Angular displacement is usually expresn 84y 6 *1b9whzpqkz hjsb4mpep)ny38 s in units of

  Angular velocity is 0c jriagp8ko;8h*v o9l (hi4gexpressed in units of

  Angular acceleration jb dp9d; wz6aur7 3uq0rpkl(7is expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at ajm 5 +tqjyjao::+/g wy constant r oy5::wj tym++g /jqjaate. The 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 ribzszenhkcmgd+7an :3f )* )p.ding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and th.*)fhempa )3 zdc7sg n +:znkbe girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merr)88 2 7kdnam-gw.tntwl gy1swy-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 greater linea. ktdgw 7w1 lgt )waynsmn88-2r speed?

  A boy and a girl are riding a merry-go-round which is turning at akdefhnpf 2e:63t9zm q:j t4 o-r.ur2 +qt ktb1 constant rate. The boy is near the outer edge, while the girl is closer to the center. Wt1k.:tdb9 q32et mjfrzteu6:+ n rp-qh k4o2fho has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant rat7m xs onzk/xuo (5y91itimy, +z4 x9pqe. The boy i5uzik4t+1 szx9o/ypn 97mxmo(qy i, x s 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 fono g;u)((e-h vd. kd/il n4nvyllowing is an accurate state-(vk ol. dd;( gye uv/nn)n4himent?

  Rolling without slipping 6of49n+ w7puewcmpm1 qqwif) ia,06h depends on

  Two equal forces are applied to a door. The first forcbh,0fye6 h.r ne is applied at the midpoint of the door; the second force is applied at hy, .h6ebfr0n 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 the doorknob. The fir 9 a2iv 88mnxmqwp/u7xst force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force e7muvanqp m8x82/9 iw xxerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the d49, fn+imekc f (8xlu (yf5ttsoor. The first forc9x+f u ftif ,5sl(e4y8n kt(mce is twice as large 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 m *9,bswx0s,ecrm uu)resistance to changes in rotationb*uu9ss ,me) r0wmx, c?

  Consider two uniform solid spheres whe8oh-;x azqpy/i115r : : xqdyjjgbh-ere both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of iner-qpo/1yxh 1 egjd ; bz q:yi5ra-8j:xhtia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radiu te nin8yz )35ivny99+fjl. wfs of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere isjtiyz89l+ wnnf)3. efn9i5y v

  Consider two uniform l8ji u:bs7- h7an 8rumsolid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of thauhr b8j-7 :mi7lnus8e smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these cx(*cm5mr ;bxad*mz p k1/fp*are increased to 2M and 3R, what happensk(pcm*am1xzx f;d r*/c pb5m* to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that objk9hk ddmc*do+ ( jt 14pjpf-:vect will

  The moment of inertia of a solid cylinder about its axis is givenj 7s uy7cbly-fbq 6j1pg-t;6 a 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 r fv(qb8r8v+amd-(dvo0 f x7.5mypbemass 150 kg, 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 th(xr a 8db-fmve57ov8f d0yv.p+ rq b(me 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 down :gmg u 9 4xc+lnrg93hfan inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline deperl:n9hf 3xgcu+94 mg gnds on

  Suppose a solid sphere of m1mb5 7xpy8q .a qbh-qwass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of thqw1hb m75p b .8axy-qqe sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net exteiv5jc hj ywb*917k5u yrnal force acts on the system." This *yvcb5ky91u 5jhjw7i statement is

  In what circumstances can th-,3u p c-kjvo jusz0-ue angular velocity of system of particles change without any change in t3c sop-uvk --j uzj0,uhe system's angular momentum?

  The Earth orbits the Sun in an elliptical h+.qfi: i0rn6l53ylyy u7 tkaorbit. Ignore any friction which may be present. What happens over yrhlay f3:qu 6k+.ii0 5nly7ttime to the Earth's angular momentum about the Sun?

  The Earth moves abouqvo8tz,v) n(piy: 7v vt the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbitip(tv 8:zvvn 7,ovqy )ing speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in vx3ccfys x,2s+ b a41arr2q-zhis outstretched arms close to his body. What happens to his angular momentum about the axis of rota a+q c1 sr3 vbs2,r24xfycaxz-tion?

  An ice skater performs a pirouette (a fast spin0-i kaqu4(e yl) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of q0u4yak -l(eirotation?

  An ice skater performs mw7cbf y4 ,jq-a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of r y4qcf jb,-7mwotation?

State the law of conservation of angular momen q7/ua vn;emg5xrb +:dtum.

  What arc length doesdah-br mq5eb /e mse:qk 1v741 the Earth travel in a three month period in its nearly circular orbit about tevbeb 1h4-emasr 1 dq/k75q: mhe Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. cc3cw a d8-am9What distance does the tip of 8c3 aca-w9dmc the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivh -ytd/v.s ve /z c e7jui-r5jztyb:*4alent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.m )up) dda/emth4y:3o What is the frequency of t mdtp3duh m)o/ae):4y he wheel's rotation?

  A pulsar (a rotating neutron staarv4sao3zj/la(l6 +d r) emits pulses at a frequency of 0.40 kHz. The period of its rotats (a4laarzod6j v+3/l ion is

  A phonograph record rotates at 45 rpm. 6ki se 9bf fcyr:e,5t4Through what angle does it turn in 0.20 s? ec bf,yfe6k9s ir:5t4

  A wheel of diameter 26 cm turns at 1500 rpm. How g,c m w/u+,h+nein 3vl9uasu/far will a point on the outer rim,+nh,/ulvsc+nim 9eu w 3gua/ move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W1i/d pfmuqyb(s+- 6sa hat is the average angular speed of the whs-/ 6y +bua(1 mfispqdeel?

  A bicycle wheel rotates uniformly through 2.0 revol9z oulgpr0-g 0utions in 4.0 s. What is the linear speed of a point 0.10 m from the center ozg -l0puo0g r9f the wheel?

  A cable car at a ski resort carries skier p:cts*d5pk-r s a distance of 6.8 km. The cable which moves the car is driven by a pulley with dip std5p crk-:*ameter 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 angular speed of 2.0 rad/i4i:qn b:(i -d5ix7 a/lxvsrbs. What iax:5v d:ns/ 4li-7bxirq(ibis the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If tk j2k3dh58opc(yjdh+he motor rotates at the rate of 20 rev/s, what is the approximate linear speed kdhj 3yhd p5(8 +cojk2of the end of the cord?

  A wheel of radius 1.0 m is rotating with a5*d 6amw:zvo k 0 b2dia+sysb- constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point oni syk*d20vmza5d+ :baobws- 6 the wheel's rim?

  What is the centripetaldna2 kq 28 +45vtm fhwxu1f. dyta35dz acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bim tz d1+5d2 yn5hxkav4t8ff 3qwuad2.ke is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a: bmvybk e;s*i:69k hv circular, rotating space station (r = 1000 m) rotate to produce an artificial gravi6:hk9;y*v mi k:bebvsty of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radw,id 3h,rlvu-/s 1qjkco+n/n ius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static,/cv/r siqujn, + okl31-hnd w friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circ-v9 e dun ln1n,kp8/k:z pgvt 7gub:;wular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force u 8:z,vgn;n1tvul:p7pgwe 9nk /-b kd(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 oxy9hqa2)xc* 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 cay)2*9xq aochxn the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radiu l 6r tvvk ,rvq1. q9ut2;rdij+1qjy*ts 9.0 cm rolls without slipping 10 m down a lane d*u yj2 ;qkrtl1jqtv 1i,rq+ v6v t9.rat 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 constar(n/ t r0 f4(wcw.-qpwikklw7bb sa),nt 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 angums.pw ui9wnguxpe- a j1,q/;8lar 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 automobile q77coum1w -zcko2ge. ras :; ctire rotate after starting from rest an ao;27og7 eccmksz.w-u 1c: qrd accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratd2 h+f 2v;yvbp4* yhtwion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/suyfkwo -emr,j* n.l y5:k83dy decelerates with a constant angular acceleration re,-jnyw: yy.m8 ko kldf35*uof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reachetxi5)6d6 weihs an angular speed of 6.0 rad/s while turning through 2.0 revolutioie6xht 5wd)6ins. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s -;p .- yk.b8 k9qq puajwzjb3gto rest over a distance of 115 m. What is jp-; ag3.p k9bwyq-u jz8q.kbthe total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slw-hs.dkq,k+k 1qvw 9(gpcn9 nows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleration?q-kw9,nqwph( . sc+vdkk19ng

  A wheel of diameter of 68.0 cm slows down unifpkz zyu2 n7;st;.wf3gf4:ytxormly from 8.40 m/s to rest over a di;z7 f4;:zs ny3tfxtp2 gwk .yustance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotatel nf csth4qtm5z z g.),nhc f1;,jlx9/4:rkkus at a rotational speed of 3600 rev/min. When switched off, it rotates5tlk)4x,j uzn1zh,4;q stckfn hrm.cfl9/ g: 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. m, 5spw2)w hfwokmh* 3If a 30 cm long wrench is used, what is the magnitude of the force ,fhh*mw2ws5m3pk w o )required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a to: cfpqb oz 2il+jyw2,(37h g(vlk6 nvarque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force require3c (hz7 6g,w:fbqkyvj+nla o lipv(22d when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine7 w(70dpck; y f jqub4uhj,,nertia $3.00 \; kgm^{2}$ 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 2mw;mswuo .b ,xxkdl9d w+.m4 x2 is at x = a, and, mass 3m is atxmu wddl+bswx,ox w 9m. 24.k; x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is ps7-m +,mcuxav iv(ep)l*am 5x ivoted about a frictionless axis thought the center O. A rope wrapped around the outer )5ml+i v v xxaem7a pu(*,-scmradius $R_1$ = 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 pivoted about a frictionless axisk *6d4e2pkcdpk 4ms3/juv.w h thought the center O. A rope wrapphvsd mc 6*kk4/ wdp4 e.k3upj2ed 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 e cz rh/7.mvd6ynd. 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 ihv/6zc7d rym. t 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 1.5 kg. Neglec+li.sp59shj.m1z3 ftk)p qk rt the mass of the axle aq+st1kih.mz )lk3jrs 9p f5.pnd 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 arp6ky1nx 1c( enp);r fx1+yr peound a frictionless disk pulley of mass 7.07 kg and radius 66 epfx1p)nnxkep (r1y r; 6y+1c.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a cyu;zqkdb+. ;frictionless disk pulley of mass 7.07 y+kcbz uq ;;.dkg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. x e2ipl -o.+bdq ck2)e 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 inertxp 5blnqw.np- glve3+3 c (dp:ia 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 razk) c xf:nt9z. 4q(rkldius 0.010 m starts from rest and rolls without slipping down a 1kzkr f ltqnc.zx(:)9 4.0-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/*9 fso;o:ldozos n n/ 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high u*z o dn//soo ;9sfo:nlp an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is y:y3 c+ufjvp0 released from rest and allowed to roll down an inclined u: c03f+yyjv pplane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls w6wyob kjse,qthqfj 0 +j. 87e2ithout slipping down a 35e incline that is 7.0 m long. Assume it started from rest.o8 6jkqjj7fy+2 0sewhb .,qte 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 chnga um;b3 i()vanges 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 momgh6brp 8, zb 1-2rfdwment 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 5.0 e,l +q*gz7mwd0 rad/s with arms extended has a moment of inertia ofl+mg7e dw *,qz
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?