Angular displacement is usually e s,k y3ddc-z*express in units of

  Angular velocity is expressed in units ofbda*h8 nfp50n

  Angular acceleration is expressed in:zv:1)yb srod/n xle9 units of

  A boy and a girl are riding on gx5o0 cs-77tby qh ;jca merry-go-round which is turning at a constant rate. The boy is nea 77qhc;jx y-5to gb0csr 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 -qjyl bl7y82j-kl0vo turning at a constant rate. The boy-y270l8 bovkyjl -lq j is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a condivoeu74 ,8vc stant rate. The boy is near the outer edge, and the girl cdo7 iu,8vv e4is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding *rdk*pgqkwm3+ b(z p *a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl pd gq*mb *rzkkw3*(p+ is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a lu ;idmk7ylz3 e.;dfss g+pj6: az +r6merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is clos . rmdfi7j;6 s3+ 6y;:l +elzspzgakuder to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of tl 7h)f4lkerdto : j55whe following is an accurate statementwtj55 )lkf4 oelr7h:d ?

  Rolling without slipping depends o(2kxqfvq f d63n

  Two equal forces are applied to a dmd8iihg g vaedqfrd4z - 19)s sr31t1vlj6c ,.oor. The first force is applied at the midpoint of the door; the second f 4c sv.fdegad1i13 8zlm,g)ij- sd1vtrqh r96orce is 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 the doorknob. The firsofc ow9/xee81t force is applied perpendicular to the door; the second force is o xcfew8/oe91 applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to th8t d-y9ecg (esonz):ee door. The first force idsg(t89ezc-yee n: ) os 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 objec6.m+pktw,wm / qde. ow7up)eut's resistance to changes in rotationwpw6.ewu . 7)q+m/,m o updekt?

  Consider two uniform solid spheres where both have the same diameter, but oni qsi; 5zti20t*v)wjle has twice the mass of the other. The ratio of the larger moment of inertia to that of the smalle)i5ti0iv *2qs;l wzt jr moment of inertia is

  Two uniform solid spheres have the same mass, but one6q j03accr z5 /envd1 mw8ip9a has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere e96 djn 1qpz8a v /car35wc0imis

  Consider two uniform solid sphe7n ng6rqe./dh ni*um)res where one has twice the mass and twice the diameter of the other. The ratio of /q7e6 rud)m n*i hgn.nthe larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius h/x:y.n2ycq w R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a centraqhn w:./y2xy cl axis?

  If a constant net torque is applied to an object,j*p5vflhvd2m 6 uq5b0 that object will

  The moment of inertia of a solid cylinder about its axis 3u:a /wcg d,a1v 5mbiois given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinet1a3,i/ w 5moguav:cb dic energy to its translational kinetic energy is

  Consider a motorcycle of maqm(lkd.ypf9 t-ia423cc t. p- ke1qvlss 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What i9mly.kf1at(v2k3 dqpil-te- cp .cq4s the ratio of the rotational 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 witho 67om)ugp(zgj35 , g ee4stxmkut slipping down an inclined plane starting from rest. The linear vel5)o p3sgt ,mg(74zx kmj geu6eocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls 0 qf vtyz j:83+-qk weoea8hi+without slipping down an inclined plane starting from rest. The angular velocity of the sphere at th :qoiez8f th 0ae+yj8vqk3+- we bottom of the incline depends on

  "The total angular momentum of a syst1dj3sav4s0 y( 8h gsafem of particles changes when a net external force acts on the sysavg(a s sh0fd481jsy3 tem." This statement is

  In what circumstances ca3anu u()yyi 1b-vr y+hv;nz r1n the angular velocity of system of particles change without any change in the syu) n- (zvn13yry+u ;ya hvibr1stem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which m z ..wtz-4dc;rnm9akcay be present. What happ.;9rmdckza- w. zc4ntens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipticagk3 u:gfoe 5*pl orbit. As the Earth moves close to the S 53pkgo:u gf*eun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirw* )hl2rc p8 a4prdm+yeuww98ouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentumew cwr+da4p 2hy)9r mp w8u*8l about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstru+gr q8ah7 7o93oy zv 4cje/ygetched arms close to his body. What happens to his rotational kinetic energy about the axis of r89coy7yugezv /g hjr4a 3+o7 qotation?

  An ice skater performs a pirouette (a fq n/9y7-qhor cast spin) by pulling in his outstretched arms close to his body. What happens /cqq7 r9-y ohnto his moment of inertia about the axis of rotation?

State the law of conservation of ,7.es hb u anyi)f2k:fangular momentum.

  What arc length does the Earth travnbvtl /b;34 9lwp2ihjel in a three month period in its nearly circular orbit about the Sl92v4niwt;jpl3b h/ bun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 03;yel 9btrj. h.30 m. What distance does the tip of the second hand sweephrt3;j .lbey 9 through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minum . xmi.flt1j(te equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 40 igqz)fqw):c.0 s. What is the frequency of the wheelgz) wfc0: qi)q's rotation?

  A pulsar (a rotating neutronkgxu 1 -bf)b gkq00lu7 star) emits pulses at a frequency of 0.40 kHz. The period of its rotatiokf)gx 7gb-lkq0uu01 bn is

  A phonograph record rotates at 45 rpm. Through what angle does it tnhfd3*/: wuk gurn in 0.20 s3d:f *wknguh /?

  A wheel of diameter 26 c66yv5, shxkbl uo9zp8 b9ub o1dm 8o n-p*bs9cm turns at 1500 rpm. How far will a point on the outer rim move inx,obspz89u n1 -p69shcd96y bloo*85 kbmu vb 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions inf lbg+rpod6v )m++g 5 oidf(at9l, p-u 4.0 s. What is the ig5lu9ad p6fg+vd-rf) p to,o bml++ (average angular speed of the wheel?

  A bicycle wheel rotates uniformlyzs5 sjpim/; om5/l f59w*vt if through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from thezov5 /9;m fmi5*5s/f ptlwisj center of the wheel?

  A cable car at a ski resort carriei j(:nffzg m z+u w/:x;yh8d;js 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 slippage, how fast must the p i;jz(:hn8:zxf ;wfy dm/gju+ulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1. 7qsdm+aa*u .o0 m is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a pointdaoas7*um + q. on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0 f4lujbf 0yz6d.wax. wst4)rv vl3 7k5.16 m in length. If the motor rotates at the rate of 20 rev/s, what is yv5j.d 7akwbs)4lf xuz4ftwrl6 . 03vthe approximate linear speed of the end of the cord?

  A wheel of radius 1.8kw4 k1 parm6pnl./ ig0 m is rotating with a constant angular speed of 2.0 rad/s. What is the centp /rwn6kk 4imp ag81l.ripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceo5 byxem g6.p0m5wvq,leration of a point on the perimeter of a bicycle wheel of diameter 70.gv qm.,peb0ow 5my5 6x0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stationxsyu7v5ytob + ;6xec. (r = 10;vx5osxyu6y c+.t 7b e00 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circ 3*a4ggw0ymc i.ai68xp .rpfeular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (progc4iw.yr 8mex6gp pa.afi*30vided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flatg7)5es4c8 a6v aeeksk circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) ckee agvs)4 7ake6s 58is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m*drnhuxq r ole5,1*4d string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum lineardu4 nqx ,ol e1*h5d*rr 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 rolls witho bw+e*zuwpbgxa,r6u+ c2a9) dut slipping 10 m down a lane at 4.3 m/s.6 +c*xz urb+bae ),wpd2g9 uaw
(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 constal5)5sabuexa7f1 ey f 4nt 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 const3 s4dt uqsyyzu(:silo66)hm8 ant 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*tsx (xvge) *e-m radius automobile tire rotate after starting from rest and accelerating at a constant angular accetx(* evx)gse *leration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hart1dlfv;) u q+s 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 dece3wc2n g7ar; hmlerates with a constant angular accelera 2 r;hag7nc3mwtion 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 of 6.0 rad/s b cnw xs*jv-,bv8y;6u while turning through 2.0 revolutions. What is the average angular acceleration of the wheel?8sw,6bvbnc-j*vy; u x

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 j w9dr)6dw)uomdjpboe( 15*i m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in jup9ow(*o re bj)dw615dim d )coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from y)hpg1 2hp +pl8.40 m/s to rest over a distance of 115 m. What is the angular acce1h+2 )ppyh pglleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over a(nt(n6p-rsp p distancen-sr(pp t6 (pn of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationzv y05jdm ,v/qdmwts 2 r/6s(nal speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant anguljv/s5n zqd02mds rm6 wt(v y,/ar 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 requirl+ svdfcw mrrg.a;mn8fj95 (+e 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 is perpendicular to the md5(rmc8fj9+s. v+fr w g; anlwrench?

  The bolts on a car wheel require tighokenkaznc8k7b h ),wg6ts+,e7t n.c ;tening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forcneb,en k87)n 7kctz,c+.hg ;kws ota6 e applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiaqieyqj 9gmn*gxb0 rh4rt f1ocf5c. mc4 )245k $3.00 \; kgm^{2}$ 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 m68j bv1f)yu bg k38r,py3k 2em sfz9qtdcx2o+ is at the origin, mass 2m is at38)+kft,sfxbgdu c p6z2okjb2 3yyq1e8r vm 9 x = a, 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 frictionless al6 d3r:vq3 /5cq xnhtmxis 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. :v lm/x3q qc 53rt6dnh (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted abju*rlk) o/lj+out 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 d*+ur jo/k )ljlownward. 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 p )ufi.b 94ddpend. The rod is initially held in the horizontal position, and then released as the free efp4.d) dip9 bund 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 cm and mass 1.5 kg. Neglec+xv dszg2on -)t 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 linearx+dngz)2 v so- speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapckxqo/t-0 ns zj.(kft- wdb-kf6n2 x 5ped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pull-0q/toxk6( 2nj sdcfzkw--x5b.f tk ney?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley y+ ;6gps6h x:f*e ,l4fswlklv yfr)a2of mass 7.07 sx6vale* hp ,r f;)+sw:4f2k6yl fgylkg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is aa )bgzg;wr 0 d-zrninfv(6,c 1-1qfsrequired 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 :vv) g1 z8h-le5-xj jc dgxy-ninertia 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 from t( qfouv2) z*o;c:qfzrest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bot*qo;czzf ( 2ft)vo:uqtom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls :nrkx8 j.)(g k2alea hwith a speed of 10 m/s. How higl:k2 kn)j(ahr.eg x8ah up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.206ofgjqb5/4bj+gecz t: a3/nt kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a o z/5 +gj34a:6gt jtbq bfcn/evertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and rxphj4mwd85h rkey i :*q4v2j) adius 15 cm rolls without slipping down a 35e incline that is 7.0 m long.485 i hvmd kjqhxe4y2)rw:*pj 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 changes8q3 / t4cbt-wpc,tnt .f9 unut 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 inertiaihhpbw ,-4c* ,*wfb mq 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 moment j6w (9sv(xhjl of inertia h((jl9 vxs6wj 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?