Angular displacement is usuall 6wgxurk9a7b9rdblc3t 8/;rk y express in units of

  Angular velocity is expressedobmd83jrj* bm4 ml* 7t in units of

  Angular acceleration is expressed in units of5baoij( :gx /og:cj0h0m r6os

  A boy and a girl are riding on a merry-go-round which is turning at a constant z9 87tmuk k auljmz0lqj1z cr.*+( 4israte. Thej+9j.u1 lk mi z87lta(kzzqr4um*s c0 boy is near the outer 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 tx59e cor7a) *uec;ei 1obf0g turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angulce 0e* b coetgfi1 uo5)9arx;7ar speed?

  A boy and a girl are riding on a merry-go-round whna lw99i v-/ng07bqe rich is turning at a constant rate. The boy is near the outer edge, and the girl is c7r -b/ nevgw9na9 li0qloser to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning kvy 6+c,63 s3efrprhfat a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal accelerrp+v3ksffy 66er,3hc ation?

  A boy and a girl are +z ha f(yae-r8riding a merry-go-round which is turning at a constant rate.+a-ar (hefy8z The 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 followinlyp5tvn)mqsq r 0 *,,cd6s/guz)x1 ljg is an accurate stagr))zssnpm6j/dq* ,yu ltc 0q5l1v, xtement?

  Rolling without slipping depenr ,:mmr9mq5193jc rsfsdyba; ds on

  Two equal forces are applied to a door. The first force is apry(y+ qr8 rbk)plied at the midpoint of the door; the secoryr8rq(+y) kb nd 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 too+s esv7vy ;w9-4qdns 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 greater torque?s v+n syws veoq7;d9-4

  Two forces are applied to a doorknob, perpendicular to the rf0-i fhvy2 u-*frh w3door. The first force is twice as ly0v3 riffuh*h2 wr--farge 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 resistance to changes in rofm;uk ;o/vwxq(l.9 bm;sqqe ,,ynd6o tationlo;mod nqs bq,9.;kmyu/e vqf x,6 ;w(?

  Consider two uniform solid spheres where bxba/k p; rp43foth 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 in /p4xark3; fpbertia is

  Two uniform solid spheres have the same mass, but one has twice th od-3:tfmls.0.nt6 ahqigs9n; 5 uhbhe radius of the other. The ratio of the larger sphere's moment of inertia to that of the smallm. nbtt:lf 6ihnuh do-5asq;.3h 0gs9er sphere is

  Consider two uniform solid spheres where one has twice the mrim8j1pyj(0hq 97mx nass and twice the diameter n7jj8rx( hp q0y9m1 imof 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 thesxx0/aq9qf91 zt abdn2e are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central99qxa /x 0n2fztadq b1 axis?

  If a constant net torque is applied to an object, that oa2:;liecaan9zthe 5i6hh *.pbject will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2.djq+ao09n7wklfe t -+ If 7jq+f0 el9 todw-+kan 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 of which has a mamuu nu8p9 ikd k/ps;k8a-p5jn9 7y9i jss 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 eneua9m9 9/pn j7 y8usi npk-kpu8 5di;kjrgy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippinga0*jgem(lia-06nt bw down an inclined plane starting frwit- (an0 ebg *aj6lm0om 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 slipprdg51and2:vqcrc (t 8ing down an inclined plane starting from rest. The angular velocity of the sphere at the b8g5rn:2dr c c vt1d(qaottom of the incline depends on

  "The total angular momentum of a system of particles changes wht9 rdb t9x30doen a net external force acts on the system." This statemrtt9d03ob 9 dxent is

  In what circumstances can the angular velocity of system of part7cg w.xs51g nnicles change without any change in the sgnc 7wxsg5n1.ystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which r4jz u5og*w;a may be present. What happens over time to the Earth's angular momentumgou a; 5wr*jz4 about the Sun?

  The Earth moves about the Sun in an 1ao 7 . ch 3ntlnn ohpl(dp.w;hh87f2qelliptical orbit. As the Earth moves close to the Sdh1f7 2lhqohtp ;pna3h.on7 c(n 8.wlun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirj/hz pu/n iywtx 69(3souette (a fast spin) by pulling in his outstretched arms close to his body. What happens to jy/6tzhuw n 9(xsi3/ phis angular momentum about the axis of rotation?

  An ice skater performs a pirouette wbglc1 q; pk8s ha5j00(a fast spin) by pulling in his outstretched arms close to his body. What happens 0bapw 5j1lsckq ;8 0hgto his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast sp (:aplqcx*ic-fx 08x fin) by pulling in his outstretched ar8qla0x fi-p(c:x*x c fms close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation o) )nk0t y;bxfnb ./scbf angular momentum.

  What arc length does the Earth travel in a thre)z+h-jgt ngsepx 6)xt6g zm3 *e month period in its nearly circular o)6g*z st-g6jp g+x)ne t3xzm hrbit 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 does the tne6 ei esr4,u4cis x7s6irmg-y)1w+ vip of the sei,e rm s ig66x+1iv47u) ewcrsny4-second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalefom)z c/y)lmcj8g2q* nt to?

  A bicycle wheel rotates uniformly through 2.02( gelic9b z u/cz4ee r6n5ec3 revolutions in 4.0 s. What is the frequizc64/gez rcb( ne259e ce3ulency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits p8cpx;y/0) s4zo np8vbf 9shal-4b iteulses at a frequency of 0.40 kHz. The period of its rotaticz)fa p t4e h0sx8y- ov;9b/pilb4n8son is

  A phonograph record rotates at 45 rpm. Through what angle doesaxsw4 )+z t)mf it turn in 0.20 m) +4 f)wstaxzs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poikpu*o5 qow7an3 z;w; znt on the outer rim move3w; uwkozn ;zp57aqo* in 2.1 s?

  A bicycle wheel rotates uniformly througm)(xf10 i,9o4cl peccr d5mlmn b6u2 eh 2.0 revolutions in 4.0 s. What is the average angular speed of the wheel? dm c9fcelon1r(0, 4cmx5)b le26mupi

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wh;lrggia :k+3nat is the linear speed of a point 0.10 m from the cenkag+g3l;n ir: ter of the wheel?

  A cable car at a ski resort capndwe4 qw+q b/20r(r wrries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slip2q0wq edp( b/4wwr +rnpage, 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 rad/s.7*d1 da2 fbply What is the linear speed d y*2 fp1d7albof a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16)s:1kzwa*t)t g (7 yxfiv qxy. m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of thxgk7zx1)at *vf q:( w.y) ystie cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed g p4r)za; 7scx0r hm3uof 2.0 rad/s. What is the centripetal accghux; zs07mrc4a3) rp eleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on th9jfr)ygceto7gms.s*7z mer , i 0d*2el1a+sqe perimeter of a bicycle wheel of diameter 70.0 cm when the bik.slfzsege 721rce+ oaigm *dt *rqmyj7s 90),e is moving 8.00 m/s?

  How many revolutions per minute ( z6e0p4ff d2aya9wap 40qelz 0rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity 6p 2al4edq f400z0f ya9zpaweof $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 o(o/ 8oexqe -xm with a speed of 20 m/s. The maximum centripetal force (provided by static frictiooo8 q -o/x(exen) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating :-uyvruh plgaw066f; a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum ceav66- fwl: ;hgur p0uyntripetal 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 pc/ gc hr7(*inpx0/ yb.f*)3nmextzm 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 the mass have if the s /*exft0crcpn/ .g m)3*xp7 mhynzbi(tring is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 m dowg wh:p -sw,r38/u ge34xnmzuon a lane a :wugrsg/ 3m-, 8 eop3xzhunw4t 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 accely. lvk 6vn.)maeration 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 wifenvec94f ndu22s9 4yn l vq*4 m+2ssfth 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 rjyb2,za1yvmn)a14sa i/wy z; adius automobile tire rotate after starting from rest and accelerating at a constant angular acceleration;4 m)abszi, zw1yjy/ay21 anv of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an ak)w-r*,uf 8-fjxz.wtg b6so mngular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatin/ ;guvo /r/3fk csxy/pg at 20 rad/s decelerates with a constant angular acceleration/3f vo;/u/ p xs/gykcr of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and klv ml (,44hxga7 xx,vreaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acc x ,xklhxmval 4,gv4(7eleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to restvjy5w,d. (sdu4* ql: , doucnjtx* cg) over a distance of 115 m. What is the total number of revolutions the wyujgc x.nt,s qjdw(*d ,cd54*u :ov) lheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniform* jpt.v 9.bhsaly from 8.40 m/s to rest over a*ba.t9 vhjp s. distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to res2/ p7z isgh-pz4k sf.pt over a distance of 115 m. How p-k pgzphis2 sz4.7f/ long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotati8n7shtdya -o:jf37 f yonal speed of 3600 rev/min. When switched off, ia8f3 t7syndj oy7:hf-t 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 90 Nm. sq ba*o1cux.8 If a 30 cm long wrench is us1s *uq.o cbxa8ed, what is the magnitude 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 Nm. If a 30 cshk 4wak468mq m long wrench is used, what is the magnitude of the force required when the force applied k6 maqw48ksh4at $53^{\circ}$ to the wrench?

  A wheel with moment dgkyh-gwyp3*a25t 9i of inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows:l4p iu*(vbt4n mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is vbt*(u4 inp l4the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axi/u sqeuhm y2./s thought the center O. A rope wrapped around the outer radius R1 = 1.0 mqhsu u y./em2/, 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 pivotse-gc; x3yco 0bjgk, 7ed about a frictionless axis thought the center O. A ybc k,7 x0e;cg3 -sogjrope 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged aq9v a3b;- epljt 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 one enej9-qbva;l3 pd is ML2/3.)

  Consider a bicycle wheel to be a ring of radiusm4qm *mh+y.l f 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is ap q*+4 y.mmmhlfplied 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 manmr:9 bbu( o7 mwn+n,qss 7.07 kg and radius 66.0 cm. Wm7n9ou m(r ,wqbn+n: bhat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionleszd*d27q8kgz)1varwgs 3 :grn s disk pulley of mass 7.07 kg and ds13gkz:v 7ag *dn2rz )grw8 qradius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can beea i mh+c :*s8s qfhzkt)(o(f: 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 odg 5mrx0./ c0q2lqd upuyo 1m6f $5.00 \; kgm^{2}$ 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 and rollsmd0c6: fl.w)oy,nkh4:/;1nh rdrp zpv( oq lo without slipping down a 1.0-m high inclined plane. What is the speed of the sphere whe,nl0:c w(h r kz.:1hmy4po/6 vnl;f )d pqodorn it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a spee :gresp3a-,idnz p-8 c5toec4 d of 10 m/s. How high up an inclined plane can it climb bef- epcr3:8 np -zgei asdt5oc,4ore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from resui(ml8 ww 9w(gt and allowed to roll down an inclined plane. gw(8wi mu(lw 9How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kgtfem9xzn90. kdo:+ nb and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment o.oxdme9+ntz9 0 nb f:kf 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 -9;g8 dltr 9 nhi6zflcmomentum 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 inertia bl 2q iz: 3i4f6 cqe)x-rj,ktdof $5.0 \; kgm^{2}$ 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 h - m i(p/4p6q 2suexj0eg;9uan.wbnua moment of inertia 9 n2hewspup 64e niqx 0 gmu(/a-j;ub.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?