Angular displacement is usually express in units o6k)40wwrl uz m 0ymq1bf

  Angular velocity is expressed i:x-n;(k upiy in units of

  Angular acceleration is exlt zmz6rnlep2:l2+s. pressed in units of

  A boy and a girl are riding on a merry-go-round which is turj2 j;pdn9:slm7zdo k96 6qccbning at a constant rate. The boy is near the outer edge, and the gn9q2cp:b6zojjlc sm6d ; d9 7kirl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a con+o5-o euthf0wstant rate. The boy is near the outer edge, and the girl is c eof0w+- to5huloser to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-roun6 (mald;a ekjmko4)o dlg34x4d which is turning at a constant rate. The boy is near the outer e4;x loemk ga6j )4ka3l d(dm4odge, 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 whp296zw rki ya1ich is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the cena96wrp1kz 2 yiter. Who has the greater centripetal acceleration?

  A boy and a girl are ra ipqs-yn p6d :v:..1uje woy(iding a merry-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 greater y eqn:iwsd.ou-1:( p pa6y jv.tangential acceleration?

  Consider a rigid body that is rotaxoh;9.8 sgn 6a+(2(so g spu-yi yksd4)xxyls ting. Which of the following is an accurate statement?nd xp84ssg-i+ 6yo o ; x (ys.(sghyl)uk9sax2

  Rolling without slipping depxq+w) ; ib;bwmends on

  Two equal forces are applied to a door. The first force is ap2nxmct;kl y** 2 cs-ul0oc7zy plied at the midpoint of the door; xlyltc7kosy22c0 ;unm -zc** the 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. Theqtb y:uc1rfu 00 j- 6fqn-cv*o first force is applied perpendicular to the door; the second force is applied at 30e to the plane v cn-y rqc0u0f-u1tf6q*:objof the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The fzq+ ez bmj0)jug:ag3 k 3kd:x2irst force is twice as large as tu0q ggbez zd::k2x amj 33j+)khe second force. The 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 jo:j/cvi a hqk*: x.n+to changes in rotation? : i njx*ck+j/.avhqo:

  Consider two uniformw1vt clw,up 1.wuq35i solid spheres where both have the same diameter, but one has twice the mass of the other.u,tw1 uw 3l1wp5q.ci v The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radiu+p1f nb bm+z km.cs0:ut;pw-r s of the other. The ratio of th0m+;f+-wnrs1up. kz c :pb mbte larger 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 the d:riu0 :n;sbx 5pyr3thl 3 p(lliameter of the other. The rat (:nb0ysprlpr;ul3lih5t : 3xio 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. b05kdtrywe 8k2,b;tr If these are increased to 2M and 3R, what hapbkwt;y2bdk e85r,0 r tpens to the sphere's moment of inertia about a central axis?

  If a constant net torq7yfp9 j9u kg;; mlyq+r6; tnrque is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5z:qn my2 :n8dk MR2. If this cylinder rolls without slipping, the ratio of its rotational k8n:2k:znqy md inetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whic( kpc8be+: g s9op)6hxvl7imkh 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? Assume the wheels are unifohe9cbsp+x 8 l k6k)7(iovm: pgrm disks.

  Suppose a solid sphere of mass M and radius R rolls without s94ls1y fc dfenb l0s.;lipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incll4yceln1f 0d9f.;b ssine depends on

  Suppose a solid sphere of mass M and r)bxs2b b3hazmt +o 30kadius R rolls without slipping down an inclined plane starting from rest. The angulaasb3 bzmkt2o0x ) +3bhr velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a neru ps 5oh)*;pit external force acts on the system." This statemeuohp);s5rp* i nt is

  In what circumstances can the angularjisw)+t n2 jz* velocity of system of particles change without any change in the system's angular mo +zs*)iwjn 2jtmentum?

  The Earth orbits the Sun in an elliptical or2n hkd6 0lhz2fbit. Ignore any friction which may be present. What happens over time to 20hlkzh6df 2nthe Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Eartw5; adlp7;.*9eozoxekyd.l kh moves close to the Sun, then which of the following best describes the orbiting speed of ew9ly* ;.kdeo 7l.k5op xdza ;the Earth about the Sun?

  An ice skater performs a pirouette (a fast sp)v0xy k m jz8w9a7h5 )ovbtiw8in) by pulling in his outstretched arms close to his bodymka jx5ztv8)wwv8o97 i0 )b hy. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his o2v5+x:7 warp+tzojhyy *j n, futstretched arms close to his body.+, :x+rypf 7w* zvy2t5nj jaoh What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirplr4.fcpu ouj j70y6elu83y 6f3t lt;ouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to hi6tl.6uo0t yp3lc 8;7 ujjufp fy4rl3es moment of inertia about the axis of rotation?

State the law of conservation of angular momentul5l 4dv+ f 1cwr,x-llym.

  What arc length does the Earthwl7 w4lv1 )brc travel in a three month period in its nearly circurc)lb 7lww14vlar 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. What distance yos3par8x(z, f/ n,qc does the tip of the secondofx,s /8pcny,(rz3aq hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minuti 3q .ol2vhivxp6(ixi7 )ifjl .rmg3 g+ v;5tue equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revoluti/rl a41ud hew1c s9.taons in 4.0 s. What is the frequency of the wheel's rotatios1/clar.d9 a w tehu41n?

  A pulsar (a rotating neutron star) emits p1tuzyvi089 plulses at a frequency of 0.40 kHz. The period of its rotati9 8yvtu0pi z1lon is

  A phonograph record rotateje3 r4tw ox))gs at 45 rpm. Through what angle does it turn in 0.20 jtw) geo)3r4xs?

  A wheel of diameter 20zvufl-sl 4(h3o xjx -6 cm turns at 1500 rpm. How far will a point on the outer riuxl0z 3(f4sxj vh-- lom move in 2.1 s?

  A bicycle wheel rotates uniformly tz1n fc 7dm p,kl)**dwnmas)v ,hrough 2.0 revolutions in 4.0 s. What is the a dm 1sv,,d*)wc kmnap7*zln)f verage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revou3:;jqgnx,, d377 m ovdyz )s tsmw-walutions in 4.0 s. What is the linear speed of a point 0.10dtawqunxgw mz-v ,d7y : oj)ssm33,;7 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. -1ftm, 8ibwta The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley 8-1fbm wta,itrotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatingod;wq3q 95/*u zi z 4zpbuo4gm with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's rim35wmu/z4d i4qzobqo9 ;*uz g p?

  The cutting cord on a gas-powered wee4rel p+3b7sqf bawu:5 d cutter is 0.16 m in length. If the motor rotates at the rate of 20 5qs 4 pelf+b:buwa37r 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 cv0hnbwgyn/2 j,4dy) angular speed of 2.0 rad/s. What is the centripetal acdngj ), cb0vyw2n/ h4yceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on th q i3i xjl,vk.uhak qt)s250-ue perimeter of a bicycle wheel of diamlkuj-svxq a. 5t3 h,i0u 2)iqketer 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circfl5,(q z9 ylzia al3w*w4w9zp ular, rotating space station (r = 1000 m) rotate to produce anwaq5 lz3yfaw,pw9 (z4 il*9 lz artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve2 runrs4 :mr0c of radius 50 m with a speed of 20 m/s. The maximum centripetal force (prors u:m4 cnr20rvided 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 curve of 2d /n /-0rx uqauws (ldu:fx7lradius 50 m with a speed of 20 m/s.xfw/saux07/: r-u( q2ddnll u The maximum centripetal force (provided 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 of a 0.750-m string, is whirlh4e 0in30erdred around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear spe3e 0 4irrnh0deed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 ko am xn-*l5*71he yfotg and radius 9.0 cm rolls without slipping 10 m down a la*ay7oeh* 1 m-ftonlx5ne 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 ay2bh jdwb3c: ut/o 4trt4 q4w9 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 constant angu;.: jsaq iqvg+lar 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 rotate after starting y9hmy/ki)i/n from rest and accelerating at a constanim/ hniy)9/y kt angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accuarl-c.d;/g w eleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceler 5l,-qdfxn kkadcq8-4ates with a constant angular acceleratkl-ncd-qqd5 xakf84 ,ion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from re8xcrp wk*-0a)j3x0 gm- mla0b cf6v qdst and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration cgv*- 6ca0ldkj xbpmmq30fw 0)-8xa r of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tq*fzlg d jgsgar/w3iqmvg4: 6zf + ,7)o rest over a distance of 115 m. What is the total number of revolutions the wheel rotates gf/l *76q3djm g g:gz,z) aqifwv+sr4in coming to rest?

  A wheel of diameter odya ht68vhx4*f 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. *xyad864 thhv What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fm *.ts,m *m 3ku3osx-mog+ntkrom 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to tmkgmo * *n+s 3 xmo3sk.,utm-the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600w)/avwfx,xw/6:i sfx nvcb2 6 rev/min. When switched off, it rotates 50.0 times at a constant bxx:ca)wf iv2, nx6f/v 6 w/wsangular 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 vqht48t r q)j.pm7vp9 90 Nm. If a 30 cm lon7t 9. jh)q8mvqrp tvp4g wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel r.i f o3lxdz9,;9fj9 oiihuby98ago 7cequire 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 ;xu d3oh9l f , 9f7i9.oiojb z8agyic9applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerlgp4y. kc70c3hz qqi )tia $3.00 \; kgm^{2}$ 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 h)96klwb7r yq;mjpvw ,92xpem is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is 9w xlqj 7pywp eb,k2 v9hm6;r)the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thk 0 r9c4dfcpf9ought 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 radk9f0 pc4 9cfdrius 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 thought the l xc :uyh(7.uo/qta/e7xlm k *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. How many radians does the cylinder rotate through in the first 5.0 sxqcl/m*ku(7 /a uly ot .eh:x7econds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initiallvjj1k)zi kq:9qu9 wc8m 1*t jmy held in the horizontal position, and then released as thq9jcqwjvij8mm1t ku9z *1: ) ke 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 09x o7nwvb ;4r hjq8jspxq*z:cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is apr8z* 4:vjsxxnbqo07; qj9 whpplied 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 frictionless disk pulley of masse thspwaupwp*yg;w-z)x/,g g p:3 -7 a 7.07 kg and radius 66.0 cm.-y -7w3g/* x:a,atge;gw sp pzpwuh )p What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped arocl/gwkpo r62rrs g 3dbonn 69j8/)lz 8und a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratpw 9g 62gn)r88bj d3o/6/ollznksrr cion of the mass?

  A rotating flywheel can be used to sto k)lb *svv8n*rre 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 inerwhsgqbsd9w /v p5t8-j-,*m zitia 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 rmt x9b:g3pfas5ay0u /o ;*feradius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the boa:sg;pb5f* ef mu/ 3xa0yor9t ttom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m9f:i 0qx(th v+ez + krayk:w)t rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to rest?a+ivt rqhw 9ty0z:f+e ):xkk(

  A hoop of radius 0.50 m and a mass yv. 77t4qehs5 jvzzk0hp1 ,ebei5 f3oof 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is 413,if.5pq7e ezy h5zsko7vje0ht vb it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 t lc25eo.qgd22xt7 er kg and radius 15 cm rolls without slipping down a 35e incli2tl qr52c.dgee 7ox t2ne that is 7.0 m long. Assume it started from rest. The moment 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 m-vv 3vkbl nay13(1xoeomentum 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 moment of inerti4o6f5uye4 mfnkan1t of 93 /exa 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, b+slwydy;b+vb6 g,ql2mr ,w 28sndi a moment of inertians6y+, w,2+w rbg,bq sy8d;bllvdi2 m 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?