Angular displacement is usually express in uni0k e wlu e.sd2il) 3-ztdy5.(ofl ca7tts of

  Angular velocity is expr :vka/p.y/n voessed in units of

  Angular acceleration is expressed in un1j(okdbtdn g4/x g09xmli( idjx 105dits of

  A boy and a girl are riding on a merry-go-round which mz8ao+ro i p*9is turning at a constant rate. The boy is near the outer edge, an om89irao+*zp d the girl 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 constanqfeip2f; 4b b+t rate. Thef24+; efpqbbi 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 which is turning at a constant,b8fg ztcg-+kcp0r b . rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater lipt - kb+zgfc8gr0,c b.near speed?

  A boy and a girl are riding a merry-go-round which is turninsnr-kfa 0 *u/cg at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acnus0*rk/c-a f celeration?

  A boy and a girl are riding a mef ejjg+cy 0-m1rry-go-round which is turning at a constant rate. Th1-cefjmyj0 g+ e 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 ac+k ,a )xx1vp4wd,fm igcurate statement?)pi1x axm+kd4wf,vg,

  Rolling without slippiyrg q-)fjo,fe8 4a7arng depends on

  Two equal forces are applied to a door. The first force is applied ws8ax /18zu /hyv cml00xomr/at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to 8rc/a8l/1zhv0smm0yuwx o/ xthe door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The df 5lf08mqgp( first force is applied perpendicular t8mpflf d 5(qg0o the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applidiy+) myd5 oor */), rf,iubwned to a doorknob, perpendicular to the door. The first force i) d/5u bw+mirodriyn,*)y, f os twice as large as the 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 resi0 ;4rda 03 prbpji:milstance to changes in rotati :i03jprd;ib0lr4m apon?

  Consider two uniform solid spheres wherat 7n2nxa xt 1h,o;rzl4z+0gjc9s kw.e 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 of7a9n, ks1 zx;ojgw.hr+l 02 t4zt caxn inertia is

  Two uniform solid spherespxf4w8()eslxf + c3e+ iiaro* have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's+w4fosei)ciex+*pf lr ( 3ax8 moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheresk3ngyx 6wu8f.apf s;- where one has twice the mass and twice the diameter of the other. The ratio of tp;nky .fg w3 u-6fas8xhe larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R.sf)4 tl ebpd 2q,u(pro *2wy*bo,ek f0 If these are increased to 2M and 3R, what happens fpd o *4 bku0er pl2wy*,)2bq(s,eo ftto the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wiahsk k u -gi.qmv8qk58v:lmv:wg5 /e6ll

  The moment of inertia of a solid cylinder about its axis is given xxac5tui,*zv -5qh)b by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetx zt vbhxa,c5)5iq*u- ic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass o4;zqp.qa 7 es9jjv. xw d8ohr:f 10 kg and a radius of 30 cm. What is the ratio of the rotational ksjae4 h9:or8d xzjvwq.q .7p ;inetic 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 aa b)9gnjrlwt7d7; fsfz cq18:nd radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the saf8;wn7g 1jb z9 rdfq:ts)lc7phere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls witj bxr5q () lqbxjlboo)*84wli l qca,*h1:5 oshout slipping down an inclined plane starting fr)o l(sq:1o,aclb l jr4h*xw*5iqobjl 85q)xb om rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a systemti*m qx) o3(ty of particles changes when a net externalo(* t)ymxq it3 force acts on the system." This statement is

  In what circumstances can the angular velocity of system x;usnx8vya(/cy8 nvgp( z(- sof particles change without any change in the system's syzx(u 8 /py ;sxgn (8v(vnca-angular momentum?

  The Earth orbits the Sun in an elliptizhd))bzsz 4eq9jv uh72o9d gzat 57;c cal orbit. Ignore any friction which may be present. What happens over time to the Eastjzv5 h)qd)gdb4ez7a 729o hz;z u9 crth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves cle7q , pjj4ct-aose to the Sun, then which of the followipjq j ,-7cea4tng best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a 2 b w/sm9x9lwtfast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotat9/s2lmxw b 9wtion?

  An ice skater performs a pi hf ki(*xgbwk6at0dwn8e5+;,p hbn6srouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kw 5i; 0dt ,wabk8 x(snpf6khh *ne+6gbinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretch+z2+ p* lrdmg+rcuc 9sed arms close to his body. What u+c*p+ g+rml9sdr2zchappens to his moment of inertia about the axis of rotation?

State the law of conservation of angul8qr*sesr0z0 c og;cw 9ar momentum.

  What arc length does the Earth travel zkss-rok*m)19mvye)qq gnw 8khl ,2-in a three month period in its nearly circular orbit about the)nqk *1kk2gow8m9-zel,- ms yh s r)vq 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 does the n. t ;wyk/d1tgtip of the second hand sweep thr ktw.1ydtn/g ;ough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolu 2hds p0wcas2e5+3y qltions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is tgh(xfe/:a qx1he frequency of1( q/xga:f hex the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses q4xo g kke (p484+me jgxaa/d)at a frequency of 0.40 kHz. The period of its r4)x4epkxg/ aogj8q d4k (a +emotation is

  A phonograph record ow/h2b;xj4 1-gxczm n rotates at 45 rpm. Through what angle does it turn in 0.20 s; jn1go2wz/x4cx hmb -?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a9 / kdrekhjt6w,(+ fl-a3kdda point on the outer rim move i+/6 l 9k,arah (kwddf kj-dt3en 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 9kyf.w)t 5 -nbfx1c dfzw2bo)oepj8(What is the average angular spw zo.f 21x)t8p)9yw-k(e oj cn5ff bdbeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolu25 m6fv:4(izzpww xorao9 +w utions in 4.0 s. What is the linear speed of a point 0.10 m from the w mrz(+a uxpw:ofv49w6 2i 5ozcenter of the wheel?

  A cable car at a ski resort g-7p ovp2qu0hfs np 5z b0;+r.al5tylcarries skiers a distance of 6.8 km. The cable whic.-l0pnr2ghof y ;s7ula pvtzq550b p+h moves the car is 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 angular speed of 2.0 ra ,/ dtjhoc)-e.vnqq60ukats:m,za x*d/s. What is the vsdh-:xqzqm,*6aa/kjtt0)n u, eco. linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motor)zj ky 9ls.-u eo5vs-fzev+ q* rotates at the rate of 20 rv-)ofe*szuy klz. e5v+9j-sq ev/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 of 2.0 rad/s. k;eml .:rhpyj15rb/pj9wg k* What is the centripetal acceleration of a point on *p .ye5;ljr1 wjrm/kkh gbp :9the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of nvq9w uc-9.pca bicycle whe9q9cw c. nuvp-el of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rot* gl)lhx ) , lwirs0yziiye.5-ating space station (r = 10000w .g5*iir,li) z e-llsh )yxy m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speedv a0mehwc coi3i, , p*6j,0tct of 20 m/s. The maximum centripetal forcj0p3, com i 6ihc,*aewct0t v,e (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 circular curve of radius 5if cv,3sa2 eh .a(:o ey4fv,ad0 m with a speed of 20 m/s. The maximum centripetal force (providedvac e .io2f,daf:,h43vesya( 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-ho i q46eb6jm bwsi./(m string, is whirled around in a smooth level table. If the maximum tension that the string can b6 j h( wimos/beq.6i4withstand 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 cm rolls without slipping 10 m downie -1vmfszix 5jge.s85lc,9x a sj,9ml x8ev if -g.zci1e5 x5slane 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 acciok4kne+ c; t)eleration 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;xfet w mm2l)b6w:qq 0vx(3y79sl kiv a constant 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 qn9c*q 9u2mki a 0.300-m radius automobile tire rotate after starting from rest and accelerating at a consq 2k*uqm ic99ntant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an adu3yzxk.)a7 b ngular 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 wit bm65 fu6j;auc )mnbi5h a constant angular acceleratj bcium65u 6bf5m; a)nion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and rerrv8p 8yhu 07k2 e gji.my6b9aaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What ijmeg u8 v927p.y6r hk0 y8biras the average angular acceleration of the wheel?

  A wheel of diameter /j3hba* 6gupt of 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of rj *3tgb/6uhpa evolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over *yg/aacg:l :eb5r4( xj t0uc ga distance ofgaj t5b(4x* g gecu:0ya/l c:r 115 m. What is the angular acceleration?

  A wheel of diameter of usnao . s *v7xh7kbt,vlyh84468.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does h74ahs4 k,osvtxubv*y.8ln 7it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of froarnv -b2313600 rev/min. When swfrvr- 2 bn3ao1itched off, it rotates 50.0 times at a constant 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 require tighte4z -(s w masvr+pswp)1ning to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of ths+spz14vw - w)p (rsame force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require m3gvof(rr-iy+v 7mx-a /+-a3e cd:gpfvy0bf tightening to a torque of 90 Nm. If a 30 cm long wrench is7yr e+oa:/c+0 (m f 3vrfvgypiv-ax-g3 -mbdf used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerk2 qdn-j+ mts: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 mo cik nl;v(4e1xdeled as follows: 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 th 1e;x(i4lcnkve origin?

  A solid cylinder of mass 10 kg is pivoted about a frictio5i+ ly ord q00h(hw/sunless axis thought the ce( isu +roy5hlh wq0d0/nter 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 is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the . ykwtn5:di b9center 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 nydit:5kbw9 . 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. p o7x vv0*mj,gThe rod is initially held in the horizontal position, and then released as the free end is allowed to fj,mv7xp*og0v all. 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 (n 88l/kaxyei cm and mass 1.5 kg. Neglect the mass of the axle ank/y a nxl8ei8(d 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 frictionless disk pur a9pwgnsz*4q 9u7u:klley of mass 7.07 kg and radius 66.0 cm. What is the angular acceles9z unpg:ru*aq9w4k 7ration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of 67hnsjwsv rz1o3tt bl7f*/z:mass 7.07 kg and radius 66.0 cm. What is the 1b7th3lt:n z7* f/6vzsrojws acceleration of the mass?

  A rotating flywheel can be used to storgfp-pbvnlb w (9c,z1- e 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 **jurg ee 6lz1$5.00 \; kgm^{2}$ 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 m:,de2-nli7(d-u vxtzw -e ;wxrf;c b 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 bottom of the inclined plane?2e:;lxm,d-b;t -c(dx-fvwi7zr n e uw

  A solid sphere of mass 1.0 kg and radius 0.010 m rollsq:631y.udo zyiku s i5 with a speed of 10 m/s. How high up an inclined plane can it cl: syoz. q6uyi5k31udi imb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed)4 rggv cil hg)070xh;(ld kbp to roll down an inclined plane. How fast is it moving aftedv)cibp04 hl()k xglgg07;rhr 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 356 8/0pxlb4gx.d 1+erbeq lbo re incline that is 7.0 m long. Assume it started from rest. Txder0/r8lpb64bbx1 +.gqe lo he 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 mom1zx0 j1hyvrs*entum 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 m4*xhh*hf0-7 j t igeywati1vv+ /w6aiv nog/.oment 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 5.00 rad/s with arms extex xhko.mvpkik;r2ub i 4wl+ 266+-diynded has a moment of inertia of yhl-p;2k.6iikmo+2 bx vu4w+6xi drk
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?