Angular displacement is usually express ia1ma e -z8-yrun units of

  Angular velocity is expressed in a. bz6cmr 6o55+tw vo l07nlppunits of

  Angular acceleration is expressed in und b mo5zjbsoc-)z 5;e7its of

  A boy and a girl are ridip. ae*6dkxzuv +kr1 5/e*l m4kqtai4t ng on a merry-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 greati*d4ez5ettka+.pq ra6ul41k mx*v /ker angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant 0:pjsd((jz6 mhnfw l6rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angul hwzj6jn sdm(l:p 0(6far speed?

  A boy and a girl are riding on a merry-go-round which is turna:5(alt. ( s+g :stbji uw e-0vevu(-6hg kliling at a constant rate. The boy is near the osb:i0 (ast tvkh(.i6 +:l 5evl- g-uwlagju(euter 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-round which is turning atzpa7o,puw hnk2*jb5( a constant rate. The boy is near the outer edge, while thbjk 52hp7 on,z(p* uwae girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is t1upj-( ktd-r hurning at a constant rate. The boy is near the outer edge, while the girl is closer to the centerpk--hjd 1(tru . Who has the greater tangential acceleration?

  Consider a rigid body that is rotatingtwf4 n,q57 xijpv* oc8. Which of the following is an accurate statecpqon8,jtw7 xv*4i f5ment?

  Rolling without slipping depenf(m(whm35;/t crjk- m7gt ndv ds on

  Two equal forces are applied to a door. The first force is applied at the mi4 v os(.c-xryxdpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Whic(4.sv rxy-ox ch force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. jx 8gtw6 )z;bz7kv,-s cmm e)j The first force is applied perpendicular to the door; th-em z,7t;g)mb)kj vjwc6z 8sxe 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, perpendicular to the door.ps+9w: yzt gt) The first force is twice as large as the second force. The ratio of the torque of the first to the torque )zwptt ys+g 9:of the second is

  What is the quantity used to measure7e17yzo xzr7jkd+ 0p ca0feq) an object's resistance to changes in rotation?7akq 7z0ezf1e0)cy + xjrdpo 7

  Consider two uniform solid spheres where both have the same diameter, but oz1 9 8) )fyni idegna5t0;gotine has twice the mass oft t 8 zig5d9 1n;ingaf)y0eio) the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same massiwas mowq*: yjg6c/b/7e a1p0, but one has twice the radius of the oth 1g j/ya:wqw*aoi6c b/e0mp 7ser. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice t :dbbh(f-xndoa.js ,*wci ,q8 he mass and twice the diameter of the other. The ratiow8b d.qx(nd si,-,aoh jcb*f : of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radiusc obeanas5cx7in 86bg6p*r( c+dj,- a R. If these are increased to 2M and s6,ga8r+ac b(5o-pca7 x ndc6ij*ben 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, thatu ybzil9) 5(ei object will

  The moment of inertia of a solid cyl c-2d (xh2tvdkugsab ;+e:;mhxh:a 4r inder about 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 wheel of which has a mass ofk5q l *1i1 utbwzu0o(c 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic e0( *kcu1 wtq5lbuzo1inergy 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 down ankpm/hv3i x4r8ue /fim7gi7y6 inclined plane starting fromx4yvu/m7fr 37 k8 ge6 h/miiip 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 slip5nkywu1w. xd 8ping down an inclined plane starting from rest. The angular vel.ww 51u8 xydnkocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes wu6v tsdo:- xn4,l(ajw(p ,bg+m byu,g hen a net external force acts on the system." Thup v6w 4j+ aysm,:(b-tn,b(,oxdgl guis statement is

  In what circumstances can the ayzl3c k yd;hhhn 041-ungular velocity of system of particles change without any change in the system's angular moment04n y-huzhhyck;3d l1um?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictionyor*b2j0ks; eym9a3 k which may bo2j3ym;90sayk rk e*be present. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves c)2s(t- d v ;*zbcaq7yxu)kxtz lose to the Sun, then which of the following best describes the orbitads()z7 q2x)c*yv u- kzb;xtt ing speed of the Earth about the Sun?

  An ice skater performs a pirouex78qyanp c +lq ,a.3tjkj4*zftte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotatiof4,3qzayl cn a8pjx*tkq.j+7 n?

  An ice skater performs a pirouette pw p7i+/ j2vic7 w8* 1baeh cx5-kuwpp(a fast spin) by pulling in his outstretched arms close to his body. What happens twu cv* 7pw+jp2-k5h8aec pbwp/7 i1ixo his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche4 v4te i2jv(7(ap3birqo8r ks d arms close to his body. What happens to his moment of inertia about the axis74 4jpv tr(io(ieqav3b8s2rk of rotation?

State the law of conservation of any e+w,tgs uq(2mnx2x3 gular momentum.

  What arc length does the Earth travel in a three month period i pi8,pf.7 :tl ycm)mktn its nearly circular orbit about the Sun wm.: 7,tfpikyptc )lm 8ith 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 theoy26-o-cs l:g xwg; af6bbr x: tip of the second hand sweep through in 3 minutes and 45 secg-:26- 6xr o:af;wcbxgosyl bonds?

  How many rad/s is 25 revolutions per minute equivalen *isd .1uv-jght to?

  A bicycle wheel rotates uniformly through 2.0 revolutions ii5i ue 43on1q:4r ly*yivu;gl: bioko8 c3n -cn 4.0 s. What is the frequency of thir4lgu3bo1 4vic5ck:yl8*yue qi: io n3o- ;n e wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Th+y tcz u6r0as2e period of itry+ta620zsc u s rotation is

  A phonograph record rotateyctd0 9n,1k,ao7o h g lw7(rrxs at 45 rpm. Through what angle does it turn in 0.20 s?h, x,w r7tad7o0g( cy 1n9olrk

  A wheel of diameter 26 cm turnq,t3yljm a7 ,cs at 1500 rpm. How far will a point on the outer m3qjt 7yc, ,larim move in 2.1 s?

  A bicycle wheel rotates uniformly thl2r xr kiem24.rough 2.0 revolutions in 4.0 s. What is the average angular .rixmle422k rspeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wh*2pqf70tj )mkmc vs u.at is the linear speed of a point 0.10 m from the cenvc fkmqu) .t mjp702s*ter of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable fux186 tcx:y.mq )0jce +qinhwhich moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage,0 xh6 :n. xy+ft8eqji) mu1cqc 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 yy9a 45i1o , s0lxdmm8 ir97uic4dgqv 2.0 rad/s. What is the linear speed of a poin l0g94 dymx4c1i 8ys,vi u7roqi5 dma9t on the wheel's rim?

  The cutting cord on a gas-powered weed cutter isas+*u;suj kx( s.8ofx 0.16 m in length. If the motor rotates at the rate of 20 rev/s, (a.sjsu*kfx +;ou8 s xwhat is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotatingvy,1g yj jhu2s86 p+jicdo-xn(ed oev,h k7 :+ with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheelygdjoi2 -pk,sj ouh d evh+:,x(7v+j61n c8ey's rim?

  What is the centripetal acceleration of 23w u9 o 1p-7t fctzhviqq)x4ca point on the perimeter of a bicycle wheel of diameter 27-)zcfquqoip t3h xv1t w94c 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating sp9jstk0:f if99i6p ogqace station (r = 1000 if9qftg9 09ok p:ijs6m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20g:a(kx8a8+b aes e/kne-bq9w x1 gwrwei+ 4k8 m/s. The g x(b +:a8b8eawi84 g/k k+eqkx w-9 newa1sremaximum 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 circularxd1sx3ywmyq 4/s qn6h4;ec(zgdm 5u8 curve of radius 50 m with a speed of 20 m/s. The maximum cenyd;y43/gz5xs 1qdqhmmx(4w ue8 s 6cntripetal 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 enqemj : g ab4dh.18h z/)akqkc9d of a 0.750-m string, is whirled around in a smooth level table. If the maximum 4 akk /z 1qdqbgc:h.m)ja9e8htension 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 r jhk( 2mnl/veocs j.dj8-j5d :adius 9.0 cm rolls without slipping 10 m down a/djs( ljdv 2h cen8om k:.-5jj lane at 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 const,0,xy lv6bzep ant 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 con9;snyk0e o uq+stant 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 radiyxmc254 mb *axus automobile tire rotate after starting from rest and accelerating at a coc* m2b xx5may4nstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and nu gpoh evweu.o4q9,- )3kw ,jq7.ffhhas 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 decelerates with a constant angular ac5.o :.sziicjn 8ue2 ky8mv- haceleration o8h -uiiz osj vcna:m.ky28e 5.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. nssen- y;3dp17x)9l: uvcibu0 rad/s while turning through 2.0 rl3xbd)inu 9; -u1en7ysc:spvevolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.4 xkat(8xc k*(q0 m/s to rest over a distance of 115 m. What is the total numbakxtx c (q*8(ker of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to remx 7lnhtnqhg)m2u1ym gz31 08st over a distance of 115 zlnutmgh 30x ny1q28m1mh ) g7m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over t-:xd jzoe:q3a distance of 115 m. How long does it take for the whetz-:jdq :x 3oeel to come to the stop?

  A centrifuge in a medical laboratory rotates * ,6wyiki+*je6k lmws at a rotational speed of 3600 rev/min. When switchedwk ime6j* wkys+* li6, 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 wheel07z 8ny1qaavgx ) j3/ gste5uc require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force isjq 1guz)t/8a 7nyg30ca x5v es perpendicular to the wrench?

  The bolts on a car wheel require tightening tq1 xdwqd gduumpe *n/ke :c-+-365dvk o a torque of 90 Nm. If a 30 cm long wrench is used, what is theqnwxkgdp6d+u- *dqemv /:5u1edc3- k magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of. r))m mnn wlpjv7cec48j8nh9 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 az83v+tre pmq 0f8nu 2rs follows: mass m is at the origin, mass 2m is at x = zn 2m efuqrrv+3t8 p08a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fr p-y5istfslv )qh*sy2/5su2u ictionless axis thought the center O. A rope wp2 5hus 5u-/vqyist2)s lsy* frapped 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 pivoted about a frictionless ax j7gqikjy 3ev/um0t -*is thought the center O. A rope wrappekg v*uqj m-jt0i/7y 3ed 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 h3*tbxa,mbf/ 7c boyl) tc9h h0eld in the horizontal position, andh9)xcy * hf3 mbtcbb,/o t7al0 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 end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cmaugho .9wa 78k and mass 1.5 kg. Neglect the mass of 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 ac kua h98ogaw.7hieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wr7.lfp(r :l9xp /p tcoxapped around a frictionless disk pulley of mass 7.07 kg and rolp :(prct9 lx/ xp7f.adius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around au9 9om7ouk4/oqrzbb nf njq h 013)m:v frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?nb7qoj/1:uh9fn 4 mk 3b9o0ru zovmq)

  A rotating flywheel can be used to s )j;8*n gf04mm ebtrkp8(jiv mtore 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 in,(nzfkp rp(qbn5d c5 -mxmk04f77hu iertia 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 sta66 jonpx48 4k e;w;w o+qlscb-zwk bq4rts from rest and rolls without slipping down a 1.0-m high inclined plane. What4kwq;s 6cbo nz+jkolxe8 bpq6w4 4-w; 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 h)hg g*qbo 4ft z/5*br3bcc3tof 10 m/s. How high up an incl /bqc4r* ogc3t3hgf z 5t*b)hbined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20fztp mg0.,7bh kg is released from rest and allowed to roll down an inclined plane. How fah70mgb,ft p.zst is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm h- t 0d,dgufd4qxgq5ecw 1z. :rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment ohd0 1.df t4udwqg:,xc 5qeg-zf 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 4xj kt+yte5q 1(qj/uss 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 yvq8o-fmm p3 c8e *s7rv7wbn+ $5.0 \; kgm^{2}$ 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 jd.zz y 80 a7rcw+l z0+fixe1fwith arms extended has a moment of inertia oiyze1fd zr+7cf0+xz 08jlw.af
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?