Angular displacement is usually express in units ofj.y vzbslm yu:4t/98t

  Angular velocity is expre( ;s s bto,jcvv8+t6qxssed in units of

  Angular acceleration is expressed in f 0afim5 jg6w1units of

  A boy and a girl are riding on a merry-go-round whi a/ibmtq/4ce2i* bzu+sda-d .ch is turning at a constant rate. The boy is near the outer edge, and the girl is ctaa4bq. i e su/d+*ic/-mz2bd loser 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 const 2lqf ( wns)o1o-hc2ed(vb yk(ant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular sp((oh)1yndvl(w2 of-c qke2bs eed?

  A boy and a girl are riding on a merry-go-round which is turning at aqij:cd)3 .w lwb*6r la constant rate. The boy isl3 d: aiq6wbc*. )wrjl near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridingidi (m a5wd4wbteq :-, 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 centw :i-( biwd5mde,qa4tripetal acceleration?

  A boy and a girl are riding a merry-go-round whqxh sp 5p:m+i.ich is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who spp+qi mxh .:5has the greater tangential acceleration?

  Consider a rigid body that ils0bycr42 7 ros rotating. Which of the following is an accurate st4yoscbr 02rl 7atement?

  Rolling without slippzf5xae:tb1kjn yw ,3 8+ q,myping depends on

  Two equal forces are applied to a door. The first force is applied at the midh;wv5t :e,j t,6rb4gbwmma -dpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater to4e-;6d5gjav:tw,rh ,mbm bw trque?

  Two equal forces are applied to a door at the dooha1xb1v 3e.hz,cw gj)rknob. The first force is applied perpendicul1beja wx1g.chvz,3 )h ar to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, fuwqn:i(: cdubq;6 p5perpendicular to the door. The first force is twice as large as the second force. The ratio of;qidpb6cwqfn:(uu 5: the torque of the first to the torque of the second is

  What is the quantity used to measu-6q+wov hy u,wre an object's resistance to changes in rotationvy uq+6w-woh, ?

  Consider two uniform solid spheres where both have the same diameter, but 9b ryzq2xax;uc835 nb one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smallerxqn95byxru 8az2b; c 3 moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of z gdw81p2yz9tmd 9 2ws/t 4gnjthe other. The ratio of the larger g4p m tddnt9z2yg/w j8921zsw sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid sphey*7glu m/)m fures where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of i )f*7yumlm ug/nertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. Ie.1da*k9lm a ff these are increased to 2M and 3R, what happens to the sphk felda.*1 9maere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that objec7se.p ueqi4pa7k l9p.;r3zjks +ze ,x t will

  The moment of inerti g5z)3 yotbeyv32adp; )) fzvka of a solid cylinder about its axis is given by 0.5 MR2. If thebz5))gy )33k pa2fo; dv tvyzis cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle oit7w.ikz6-o,os l fgrmi2)i dpfv;3.f mass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the r.)w2vp f i;kotgdo3firz7i ml,i s-.6 otational kinetic 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 and radius R rolls without slipping q )8bl7mqg:jpdown an inclined plane starting7q8j):g mlpb q 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 rollah+uvlj. ;- kwu(yc /ns without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depuknw-+ ;u vc. (jla/hyends on

  "The total angular momentum of a syss.4+ ve,scho em.3xei tem of particles changes when a net external force acts on the system." This s4evm, ico. .3 xshe+estatement is

  In what circumstances can the angular velocity of system of particles change wit wrxyn7 oy(bg 4)hc 0*/tuyomp55zul1hout any change in tl(0/o yx oug)4yrh n75zcu5bpmywt1 *he system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whichdr/n13t6b a iw may be present. What happens over time to the Earth's angular momen/16abi rd3t nwtum about the Sun?

  The Earth moves about the Sun in l o6l-n*ly/wys3 di :jan elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the S-ily oy sl6jl :3wd*/nun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrets kaaml,g anabnr:m c487*n-:ched arms close to his body. Wh4* aam:-c7 ma8kn l a,ngsr:bnat happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by xja*n4u y-th6 pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about th*- h4a6 juxytne axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his b8 x+cl.l:/wjfr8)lnbug vu- outstretched arms close to his body. What happens to his moment of inertia about t/-lvrbuw)b 8jx8+.gn: lfclu he axis of rotation?

State the law of conservation of angular3 ow/ydx 6y2gia:mve p hjdp 5vs7gt0zod:1-+ momentum.

  What arc length does the Earth travel in a three month period in its nearlvb6v h63y:oc 5v4hc+xuu lj(g y circular o3(ou6h h+v lvxub4c5v cg 6:yjrbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has s9ai 1spi6a3gc+ yswugf ..0d(fk g4r a length of 0.30 m. What distance does the tip of the second hand sweep t(rg1 9sa ag kws0.6cipfd4g s.f y3iu+hrough in 3 minutes and 45 seconds?

  How many rad/s is 25 rev: .-3 sruwdpsb,ypk5l3ke6emolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions irko/vuv1(j ,xn 4.0 s. What is the frequency of the wheel's rotation? (rokvvjux/ ,1

  A pulsar (a rotating neutron star) emits pulses at a frequency of b gvfbrl35g.,0.40 kHz. The period rv gf3 glb,5.bof its rotation is

  A phonograph record rotates at 45 g3m3u:trb4db rpm. Through what angle does it turn in 0.20 :3bu4d trgm3b s?

  A wheel of diameter 26 cm tudf)k.ch;fyk;g-l jhn1 e-9u yrns at 1500 rpm. How far will a point on the outer rim move in 2.1 ud; ehjlfgkh9cy1k .;fy)-n- s?

  A bicycle wheel rotates uniformly through 2t yc7:9 yxpzs7hno ,:fh 8z9ca.0 revolutions in 4.0 s. What is the average sh:,o7y: ph8 7c y9 nztzafc9xangular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 rzbatv q16mwcbjr40 0/hz, ey3evolutions in 4.0 s. What is the linear speed of a point 0.10 m from the ctb ,rzc1q0/jyzm3e aw 40bhv6enter of the wheel?

  A cable car at a ski resort carries skiea,r )x1yn qczysdud nv-g; 116rs a distance of 6.8 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 qz6su1ag,n xy;y-dnc11v )dr 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 ra6 xeghw4k rn7obb /+6y.a4 gdgd/s. Wbgg .6hoygw n bk+/xe764 r4adhat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-po;6/2j vlwisn) zabhe *wered weed cutter is 0.16 m in length. If the motor ;aw v26nejl h)zb*s/irotates 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 wi y*t k.4x(xya8ulc ,6l 8z2nluulzey5 th a constant angular speed of 2.0 rad/s. What is the centripetal 2c6 4 .l 8u eax*uz(5xtl8k,unzl yyylacceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimf8arhm esu9((eter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/s?rf(s8m9u (eha

  How many revolutions per minute (rpm) must a circutf2 k2 fy5sb6flar, rotating space station (r = 1000 m) rotate to produce an artificial gravity of2f6tsyb2kf 5 f $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with b w;+qs 8rofs)pikogo+2 n*;oa speed of 20 m/s. The maxim+o+s2korfoo;b);gs 8iw *qpnum 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 rampv xj: o/p w.8ijq yta4;a,8adius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stat ;yjq/8apjw4.:o8xp m, tvaaiic 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-m string, is whirled aroundc3/685fslwq.alytkrly, d u0 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 string is ny0l 3uc8dywqrla /.s lt5k ,f6ot to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slip 41u-yhc/x a ip5zf-)1fztkloping 10 m down a lane at 4.3 m/sacxzftp4ky)-f1iho 1 uz / l5-.
(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 acceleration of /yrx+67 djj ln$4.5 rad/s^2$. 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 acceler3dfezvf0 0 fn7/dx,n qation 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 tire rotate after starti 5ksjbkwo*(+dng from rest and acksojk+d*w5 (b celerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, a 7moy ji .aq(yr:ykfp+t 81x+ind has 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 decele6vx bio+ nrd:xktq9-;rates with a constant angular acceleration o;vqxnt-x+o 6rbdki 9:f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0:o jes36:)3):uwlu bdgh0+p grmrzcp:.q nwc rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the wheeloh)mse:g + zgc)duw.r36u:3lr bn:pjqc :0pw ?

  A wheel of diameter of 68.0 cm slows down uniformly 3qg67avpixcd5xyo .:wg 0o r (from 8.40 m/s to rest over a distance of 115 m. What is the total number of re3qo p ydgxw50ca: (og.xvr67i volutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unifoccd5 vz:m583m ) meqnzl5u ;jwrmly from 8.40 m/s to rest over a distance of 115 m. What is t q zmzc8:)ne5um;5l3 v jmcd5whe angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformlyn *we ;(:yfkwy1kisu/wsl /;w from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to cok/fy(*;wk sui/s;nw wl:1eyw me to the stop?

  A centrifuge in a medic,u l;7r grjrf.z; .mp3w7dbeyal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constanl ejz7,w;r m ;rd.uy.brg 3f7pt 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. If a 30 cm l ig:4tt6 ke5qlong wrench is used, what is the magnitude of the force required when the force is perpendicular t ttk5i6:eql4g o the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. p, bawz2f.3hntj v1 n0-sh+zg+q6cdg If a 30 cm long wrencnth,bvzd6wq s+n.12 aczf+0g3pg hj -h is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of dty,m 3y lzbq9j0g -q1inertia $3.00 \; kgm^{2}$ 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 is-o sgpz m2ds;: at x = a, and, :opd2 m ;gsz-smass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg )kpq ,t fwa 0v2w,4vnwis 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 radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is,4na,q0wp2w wfvv)kt the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought thre ws f9j.wyv0v7k*/ee 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 radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many 97e w* jv./re 0yvskwfradians 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. i) .yx;i3 j 6sx6r)mejhs z-zd -m1yszThe rod is initially held in the horizontal position, and then released as the free end iiyx;16hzjs3 y.zrdi6xssme )--)z mjs allowed to fall. 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 radq y ej+mdp-*ul;b0 *cuius 30 cm and mass 1.5 kg. Neglect the mass ofl0j;uu q*bme c+pd-y* 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 linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlt p;e 76;.5ex a 0u0)tw5qqhca2kbbvzi7wso wess disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of thu txke5bqaqphe02cwiw; s0 ;)ob. 657vw7 zta e pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mawlc ot; q mi+25zkc,s+ywn8n8 ss 7.07 kg and radius 66. +mckn,ts2zl+qow8;cn i8 5yw0 cm. What is the acceleration of the mass?

  A rotating flywheel can be k+ryh1 d(f qt8ogxe i315i8trused 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 os v 2t/2(m81qe8wefrel8ng o bf $5.00 \; kgm^{2}$ 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 ma9* +ko xn3m1xcasiz;xss 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. Whato3xi1 xxazsn* 9; mck+ is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg igjlk,*m2 s5n and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climbjml * sknig25, before coming to rest?

  A hoop of radius 0.50 m and a4lnn9: :w dtli 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 vertical distanwi4:l9lt d: nnce of 3.0 m?

A solid sphere of mass 1.5 kg and bls 679t( leidd)grga+m 3c a0radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a gleld+ 0t 9(rgmi3cb 6aa7s)dsphere 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 c)d -k:jffj5(pope. nqo3cq /phanges 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 4,lzx5ropivhp g,4:w j g6aw2 moment 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 extended has a twspo*o+qa: o .k munbaf,)1b q8:d )cmoment of inertiaob)ndw b:qp,8cs1 t o:qu kao)m.* +af 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?