Angular displacement is usually exwg jts,h0cc6q-v 3cz)press in units of

  Angular velocity is expressef :qtot-g. mo9d in units of

  Angular acceleration is express2t/wut9z .dk f, q*m p,io1gfted in units of

  A boy and a girl are rt a7pao+w yq*.iding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Whooa qa.+ytp *w7 has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a con ibg13f:/0mj-7;hwnnl) je iqi tx5zvstant rateehf-) w7i 1gji:j zmi5nlt v0n; 3/xqb. 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 ridacqcxqb) 9 d2b4q2 zg6.w gzl*ing on a merry-go-round which is turning at a constant rate. The boy is near the oudcga)q2wq69c. lx42z*bgzbqter edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry he4m9hht 3l.(zpb9v*sxt1gm-go-round which is turning at a constant rate. The boy is near thesm.(h9g 3t1blh mtzp4he9xv * 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 z; 9f sesd9r ya7* w.hc.g,vfoconstant rate. The boy is near the outer edge, while the girl is closer to thgd;fa,9sz9 c w*fvoe .7hr .yse center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate fjkez m(x(3+g state mj((x fz+gke3ment?

  Rolling without slipping;+gjxoe29sen z6(ipo 0g wt5n depends on

  Two equal forces are applied to a door. Th-gxd(: emyq;x658/ynnarha l e first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces m:n6xay 8r -(gl5ed an/yqxh;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 c m:8e/-nwyj1jp t8 dgforce is applied perpendicular to the door; the se1ej- pmg8t cy8 :nwjd/cond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to th2 wk9, bhn3:x eisgzrkf.x 5v)e door. The first force is twice as large as the second fx:kfw3. )9sv 5zhxrg,eki2n borce. 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 ryd6nu ,ui1v rm; *uz),lo*nhmesistance to changes in rotation?yu*zr 6hd)nu;n vi, , mumol*1

  Consider two uniform solid sgz8h:dn q2i6 vpheres where both have the same diameter, but one has twice the mass of the:6n q8dg2v zih other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spzrou bir( la7 jz 62x,gi7p;0gheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inr7 0g zu,g;jaiplbr7xi (zo62ertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the dk4px70 *y/b w*snxm1pujm +lapuq+- diameter of the other. The ratio of the larger moment of inertia to that of the smaller momentdw0-bnxm *kxs ju/q7m p*+pylp 4a +1u of inertia is

  A uniform solid sphere has mass M and radius R. If tlk69 r ,iayoo z;bz0g5hese are increased to 2M and 3R, what happens to the sphere6g9 lok;by5a,0rozzi 's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object willlfy6w .o ;x0bi ib2lwhf29oe(

  The moment of inertia of a solid cylinder about its axis is given byuulm-y *6 kv4kdj f1t5 $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel ofbmt( hz)/) skaj6ytr6(gtx-e 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? Assume th skt)m( -) yatxb6g6jet/rz(he wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rollso z-rx2ajt3kh14 3(hajvpz j- without slipping down an inclined plane startinjra - h43z3txvp-hkjo j(a21z g from rest. 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 inh62nv :bwrhl, clh nvbhw6 ,r2:lined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentuc/a katmft 68o3c7z *e7l ncb3r7g 3iam of a system of particles changes when a net externala33 cg8mt 7c7t6azk7*lnrfb /3ieoa c force acts on the system." This statement is

  In what circumstances can the angular velocity of syst94 pg0dc osl2jupe l50em of particles change without any change in the system's oj d4l0pe0lu9gps c25 angular momentum?

  The Earth orbits the Sun in an elliptical o0p- glfj851jf9faquw ;ju ur+ rbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about t; ff9ljjr fjuwg u-q8a0p51u +he Sun?

  The Earth moves about thdecd( nyv2-/ zcjapt(k3 *6h)di6f p be Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes eyzhcn6d(b3dv)/fadpp tk 2*ic-6j( the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched 6qd uja kvh7:jno65zt6v3d.r arms c z6:jndo j.6ru thad53vvqk76 lose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater perfor77 opbow x1p y6b:* yksjo04h ydmlx2)wya5*jms a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic jy5oy0b hxykpwa*7)j72 *4pdm lo:wy1bx s 6oenergy about the axis of rotation?

  An ice skater performs a pirouette (a fas/ ybwzycf440 bt spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia abbyfz 4yc/40wbout the axis of rotation?

State the law of conservation of angular moh kt93k 9,pkrymentum.

  What arc length does the Earth travel in a three mo6ml6n+3u *nx hq f(gjgnth period in its nearly circular orbit about the Sun whnqf*gx6u 3l 6gj mn(+ith a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance doe+271 ia*.epyqvhl iz olr,1 lj 4nnf4es the tip of tef r .14+ *,z2hliilaj7nv y1pnq e4olhe second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute eq qngl ;hc33 v6i *hzqryc5f6*huivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions( :y*dbd d/fv-jb7k 7f4pf eup in 4.0 s. What is the frequency of the wheel's rotation? 7 d/*p(b dv4fj efy-ud7kf:bp

  A pulsar (a rotating neuysukh(g+j54gh2 (c+ava dm n4 tron star) emits pulses at a frequency of 0.40 kHz. The hu( ckajg+254(a+yhdsmgvn4 period of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it tu ljfp q:0wdb/ 2bejq)4rn in 0.20 dejq) q b/24b0fjwl:ps?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a pb6(m )3rx9 n 7x,ld,lxy4dye. d)axkam5wh tr oint on the outer rim move in 2 axd h)yl 4dyn(abmxewt) xx9,3k6lr7 5.,drm.1 s?

  A bicycle wheel rotate ik.zglj we;( zs,se.2,fsop* s uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of pl,s ,(gzfsj.w.k;e ois2z*e the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in a s* pjl*o7)nesj u:x+4.0 s. What is the linear speed of a point 0.10 m from the centespl7o*ju) x* n:eja+sr of the wheel?

  A cable car at a ski resort carries skiers a distance of 6 k9 hxn yb. d9:6a4o.2lfpvknm.8 km. The cable which moves the car is driven by a pulley with diameter 4b.d:m9 9fy.knnpl6ka oxv h23.0 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 angdz1-*l- ix:wjn z6kzjular speed of 2.0 rad/s. What is the linear speed 1 z j-*d:jkz6iwx-lnz of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. Ip,ypn:8lrmb xr 7o,.jf the motor rotates at the rate of 20,r ,rb7j:x8o ymlppn. rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating xv-n0u.a9:g; v: ezy0phvndewith a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's rivvd0ghy-:an.0 pnv ;x uez9: em?

  What is the centripetal accelka4 2uo1wsneoa :5.x peration of a point on the perimeter of a bicycle wheel of diamete ow2e5aau.1:4 pxok snr 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions pekl4v- + u9fgdfl ,fb6dv+ 3prus+y5 por minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to p5udu ,34+p +gybflp dl +6for s9-vvkfroduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m+g(v;nf w+x2a j9xjjyrihj *+/s. Thex (;gfivjaj ++n y+*r92 hxjjw 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 circular curve of radius 50 m with a spb0e, gzm i2kvyxwbiy1:,v2 j:eed of 20 m/s. The maxiyvvj:z 0ibe gw:xk,2 ybm2 1i,mum 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 ncgmjg2 rs7emeaj6lu,8e313: xr y:tto 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 y el36:sg,j:832 m 1amgexr7jcetrn uthe mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and rado z wicxt:bp*3 5c.;-wgvw/ teius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s./w*b-tw xctc.o;g5e wpv i3z:
(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 acceldgb (a6 +edwy)eration 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 accelerationum* 6, gm9etn: f/edbn 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 t 2c)k 0qp2f;v2re-id+c twmw pire rotate after starting from rest and accelerating at a constant angum) t;-+c0ep qr22 ipdwwckvf2lar acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratio2e-f.x h)syr linep6gq-hmq)/4o ejsb3 m,j)n of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with8;ur*gsm4;bm(yp go y a constant angular acceleration of g;(ob r; mgpmy4*ys8u$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speedma;vv1 a ezl6p(p-waph(yk)7zx 87p z of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration pk7a)1( 6pl8yvpz ;phazv(x-zw7mea of the wheel?

  A wheel of diameter of 68y0wd bje5ze4p gal132onz)hd v:hl5 9.0 cm slows down uniformly from 8.40 m/s to rest over a d4j90ndvldwhzo15 b lg:3ya)52ehp ez istance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly frho2zz9uf9l (qom 8.40 m/s to rest over a distance of 115 m. Whaq (9zl u2zf9hot is the angular acceleration?

  A wheel of diameter of 68.0 cm sr( jfwi)s-zi sr 3:+ nfr/wi/olows down uniformly from 8.40 m/s to rest over a distanceio( fwrinr s3-/rsf+:z) i/jw of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational da3r1 tqt007a6 fp:xxxhg o.obd 0 gt)speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acoat16h7.)xo d g0 dqxrx0pgf:t bt3a0celeration 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 requipt .n zw4cwp)5re 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 is perpendicular to the wren4)pz5t pww.c nch?

  The bolts on a car wheel require tightening to a torque ofca**ul(e;yg d yff5k+ 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forclyka*gu(;+y c ef5f*de applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in 3mae;*w,hfq4t ;vz6(r5q ot 7vjqb7m zmgd4kertia $3.00 \; kgm^{2}$ 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, mass 2m dh zacp( 4uajtu2 3p,p +y3lwd,.ex t:is at x = a, and, mass 3m is at x = 2a. Whuy(axa3, : ,pttw cl +p ueh2dzd.j34pat is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg isw41 /u b*sswvp x y(6b/t6wllw pivoted about a frictionless axis thought the center O. A rope wrapped arb/l6(w4wl1x6vwt/ bs*psy wuound the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of qp8he : h*-timo;rshg;i *6frmass 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radr 8hoh:iptie6rhsgm-*;* ;qfius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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. Thehlv4) :sazs p; rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acce 4szhv: pa)sl;leration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel aiiiy+)s)valujo3/w0 -wj8 ;h (b wzl to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentiallyi)uibs- w ()0vzwwoy3 /a li+;laj8jh 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 4h paub:ko2/cd x8 4nepulley of mass 7.07 kg and h48/x2ona4c:ku pbde 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 disk pullh+ila:+ ubk a/atf s53fm.zg) .7hhh cey of mass 7.07 kg and radius 66.0 cm. What is the acceleration hs.5++bu:)l fzf ah.hat 7m/k3 ihagc of the mass?

  A rotating flywheel cax 1-qt3iu30pwjep p/ k4ijsr0 n be used 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 inertia ofm)b :*o1qffr m5o-snl $5.00 \; kgm^{2}$ 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 revf-mj:,r. gy.*anfag a-nr 3+0mifir st and rolls without slipping down a 1.0-m high inclinedf g.jia* i.r-- av,r n+agf0mynmr3:f plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of masob76tgj y(ycri+aavjr, c+ . -s 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined pl-7a6ic vy(jcrtr.by +j+,og aane can it climb before coming to rest?

  A hoop of radius 0.50 m anx6+3m7vje* aq iorv b48r(e owd a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after d r43e w7ev+(6m v8ab ixooj*qrropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls u t hv/vz/*wk+without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a /+hkw *ut/vvzsphere 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 oav0 3twr5 zf l(se,yhx5 c3.1;iiffkix01hpomentum 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 ofbwm 3 lld 661z7q0l0 eblo3olcfytxnh5(15ju 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 ra m9f bhxfp 5cnr:q9nb-6tu,o ,d/s with arms extended has a moment of inertichb9ob qf9umxn 6n, - 5ftpr,:a 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?