Angular displacement is usually express,zhbnh;5n m ;e in units of

  Angular velocity is expressed in units meo(5 xok/wwq.gm):lof

  Angular acceleration is expressed in uniittj: 7lec1 v.ts of

  A boy and a girl are riding on a merry-go-round which is turning at a conm bmccjc,;vep-6 .us)stant rate. The boy is near the outer edge, and the girl is closb, mc- )uj6c.ecp vms;er to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which isszh1 4jcqe bf+x0.4r n turning at a constant rate. The boy is near the outer edge, and the girl is closer to the cexcrsfh40+bq.e4njz 1 nter. Who has the greater angular speed?

  A boy and a girl are ridingu w3hr3nmd; + u*mc,ub on a merry-go-round which is turning at a constant rate. The bu ,wnduhm3*3rbcu+;moy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-r -h wvwt bdc 1k.;e,n2ywy7eu)ound which is turning at a constant rate. The boy is near the outer edge, while the;w1un)tw,d.ywcev7k -h 2 yeb girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridi;3uynn- i xx) nepj,:osp+vfq,0 s,qmux9- exng a merry-go-round which is turning at a constant rate. The boy is near the ox,x 3u-fmxxqj)9n s enp;iue so ,y q+np-:v0,uter edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotayldrbm p 3 ::6eol:h3sting. Which of the following is an accurate storsd h6 3b:l:yp:el 3matement?

  Rolling without slipping d3fa.zlhr/ f6i;vi1s bepends on

  Two equal forces are applie2phr skfr*tx8 wc(;k: w5ec 3kd to a door. The first force is applied at the midpoint of the2 h 3wtrk rfkc*;wk5pc(s8:ex door; 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 ato br -yd3c 5pyy,v3z-y 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 greatd r5cyo,pvyyb 3y--z3 er torque?

  Two forces are applied to a doorknob, perpendicular to the dl9bxg-h6u +jsojp-:t oor. The first force is twice as large as the second force. The ratio of the torxbj p6us+h-g jt: 9-loque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in gr t(y/ 4xy:kqrotati /rxtgyy k4(q:on?

  Consider two uniform solid spheres where both hqh4o5wq c4vzbxnzkpzd)3c135 h qn7ih*(l ,aave the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia *v34aqzi zclb(w) hc53q41h,5qxpkhn 7d no zto that of the smaller moment of inertia is

  Two uniform solid spheres have t0zgcjm;bxm ln 6.b2, whe same mass, but one has twice the radius of the other. The ratio of the larger sphere'mblnj2;m6, g0.zwbxc s moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and 7k1mv1m49jf/ ,tfr dg6dip zktwice the dia gd1j6mk 1dvk9fmt4/ izf 7,prmeter of the other. 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 increasp-a+)c9qib bv ed to 2M and 3R, what happens to 9baq+-vpbi c) the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wil) cv( 0 jl a75f,5oai3lmluymfl

  The moment of inertia of a solid cylinder about2c . ioafz.u) e8:wcsm its axis is given by $\frac{1}{2} MR^2$. 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 wheelpj/46xyf8fc:i z o ws8 of 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 the w84w:f6/x yo8f psc ijzheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipp9q4n8uuk j3fz ing down an inclined plane startfuz8 nk43ju9qing 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 i+cq eh3fu/ +xlnclined plane starting from rest. Tq3+lefh/u x+ che angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momav 824,qwum aientum of a system of particles changes when a net external force acts on ta v,wm42q u8iahe system." This statement is

  In what circumstances can the anguglqer9 (q xsm9 1*q.alu5xp x2lar velocity of system of particles change without anlg 5ql9rx9x2u mqexp(a1.sq *y change in the system's angular momentum?

  The Earth orbits the Sun in an :qi iymh( mkox ;6zu86)7r bejelliptical orbit. Ignore any friction which may be present. What happens over time to the Eart;ijmxzrb)u7o m:6q(eh8ky 6 ih's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orb7.gh ,q/ 4 wbtq8rgt82 ej52ncp u.lzfpizs 2git. As the Earth moves close to the Sun, then which of the following best desc4czpnp.8z5whj,g.8u s tf2 /qlg g7rtq ei2b2ribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outq (zp.jeuz 0pnns.39o stretched arms close to his body. What happens to his angular momentumu snzzne309 p..oq j(p about the axis of rotation?

  An ice skater performs a pirouetteh3ygj h3ybaqv6/ipr- k(r g7 : (a fast spin) by pulling in his outstretched arms close to his boq hy3 hkg( rip/7ygj:v a3rb6-dy. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette m.rnkvv27 zgnv18 0ip (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about th7pn. v2vr0znvk 81imge axis of rotation?

State the law of conservation of an7f lxp-/gd(xc tnf,o73 bb th:;gvb8agular momentum.

  What arc length does the Earth travel in a three month period in its nqy 2/5ihsx-gh early circular orbit about the Sun/g 5q y-2hshxi with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. Whagag4g* 4 fs*t yj:i3mlt distance does the tip of the second hand sweep through in 3 minutes and 45 tl 34f gsg4:aj* *gyimseconds?

  How many rad/s is 25 revolutions per minute equgkf 0a 0dtk z6(9+ui+ymomqi5z5a xl 6ivalent to?

  A bicycle wheel rotates uniformly through 2d smm9v ymg-e/,5mxwald mws9j:.3e7 .0 revolutions in 4.0 s. What is the frequency.:l 9m 37mw9es dvmx-g j m/y,mw5sade of the wheel's rotation?

  A pulsar (a rotating neutron star) eu kpqn- ttg2.so 9*8jpmits pulses at a frequency of 0.40 kHz. The period of i2 o.pjpqt*ktus n98- gts rotation is

  A phonograph record rotates at 45 rp)qn4jv1zbmy 5akm a-mbes,g .o ap5 :9m. Through what angle does it turn in 0.20 s,mmy5a4o b9njqp5a ):- gzsbv1ke. ma?

  A wheel of diameter 26 cm 7 dt hm8anv4.xdn gvo1z8y21 dturns at 1500 rpm. How far will a point on the outer rim move in h1t8 oad.nyv2g n78dmdv14 zx 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whaiwrq:o kw rw ejv92zz4,t.4z- t is the average angular spee:rk weq4 zir4v,ww9 otzj.z2- d of the wheel?

  A bicycle wheel rotates uekb, w9 f*ikc h mh+prm+0l:t:niformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of w+9, *ermhtm bci+kh:: 0l pkfthe wheel?

  A cable car at a ski resort carries skiers a distance of 6.diu85t pi4w -o8 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 utii5d p-8 o4wthe trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s.rapg q xi;5 (rbv50il) What is the linear speed of a point on the w(qrxr bg;)55pva 0l iiheel's rim?

  The cutting cord on a gas-powered weed cutter iswt rt z+c :)4- .8o n2nr-n+erd0(uqitpzmhhz 0.16 m in length. If the motor rotates at +iqor)mhu8(h : w2z.z+ t-t4nnrzpn-e rdt0c 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 roy d) 3m11lm1z2s0zfixr5i yoar,-mlhtating with a constant angular speed of 2.0 rad/s. What is the1,am0i-f xzsyio 23 1ml )1rh5 dzrlmy centripetal acceleration of a point on the wheel's rim?

  What is the centripetal accelera; ctt(0bxy*njg.h2j2 yv r e9ktion of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00yn t k(9*rb2jceh .0 2ytjg;xv m/s?

  How many revolutions per minute (8umc r+y. lnh4rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravi nhym4u8rc .+lty of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 2h::ta/; p*ccglpeu73yl8cps +m yub50 m/s. The maximum centripetal force (provided by static friction:g:ytb ul *e+5 c/ascpu8mphl yp3 7;c) 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 speed of 20 m/sed nmg 5*r eg0nka+tv00a3l9a. The maximum centrit aeregm0l03v* ad0nag5 nk9 +petal 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 oeo /mq(s vw8g/f 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 maximum8w(o/v /esqgm 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 41 hk-hji-5 oroua4cndown a lane at 5h-a 4 iunohjc-r ko414.3 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 accel*;qzeom3t di 3eration 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 wit1z/+f*)juc k0: h jucfjl fi/mk-elz 2h 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 a 0.300-m radius automobil;wqrcrg97 u -oe tire rotate after starting from rest and accelerating at a constant angular acceleratiog9-; ow rquc7rn of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angularl lqem- 4 hbn:o;5r:ws acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s f9o64gj1x9n,fro lvs x6z6mw decelerates with a constant angular acceleration o,vn j66mo grx9s4l f6 xw1zfo9f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rajf9sh +x sl.s2d/s while turning through 2.0 revolutions. What is the average angular acceleration of th xsshljf+9s 2.e wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to reswv2x+ ;gxhzccz- ntyn* /dud 4 y3(wq1t over a distance of 115 m. What is the total number of revoludxwvc 3w- g yn 1z(u+n;c dxty*zh/q42tions the wheel rotates in coming to rest?

  A wheel of diameter wn96j*ps tzi3iaueeup 8 (7(4: wcy/eidaj8h of 68.0 cm slows down uniformly from 8.40 m/s to rest over a distawepusi3 da *an7ey cj8j9/4zp (t:ii6e w u(h8nce of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/63w zotovya +th7 lq,-s to rest over a distance of 115 m. How long does it take3th wa-tol 6z+vyq7,o for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotat.j ocz)- iclx;n*v1 6mu(vn8tf9qk m pes at a rotational speed of 3600 rev/min. Whe mczcm1qvpnlif ;xo96*kuj n.tv-( )8n switched 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 tightening to a torque of 9 tqj 4b2;*jfuz0 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forcjb j ;2ft4quz*e is perpendicular to the wrench?

  The bolts on a car whexinxv znlx27- o/p80a el require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required wl xi/az7 x0-v8o2pn nxhen the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner-v gcma3z,,m ltia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follba2 50snf0imrows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of 00s2 nmb5 raifinertia about the origin?

  A solid cylinder of mass 10 ygky-+im( t auzi16f:kg is pivoted about a frictionless axis thought the center O. A r iu1tgi: m-yzka6fy(+ ope wrapped around 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 mass 10 kg is pivoteq2ydvp -hzv (,d about a frictionless axis thought the center O. A rope wrz2qv,pyd-v ( happed around 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) 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.uclswmj:,zg 8+9 8 gyi4:rkw:ktac0c 3i mlx8 The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the anglwc 4 guj cyx m:wl 8830g8ra:zik,kmst:ci+9ular acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheenc8 cd840vih .zg i.zol 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 tangz8oc h i0 8zdiv4.gcn.entially 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 r8 sao(ez71 bb pe ta.f)8b2zxeope wrapped around a frictionless disk pulley of mass (at) zsbbe8e8oz1 a2e fpxb .77.07 kg and 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 pulley sqir2pugb+*) of mass 7.07 kg and radius 66.0 cm. What is the i2 r+gsu*pq)bacceleration of the mass?

  A rotating flywheel cl2,fs7 j:tlxm t:(jnd l3mp3kan 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 of7tmw6( vwfb jm 7s2;gi 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 starf/cno2 .heee*8+xt rs ts from rest and rolls withtceox/.shnr +82e * feout 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?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 1qb wh-ec;;4j9u)hv s q0 m/s. How high up an inclined qqew)vh-j;ub shc;4 9plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of t9 fr* 04dzl9iaf fw8r0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after droppi4az9drf8 *w t0f9ifrl ng a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls wi,w;jis,- g b*tb kx4rethout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The b,*sri, ewtb j;4gxk- 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 momentum change q9;ygt8hc 9igs 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 mohs )/*y fldi9bt 0ec-rxi s9:ument 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 wit,rtd4 b8uc.4gzg/h(c/fp) fhrzy u(m h arms extended has a moment of inertia ofm)czzph.8,4u u/ dybgrfrchft/( (4 g
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?