Angular displacement is usua9/ihaqq-gr0 q q,6 yv8wbe;i6gnt) cp lly express in units of

  Angular velocity is expressedl5lo-3rv he:u/9anff )b07w jz.bj c j in units of

  Angular accelerationnq 5t0du3 4qqysqns05f r-bxfy,*v 7k is expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a conye yd4ce 1s.cb+ob; tte+ 0n.ostant rate. The boy is near the o1 tc yb..b ensoc+eeo+dy;04tuter 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-round which is ywwf/m b t om ijykjy1kfy.68.hec(4 *5w7;blturning at a constant rate. The boy is near the outer edge, and the girl is closer toyt fb oy8j(4jfy.kw7 6.;1m5iw/wk mhy*blce the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which v,/ic 9u 0srpc jisgap833co/is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the c/930i8pvo/gapr s ,3jsuccigreater linear speed?

  A boy and a girl are riding9jqw, u b1a 2yv3ijbx6 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 centrii, y9ab ju6xvw1b2q3jpetal acceleration?

  A boy and a girl are riding a merry-go-round ; z-uh0l /nxvkwhich is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greatez v;n0 kuhl-/xr tangential acceleration?

  Consider a rigid body that is rotating. Which of th*u9 -lvbtix sqc k z8cz8-rcg/-n5(fue following is an accurate statementxgz-8r5-f ukc9(b/u ct i8lq- *snzvc?

  Rolling without slipping duazwfd3zkuj td 9t( 6* ),x6igepends on

  Two equal forces are applied to a door. The first force is applied at the g 2mosb*bnj;cm+u:8 :3zbdb c midpoint of the door; the second force is applied at the doorknob:zon;2umb bg*jb + 3mcb8ds :c. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied 35zfkf;/lue wa-w jg t,xk-+pto a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the gra-f x wg35/ j+;twkufkzlpe,- eater torque?

  Two forces are applied tv3vcrurdh/ ldjsqj 4ic wdg)hxp +2b*)/ :*v. o a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the s v ldsg)jj*uwcq/rr/ +4p*cd xb3.2 v:hvh d)iecond is

  What is the quantity used to measure an object's resistance to changes in , vwem5u.v) qwrotati5 q.wv,wu emv)on?

  Consider two uniform solid spheres where u313 ta :jzavvz+y xq3both 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 of inertia i333avax z+1vzj t:yq us

  Two uniform solid spheres have the same mass, but one has twicd 7f)mgj.yr. ze the radius of the other. The ratio of the larg.d)z7fgr y .jmer sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twicegsb arhk)(x/f*gcly+1z- x-b ; pu ;yk the mass and twice the diameter of the ot 1z hc)+py/xflbrk --g; bxa;ky*g(usher. The ratio 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. If these are increased to 2Mn**ja-b ezsz9 and 3R, what happens to the sphere's moment of inertia about a central axiazs *9jznb*-es?

  If a constant net torque is applied to a/o,b4 n t5ejigw.7lzs n object, that object will

  The moment of inertia of a solid cylinder about its axis is given byerzsbplc. c7i9;epf (ap8 0a* 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational lac efasb0c *ppez;i8p(7r9. kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which udodd +w)nexrq 96hnr9 4m14winxr-v i)nq /4has 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 eedx n4x/onw 4qnrm9-dr 1hu) 9+n6iq v w)ird4nergy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippx*zb9*kikb+ 6+nr)wm xv o l3bing down an inclined plane starting fxkbk x* b+mv obn *69iz3l)+wrrom 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 w v5fktmb12c )vithout slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depecm25vbvktf )1 nds on

  "The total angular momentum of a system of particles changes wiaxhu01u*ge(1o k,v m hen a net external forko1u(i 1,m *ehx avu0gce acts on the system." This statement is

  In what circumstances can the angular velocity of systdu29r4u8)9-v sl gv fjv 6yuttem of particles change without any change in the system's angular momenf-2jrv l)vgyut6ud t 9v94s8utum?

  The Earth orbits the Sun in an elliptical orbit. Ignore anyw4ukv3* tz9uo9 )yei)qp)egqg*s .xg friction which may be present. What happens over time to the Earth e*i9 z9)q) vxtug4 e .)kwo*pugysqg3's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical otdx( vc:upt-kq9 r( /nrbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting s/-rt( xc( pt9 vuk:qndpeed of the Earth about the Sun?

  An ice skater performs a pirouette (alx-lz u 2cpel65t90 wl fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about w-lpc9 e65t2ll0lxu z the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his( 6zt+ fetm*d,zp;as n outstretched arms close to his body. What happens to his rotational kinetic energy about the axis t,*p(nz+ez a;dfm6stof rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrqtm coby4y5n j t86vb8)4 oty,etched arms close to his body. What happens to his4 4jot5yyv ,tb 6)8qomt 8cnyb moment of inertia about the axis of rotation?

State the law of conservation of angular ttxdq.-pv a1tc g+s0)gk2 gig3 g3(rt momentum.

  What arc length does the Earth travel in3( b:cu d6w fv6dc.hpl a three month period in its nearly circular orbit about the Sun with a 6(. cp6 c3wlvdbu:hdfradius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dism) nb3qwb n80bw elksm.c:,ze :70upmtance does the tip of the second hand sweep through in 3 minutes and 45 secondp:7mmumelqneb0: bbksw0,cn 8 )w3z.s?

  How many rad/s is 25 revolutions per mindv 5ueytous qyew58:x.f.q (+ute equivalent to?

  A bicycle wheel rotates uniformly thw;;fmix j)x,3 1xwm oirough 2.0 revolutions in 4.0 s. What is the frequency of the,j wioxmx f;wx)m;1 3i wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Theob1l.ax y.)jssc29hny d;e2 w perio js)h..;l22xsy9aw odyeb cn1d of its rotation is

  A phonograph record rotates ati98fm54 ryfkq 45 rpm. Through what angle does it turn in 0.20 s?yif 8rmfq4k59

  A wheel of diameter 26 cm turns az5cz:92ax wl lt 1500 rpm. How far will a point on the outer rim mlc:wlxa9 2z 5zove in 2.1 s?

  A bicycle wheel rotates uniformly throuq;/f mqmck/-pc;py;e+2pt p sgh 2.0 revolutions in 4.0 s. What is the average angular speed of t2/pe;q;;q +-m/cy pkp pscmf the wheel?

  A bicycle wheel rotates uniformly through 2.+ / isol,a*qdq.6 k gmf5jombd+6 l:vh0 revolutions in 4.0 s. What is the linelsjlih:5*q/.g+bdo qv,mk+f6d o6a mar 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 6vbiy,o s xrb(vc4+-2k .8 km. The cable which 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 mic 2 vbi,(ro b+-syk4vxnutes?

  A wheel of radius 1.0 m is rotating with a con6d:+9mjbsvd tstant angular speed of 2.0 rad/s. What is the linear speed of a point on the wb sj d96vdmt:+heel's rim?

  The cutting cord on a gas-jrf:g wouwx 3s 4e(tt vm+cl/z;vf4 .1powered weed cutter is 0.16 m in length. If the motor rotateswu/f;:et1r v j+movx( z4sl 4 cg.3twf at the 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 cone p4a3z41c sai3bdps--hfva ; stant angular speed of 2.0 rad/s. What is the centripeta caa sd 1hppv s;3zab4i-4-fe3l acceleration of a point on the wheel's rim?

  What is the centripetal ac86e 2evmgzr0n qi v6 rh9p9*kdceleration of a point on the perimeter of a bicycle wheel of diameter 70.0er zv2kdq* e gh69 8m0r6vip9n cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stp)an; ij*j:nkation (r = 1000 m) rotat) npa; :jj*kine to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular s 4 dq1wqefi23curve of radius 50 m with a speed of 20 m/s. The maxiei q4f2sq3d 1wmum 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 spyweso ndf,35 ;eed of 20 m/s. The maximum centripetal force (provided by static friction) isn o3;d f5ys,we $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is whirled around in14 7kilhz0 zg(m alxe) a smooth level table. If the maximum tension that the string can withstand is 25 )zz0lm l4ga1ex7i hk(0 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 d2vuv+o)+*almcc 6vr,wwb:j y u+)eb jown a lane at 4.3 m/s:b)6v*vuv ,lwb ua 2c+m+jceo w+)j ry.
(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 q9fc p.f4f :,nfj5owo , x1vopa 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 angular accele/c 6;;2z+wgvjmrcq c dration 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 titrf-mv. (g5968gjx 4gjad1 i )wueksf re rotate after starting from rest and accelerating at a constag4 gia(jkr- d6j)fsxm gu9e1.5 fv t8wnt angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hkse8u-;3cq2s ib cc(s as an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerk zl j-zkyl. -4h.pdq3ates with a constant angular acceleration of -3.p d-zj kzhyl4lq.k$-5.0 \; rad/s^2$. 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 whia9/ f+dq -(bsqs. blorle turning through 2.0 revolutqr9 dsbaf/s .b o+(ql-ions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down;v /w) ud fw0,pcz)ghi7b. byw uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number oi)bd0wg vpb,7 /zy;)wfh u. wcf revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unifjc,b q/u t c*s3w6u xodt:.i-wormly from 8.40 m/s to rest over a distance of 11jc w:*db /ox qt.u, uc3it6sw-5 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm sg em.)8pzzx ab-/o1iqwe l1,ca7ear + lows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to w+ea ,pg eax. zireqmcb/-8o)l17 a z1the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed ow d 6zk+b0s;pef 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration pw0ze6ksb d ;+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 whe *)(yy oh0qoi hflkczgej37yr 374sk 1el require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magh7fsok ( 7czkq0lryy eg1* )jh i334oynitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nmmt: vl/31ayz jm y*8.hkv ti1s. If a 30 cm long wrench is used, what is the magnitude of the force required when the fz t:lj* t.s3y1/a1hvkm vi8ym orce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inzq/ra9 z/4tuykv6*lt ertia $3.00 \; kgm^{2}$ 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 rzr3e6reb 4lp (iwt)ex3j i4c:z/m6eorigin, mass 2m is at x = a, ar4 (m3bpexreei4 rzc )tji:6zl/e6 3wnd, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fribcqu-lo+nz bx6zf97)ctionless axis thought 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 radz +c 7-qf6x9obl)bnzuius 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 zm)tx o3b1 ph7 nkzr-5is 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 to the right. A second rope wrapped around another section of x1r) hz bo7n3kp5- tzmradius 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 hij62 eifdp h46wnged at one end. The rod is initially held in 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 oneiwhf4 jed6p26 end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm andy2n5yh bvv v fdr3*5*o 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 linearf2 5*ryvnhbvy*3 o 5vd speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped arous( jpdgu1/ /kfnd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cj(u 1dgfps//k m. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs p a9zor-9q.n non a rope wrapped around a frictionless disk pulley of mass 7.07 kg a 9 .nnqzaor-p9nd radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is rexzp );r /bw2etquired 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 inerx0ldz/wk3lp7 tia 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 an1e:lg0z)1: mf u)uxpffcjg *od rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere wh*:mgl u1upe1fo 0 z)j:) gxfcfen it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg andj wmi5f:dm .5vgkf2ac sk6;1 ,g fjf.n radius 0.010 m rolls with a speed of 10 m/s. How high up an inclinedigwfgf k5fvn6: d1;,jaf5.c.skm2 j m plane can it climb before coming to rest?

  A hoop of radius 0.50 m anz2w+3.fl*i /b mcl z,l1jp suqd a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a v2 l /ziu s.p*bw3j ,mlzf1lc+qertical distance of 3.0 m?

A solid sphere of mass 1.5 kg anpi:d;8.tc 3 au2+hunszu.ubrxra t od)/3j +ld radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assumejrd+;p.tr)ubs:l3/ +ha2uan z uoc i du.t3x8 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 momenjtp+ +6juxp0 ltum 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 if k.xx 2djsjxyg:v ,44x:+wpx nertia 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 raby(15 )q38n6asa/rfas w,zf3wtb jdfd/s with arms extended has a moment of inertia orna5q/b8wjftda)f(ws 6b3, 1saf 3 zyf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?