Angular displacement isw;v 0x 1z8bju zris1u, (twtx8 usually express in units of

  Angular velocity is t 1vj. c9gtqj;expressed in units of

  Angular acceleration is e qlru,9c7 n1pf(99k zat6zsvuxpressed in units of

  A boy and a girl are riding on a m36rf4hej p2u6ghbd ;dtl l,2merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the great 2jlb6dm e gl4h6p h,2ufrd;t3er angular displacement?

  A boy and a girl are riding on a merry-go-ro er4met04-cd gund which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center.-d4mre0 cgt4e Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-roundko.f) pkd:hs-o:k9zf ,prq) 6 zgaj ;8ju8ve f which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to tooh.g:p :s8;fu8)k, zz) 9v-dffjkk jq 6repahe center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-ror23h- ) yv7s(gzd fug:0(lcpl wet f7bund which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to th: sf (-b zul)tflywp2(c7e7vdgh g3r 0e center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turninpbx0jpu 5 k:lb 7+lrzp y199cag at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tanxp5+k9acp lby:j 70z1p9b ru lgential acceleration?

  Consider a rigid body that is rotating. Which of 4 29(gln rortfthe following is an accurate sta2orn(4lf 9gt rtement?

  Rolling without slippihhf az87/n s/jtxt-a7p6c.h u9 86asxs.moz eng depends on

  Two equal forces are applied to a door. The first force is applied at the mihhehm 9u-11j+ 4siwlzdpoint of the door; the second force is -jm 1hw1 lhhsiu+94ez 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 at thn y+oy(rl rd9+e doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the +yr9+nr dlo(ydoor. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first for p7-lkk8 4mh0 qlm8ndgce is twice as large as 7g qpkd 880n4kllh-mmthe 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 rotaqhz:il.m(u0k *+8cu0wkai kh tion8* qk l+:(i h kah0mw0.ukiuzc?

  Consider two uniform solid spheres where both have the same diameter, bu6x(bai 448 mye ;trpert one has twice the mass of the other. The ratio of the it;e6x 4r8m (rbeay4p larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have tcov /r;*qu 2bbze,(ol he same mass, but one has twice the radius of the other. The ra(c,;b obo2*r u/evzlqtio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres +,:e* 7adjox;lp4maqta k f( hwhere one has twice the mass and twice the diameter of the othe oafq:pte*ka(7xl h4 m ;+adj,r. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphey ,*iul ye51cne0y wo ,mleu77re has mass M and radius R. If these are increased to 2M and 3R, what haycmn 5e7l,yye 1iluwu* o,7e 0ppens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that objr6 +l + s*w2cx0lpc7 (uy3w4cd6t xkajke:o yoect will

  The moment of inertia of a solid cylinder about its 1 xpi,gg3*bxy ,y 3kawaxis 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,o )je w/tw2a3/6 ;frej0zdh gp one wheel 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 wog36e2zh ej tw /r0a/)jwdfp ;heels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping: g.7g7y p1z4g0 blafhvi 6tsq(ln,pv down an inclined plane starting from rest. The lineg7y vp:la67n t1(.,ibpfgv 0zls4h gqar velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippit+ nr8b:f 1xjh qyd uh(2u3-erng down an inclined plane starting from rest. The angular velocity of the sphere at the bottonx+qu 2(ue:hht 1r3b-d8rj y fm of the incline depends on

  "The total angular momentum of a system of particlwlm 9,fly *8j3wxy;) ipxl,hibw- xh5es changes when a net external force acts on the system." Th lj mfwi wl x8;p 5bxh39xyl,*wih,y)-is statement is

  In what circumstances can the angagj -l qy8:;urular velocity of system of particles change without any ch-j:ar 8lu qy;gange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbiq h)i(svv t.so/nyl 44t. Ignore any friction which may be present. What happens over time to the Eli)t s/y44vv q nh(os.arth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As t*dhgk8nno *;ea*n zg 0w9kym7he Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth h7g *0*;98mgy zk o*aeknndwnabout the Sun?

  An ice skater performs a pirouette (a fast spin3 g qldj1js/7cfvb .wbo05;io) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotatiob w .;jlcv qjf/id1bo7o 35s0gn?

  An ice skater performs a pirouette (a fast spin) by pulling in his outst;uvcd( v,km j,retched arms close to his body. What happens to his rotatijdk;v v,u,cm( onal kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in h9d :sy(wao5ybis outstretched arms close to his body. What happens to 9sy do: yb5w(ahis moment of inertia about the axis of rotation?

State the law of conservation of angular moment)5m (f)xrvru)pr mi* dum.

  What arc length does the Eart()9pz4nuso il f3oe8t h travel in a three month period in its nearly circular orbit about the S)(toel94n sfou38p z iun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dis :lwun 9n/e- jnub0w)rtance does the tip of the second n:/b ul 0)9ennuwjrw-hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute1o2 cob y+fjys0zug-1 equivalent to?

  A bicycle wheel rotates u( +km 95zq6ivv,t6sq a+vid sj.m2mheniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel'd qjvtm.zek vs2hmia,v9s i6 +6m 5+(qs rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Ty-u8q mom* wyn:(w0co he perioy -nc8(m*0qm wy woou:d of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle doe.** aweq4 fsbps it turn in 0.20 s?*apb ew sq.4*f

  A wheel of diameter 26 cm turns at 1500 rpm.c3y2)d6 3t arzon 0hjkwpz,t7 How far will a point on the outer rim move in 2.1 s36j n0rd3hkap 7tycwzo,z2)t?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. bw3 k evyzlz, ye;nkh(wyf 6v h:6-46hWhat is the average ang-; bhhznyyk:e v( lzw6 hv3,fkey4w66ular speed of the wheel?

  A bicycle wheel rotates uniformly thrd, m0 d- dra-(hn1ddubo)mn6hough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the a d-nn )0mdbo1rd 6,(dmuh-hd wheel?

  A cable car at a ski resort carries skiers a distance of z 26 /ep pcexc+e84bvi6.8 km. The cable which moves the car is driven by a pub4pceei8c2ve+ p/z6x lley with diameter 3.0 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 angc6sg7rrd)+;3 eh(z p3xc udb uular speed of 2.0 rad/s. What is the line h+x)cg(3sc;rpu zrudd76e3b ar speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutpn4v9 s0rc/ o2n( sgyrter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of th2 nrs 0gp( ncrsy/vo49e cord?

  A wheel of radius 1.0 m is rotato (9s4-j0a3volyhnz ping with a constant angular speed of 2.0 rad/s. What is the cyl 34- sv o(0pazh9onjentripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicye dyh7i54.azt cle whyi4h.a dz 5te7eel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statioaodu5.hf.j)z,/n x,v.ll x m* l1ut dgn (r = 1000 m) rotate to producex *dldlmjtx .n1 ,l uao5fv.)z /.uhg, an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of rlgp45llq4gv*i : i3siadius 50 m with a speed of 20 m/s. The maximum centripetal fori5s *:pgg vi44li 3qllce (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 speed of 20 m+ w3u z, 0c)6uu1cnm 6qgezlcf/s. The maximum centripetal force (provided wc)601e ucq+fnuz l3gumc, z6by 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 of a 0.7t,j/as/3yjty1tbk ts6t c,y2 50-m string, is whirled around in a smootttkbtcsja/ 623, ty /y y1s,tjh 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 not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm roln,mtkf 3 p/tr5r; avk/ls without slipping 10 m down a lane at f/t5m k3/nrt;kp, avr4.3 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 constantn*yt ab6 1 /mdziw1pm( 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 an2juo(a:o;ss6bjcw. xgular 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 aqrj.jmn 7-:jralk7 / lutomobile tire rotate after starting from rest and accelerating at a constant angular accelerati7mnjr7j/ljq:rk- . la on of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has in ,4+uviw/i a5wtg n1an 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 decelerates with a constant angular ac* 0i :lsy(vdlrp+c vifbcj+; (celeratio py j:bsd(iv+( * 0ri+;lcvcfln of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed o()c eweh l/,pj i16glff 6.0 rad/s while turning through 2.0 revolutions. What wl ig) ,(1cfhp/6lj eeis the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down ub:t .am s(on2d5(ys9j lc +nwoniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in l (. ao5sn(djnom +syt9bwc2: coming to rest?

  A wheel of diameter of 68.0 cm s3 jcxu /m1-egqlows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is m-/ u cxgqje13the angular acceleration?

  A wheel of diameter of 68.0 cm slows do wb;5h3tbjkb*apxn:o ;+m e:9r r6ppuwn uniformly from 8.40 m/s to rest over a distance of kbr;xbeoptb:w+:63*59p pnhj a mr ;u115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a mediog c2,fg0laj0; hocs :cal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times ;clf, 02ogo:a hcgsj0 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. *lz;/ibt+ qv8wb2*ufm;p wgd If a 30 cm long wrench is used, what is the magnitude of the forcdip; wbwz+ bt8**fqlm/;g u2ve required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a tpumy :grpeovd*h qt9+2 y-,n5orque of 90 Nm. If a 30 cm long yn-ogpr ev:d5 ym+2,t* 9pq huwrench 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 in kyi45 ge;l1cyertia $3.00 \; kgm^{2}$ 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, m.kbq70j 4qd puo),zwlass 2m is at x = a, and, mass 3m is at x = 2a. What is thepk0lozjq.qd7 )4 b,w u moment of inertia about the origin?

  A solid cylinder of mass 10 kg d g+xionx:p5 03 mt6ckis pivoted about a frictionless axis thought the center O 5d0cxpmx+6knig o 3t:. A rope 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 ;kxxqn;3f7ar , /:w1dxh1r7dgpw y zu10 kg is pivoted about a frictionless axis thought the cent7qayzhw,;3g/ rw; pd dn1xf1u 7k:xxrer O. A rope 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) 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. The rod is initially held in thg.uc8k kt:i g7e horizontal position, and then released as the free end is allo. g:kkticg 8u7wed 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 radius 30 cm and mass 1j;igewparq4ez65f25 vj3h wsc c(/,l.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is appli ;zpra4/ c2e 6s,vegw lhi j5j5fcqw(3ed 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 acabq4 hm5zq3 :3z qc6hround a frictionless disk pulley of mass 7.07 kg and radiz4m qhcb a63hcqz:q3 5us 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 of3;q3gy r3 5 :catnr ya:8rgrdh mass 7.07 kg and radius 66.0 cm. What is the acceleration of the8rag3qta :ndry:5y3g 3; rrhc mass?

  A rotating flywheel uzg58 s.44br3ap xyum+ma (0dei zb(ncan 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 of5c eum:e k5inm;eyfy1t+1 ( cw 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 starts f1cu sn s0ufbfc6e2.0rrom rest and rolls without slipping down a 1.0-m cc0fur0 2nusse 1bf.6high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1v/b+g 1xmq0hb .0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climbbq/+xmg 01h vb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allotmzo* nz40v *bri *1wi9tr/ p6fvn( rpwed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 9 it(nr zrf 4bo60*pm1in w*v vpzrt*/m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without sl52zkl xe/k6u lipping down a 35e incline that is 7l 5kzu/lex6k 2.0 m long. Assume 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 momentum ch7) h;fh;grmn2n ga f-hanges 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 of .qlx4ld;s:o fut/ psnk.dxem e7.5*r $5.0 \; kgm^{2}$ 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 rq6bom *,5g hxcad/s with arms extended has a moment of inerti q*xgcmo5b,6ha 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?