  What is the quantity used to measure an object's resistadwo9br -)wx kdys057fnce to changes in rotation?0yb-fdw 7 dkrw)5o xs9

  Consider two uniform solid spherel a3,lkdzvgbx bk 3110z t:6mhs where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment o 1g1hzdbkxl63a3kt l0,bmv: z f inertia is

  Two uniform solid spheres have the same mass, but one has twice thebo q scc229t4y radius of the other. The ratio 4y9 c2 tsbqo2cof the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one .,7. r 7m*hfqol bjeszhas twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller mom7hf7., bzqorlemj * .sent of inertia is

  A uniform solid sphere has mass M and rad,h* r w9l3fr 0lww/p*y-. kvd8gvh rbwius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia abou0ld9l- ph 8hbv*rwrrwv. ww/3k*f,gyt a central axis?

  If a constant net torqueh:y ajd8 7 kj;fl/dzg7 is applied to an object, that object will

  The moment of inertia of a solid cylinda(:7rnsdr .x0ct l)y ler about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotationan :drtrlx s7.y (c0)lal 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 ala,cz u3 xqehe08i07knd a radius of 30 cm. What is the ratio of the rotational 3zlieq aekh7 0x0cu,8kinetic 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 wit 0wk m:ift2x8ihout slipping down an inclined plane starting from k8i i wm20ft:xrest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphe j*ra+sne5 gk/re of mass M and radius R rolls without slipping down an inclined plane starting from ress*/rg+nk5aej t. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a synwwu x/ jq8.p.stem of particles changes when a net external fo8ww/n q .pjux.rce acts on the system." This statement is

  In what circumstances can the angular velocity of sh)g ;9v2m(j) sbjar:w/at i-w(jkole he, h9fystem of particles change without any change in the,9e( -;2o gajw/h h:k)itb)mjjflawhs (e9r v system's angular momentum?

  The Earth orbits the Sun in an elwjv6.w gq.1 ml7n jovdkgx76lf 2/tc8 liptical orbit. Ignore any friction which may be present. Wvl w1o 6gqxf26kjlwd77.m 8tnc ./jgvhat happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun i ; op)nhd9kgj*n an elliptical orbit. As the Earth moves close to the Sun, then whicjn)*pd h9kgo ;h of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs d4dqt(f +lc2bsb36ynm .ejx/ a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the n +bdcx6seybmfqjd(t2l4./3 axis of rotation?

  An ice skater performs a pirouette (a fast s badb1c +5d hv i78sgitj061ffpin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis f5i g1 1ftis0c8ha7b d+b j6dvof rotation?

  An ice skater performs a pirouette (a fast spin) by pulling gj-o4m 3bpix7in his outstretched arms close to his body. What happens to his moment of inertia ag4o3 mxjib 7-pbout the axis of rotation?

State the law of conservation of ai gl6vgo5m fbmw:n4x1 / hd6h8ngular momentum.

  What arc length does the Eart3t7 x :.sqlo;u/gr g y 8t(mihpf rl)e64epn(sh travel in a three month period in its nearly circ s:lq7x y (nt6l)u4mer83 g fhp/pit.og;(resular orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a cloc)gs; k3 :;nld9ft le9vc2apark has a length of 0.30 m. What distance does the tip of the second2d c ;;3nr9 a9t p:)afvgsklle hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute7: *plj 3*emfg noymv7 equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s .6hldqdk2:bp,hm ,g g. What is the frequency of the wheel's g6,khh dgq, 2 pd:.lmbrotation?

  A pulsar (a rotating neutron star) emits pulses at a fqobk j(*/ d(+l vughb; bd7:fvrequency of 0.40 kHz. The period okb(ohv gqj ;7uf dvbb:/+l(d*f its rotation is

  A phonograph record rotates at 45 rpmn scpz(dys 7yi3h*+ t-. Through what angle does it turn in 0.20 s?zp ycti(hd ns*y3 +-7s

  A wheel of diameter 26 cm turns at 1ax3kgd i: ty5a2iv 79g500 rpm. How far will a point on the outer rim move in 2.ig7:ygkv id2 a5t3 x9a1 s?

  A bicycle wheel rotates uniformlyu+ai+f-cov*i )/x pvj through 2.0 revolutions in 4.0 s. What is the average angular speed of t-ou xvp ai+fvc+/ij)* he wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in2, nmh*lw hi53ifw v)h 4.0 s. What is the lin5lw ivhw)f* hh2mn ,3iear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Thdwc8su c:akl wryqh*385 ng (.e cable which moves the car is driven by a pull q.: ncyg5lakcwsd(8 u8h*rw3ey 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 q aki1hg xl ep1r qfi3i78t,xoxs 7w1804 h6zqwith a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wti 1xr ka qx3 ,0iqq4ohs8fwxi 6 epl7hg8711zheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the:ny inu+5ifp i -l3sk*1ad:j5pz 2dgi motor rotates at the rate of 20 rev/s, what is the approximate linear speed of thii5i+:fn- 2pz:i13pda u ndg5k* sjlye end of the cord?

  A wheel of radius 1.0 m is rotating with a constantofo6d;n. vm yfiii115 angular speed of 2.0 rad/s. What isf1 oom16.fn ;iidv5yi the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimes a1dcrqoe 1m: )bpvo40 e01whter of a bicycle wheel of diamet sw0e:md 10pe11 b4vrahoq)coer 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) mo-w ,;m;gezfch mxk woc8.k71ust a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity. kwh gw8mxo;zc,k7c;1mef -o of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wit8ito7e j4z6 p:m1hu azh a speed of 20 m/s. izmaj oht:1z 86up4 7eThe maximum centripetal 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 flat circuv)l sg tn2yqt gqo)))0lar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided t) v2 qgtq)o)lng0y)sby static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachedz. 3z3)u.ink6 bq oysb 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 linear speed can the masb3.3z u6yobisqk)n. z s have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls wie4b 8)p2 + j5cksxdhkk hd6m:othout slipping 10 m down a lane atbk x8mkc2d4)h sk hj+doep:65 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 wita 4 m7umyo:*tqh 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 constacrxjw3tb gdjf;m15538bk pd9 nt 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-mka 5h2lfl b88s:c ejkix2yp-( radius automobile tire rotate after starting from rest and accelerating at a constant angilyl a2bfp e-58c:j 2s(8kkxhular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acqvy4ly33uzpn6h2 (r9 .bp eukceleration 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 *ce( v0d 8yt:lg7xw7cnh2 aztconstant angular acceleration owtnh x7(*ez 8: y7cl2ac0gdtvf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while tgr6 fval+7i u+q1p e+qurning through 2.0 revolutions. What is t qpvq++17er +6augif lhe average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to res p+;-hg lgt1pct over a distance of 115 m. What is the total number of revolutions the wh+t; hp1pcggl-eel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unif3ir4oohfpig9 j 5f0r /psud:1ormly from 8.40 m/s to rest over a distance of 115 m. What is the angulhuo4 or d0jp3fi91g:sir 5/fpar acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40q ld..-3jgjg k m/s to rest over a distance of 115 m. How long does it take for the wheeg dkqjg3.l.-j l to come to the stop?

  A centrifuge in a medical laboratory rotates at a95oj+nvht ( q 2, j9nskn4yqouxx+3ls rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleratl4s3yhou+ qsj 2o x,n9qjxn (5k nt9v+ion 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 z9 f2 ng), a8lrh d(;3zhscddnlong wrench is used, what is the magnitude a2zg3ns;dzc h ,h(l8dd) 9nfrof the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel rkk:trppj(w ;. equire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, ( k w.ptr:kjp;what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia 8 ymps 3ta.5xi6vm(dd$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows:l tud4j/ qq.(2)vb zsf mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the ori(f ubv2sz)j4d /ltqq .gin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thbq x5od1fh)dsbgu / 75qnn4(hought 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 wrapped around another section of bnd 5ob1g74nhq uxh s d/(q5f)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 frictionle q3 wijskw638css axis thought the center O. A rope wr33s kj86w qwicapped 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. 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 hingedav,mws eu)t: ;ya6)ro4a9p hl at one end. The rod is initially held in the horizontal position, and then r6ay)rhslpaw a e ;:4,)tuo9m veleased 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 raursum*3hkg. woy,2 1n dius 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 sk.r u*ohg, mwy31u2n wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wr8b.y x/orh-j/-gjvt mapped around a frictionless disk pulley of mass 7.07 kg axot-jj8b-/ .h/ gm vrynd 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 di u*n6 -jfcjc+3yllxieg* e b)(sk pulley of mass 7.07 kg and radius 66.0 j ecbf x6j(gl cni*-*ey)u+3lcm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requires6 xnwa) ms2o7c4rch)d 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 offn plr l1l)f2, inertia 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 from rest and- fdwn; c re.+d (3ilr2xbxut( rolls without slipping down a 1.0-m high inclined plane. What is the 2xfx;e3(uclb nr. (drt d-w i+speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radh u+(kmvuh+ kxt -5tk;ius 0.010 m rolls with a speed of 10 m/s. How h + uuxthv-k;5h kkt(m+igh up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kgzfwq)jl j9/r .b1w j iv8aje74 is released from rest and allowed to roll down an inclined plane. How fast is it mov8 jwjw.rfji9/4)zvel j b7q a1ing 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 x ovzllc;o0yg8a+)l6 a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of ;oao yzg0v6llx+)cl8a 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 changes b9p8 (mqr4pr5 cp zze)yy $20 \; kgm^{2}/s$ 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 of gy+(t3a+ b wcicz+w/a$5.0 \; kgm^{2}$ 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 wl, q09y 6tdshrith arms extended has a moment of inertia ofry ,609qhtlds
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?