Angular displacement is usuaeu ldt,a.u.odl7 .bca 5 3uj0kp)en/ klly express in units of

  Angular velocity is expso *g s+zn97ylressed in units of

  Angular acceleration is expressed in unitqhrr1xai18 wj+9 rcq7s of

  A boy and a girl are riding on a merry-go-round which is turning at a constanqbe61 z vk :6c7vcc+)drwtdf8 t rate 7d1zr6 +f6dqcbc: vckwvt e8). 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 riding t;3h5obbyob 7 i*h* l bs6jw3fon 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 greater angular spe* 65lfihbto;b7y w 3bsb* hoj3ed?

  A boy and a girl are riding on a merry-go-round which is 8by3hjb7j u5cjy.d pp+geu( )itt9 -eturning at a constant rate. The boy is near the outer edge, and the girl is closer to the.35btie py+j(8)j h guy9jut7dc-bpe center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round wh.at/taa9v+bx2 p 1yvkich is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greateypvx9bak+2 /.ta t av1r centripetal acceleration?

  A boy and a girl are riding a merry-go-round which ikt.9h37f1xfw+rif r ms turning at a constant rate. The boy is near the outer edge, while the girl is closer to the centff3 m+1rfr 7ihwx 9.kter. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is a*17k dqxyf5qd n accurate statement? qy5 f*x7kdq1d

  Rolling without slipping ,qd./kt6gan 0 dul*hc depends on

  Two equal forces are applied to a door. The first force is applied at xm iop k/5h,r*the midpoint of the dh5m /,ip or*kxoor; the second force 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 first forpo( 5mf l1v we1mbrr5h3ta l58ce is applied perpendicular to the door;fv5 5 la 5r1b pw3lrt1hmmeo8( 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, perpendicular to the door. Thes8a6h* cq9 (adjet e qvkv)(e6 first force is twice as large as the second for qjea *6qts(ve ea(d86k9v )chce. 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 chaop b+5t, ik/r; pmazk4nges in rotationi5opb+k,;trp a zm/ 4k?

  Consider two uniform solid spheres where both have thek*t73 )2iwliw2a yqy ll 8ci5n same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller mome *q7ywl)25 iclkt l8yw2 niia3nt of inertia is

  Two uniform solid spheres have the samd+436apeqg0vw,qs rg e mass, but one has twice the radius of the other. The rati drgvpe+0sqqa4wg 3 ,6o of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twihne .2 lahp4xom:b7x5ce the diameter of the other. The ratio of the larger moment of inertia to that of the smaller pmh7xn. 2lxa:o45hbe moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2de/ gz7c+q7bcf6le *d g oyq/9M and 3R, what happens to the sphere'sofzdc*9ql/ce+7db ge /yg7q6 moment of inertia about a central axis?

  If a constant net torv7-xfw3hs7g 3k al .0exc .yqxque is applied to an object, that object will

  The moment of inertia of a solid cylinder about itqa he/1tx55r0mmwe4 ws axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its r t0amx4qw1eem 5 w5/htranslational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheelaz+d9so4glfpx5ep ,y )6vzgz ge 6.e zwk w853 of which has a mass of 10 kg and a radzz. xdyo4fegg k+apv6wpzez 655w9, e l8s)g3ius 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 wheels are uniform disks.

  Suppose a solid sphere of mass M and radi; p*-crvjnn g/us R rolls without slipping down an inclined pla-* /;c prvnngjne starting 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 rmqa1t0hn:cxac g 3s,, olls without slipping down an inclined plane starting from rn, :0smq1actxhca, g3est. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles ch o3 ch5y,no)kbv9ts,ianges when a net external force acts on the system." This statement is osv9n 3hbc,t )ikyo,5

  In what circumstances can the angular velocity dytj*x/a391s w uth9t of system of particles change without any change in the system'sju/9t sad 19hyw3x*tt angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ig+f(fdb a hu1/bnore any friction which may be present. What happens over time to the Earth's angular mom(h/+d f b1afbuentum about the Sun?

  The Earth moves about the Sun in an elliptical 2yasc6- :d6ii0du hc ivh:gd 7orbit. As the Earth moves close to the Sun, then which of th-c:uyiidhv s d c:g6aidh2760 e following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hcgh*qoln0d; br. v+o8l.e 3 lnis outstretched arms close to his body. What happens to his angular momentum a v3l0bl*rdoce hog qn +.n.;8lbout the axis of rotation?

  An ice skater performs a pirf n+ + ums:ql*h (/a/oorvr3jhouette (a fast spin) by pulling in his outstretched arms close to his body. What hapfns q: /lm+vjrh/ +oh(3ruao*pens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) bak4gtq8 5ss 5-ofzp-cy pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of ro fc84kz ato-p 5-sgsq5tation?

State the law of conservation of angulaq0pvg) isu,bl jt9:+pr momentum.

  What arc length does xhri w/,1ze5g the Earth travel in a three month period in its nearly circular orbit about the Sun with a radius ohe 5i1gxz,w/ rf $1.5 \times 10^{11} \; m$?

  The second hand of a clo9gkp k2.aiuhxr1 ), xdck has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 1h.xk9)pd a2u, ikxgr45 seconds?

  How many rad/s is 25 revolutions per minute equivd vy dwe2ua w-/.jan37alent to?

  A bicycle wheel rotates uniformly through 2.0 revoleyr:* e +9uyjzh+fk: bz. s/cdutions in 4.0 s. What is the fz+sk+ * :r/h.y f9zd beyju:cerequency of the wheel's rotation?

  A pulsar (a rotatingv* wh wouztu 1b -nq3.8eimy.3 neutron star) emits pulses at a frequency of 0.40 kHz. The period8 .eho untwu1i *bmyw.q zv33- of its rotation is

  A phonograph record rotates at 45 ryn;hyy;-5w cm pm. Through what angle does it turn in 0.20 cyy hn 5-wy;;ms?

  A wheel of diameter 26 cm turns at 1500 rpm. . 5julbb9ij.h How far will a point on the outer rim movehjb.5u li. j9b in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 :x3i3dl yml;f s. What is the average angular sl;dfyx3l3: mipeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutiosu cef*;fb12l ns in 4.0 s. What is the linear speed of a point 0.10 mul f;sbfe *1c2 from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km.0ed dzwzfwpiqrif.x* -6 : 15v The cable which moves the car v150fze*:. wid- w dpixqzf6ris driven by a pulley 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 angular speed of 2.0 tb a2r gj9r/.mrad/s. What is the linear speed of a point on the wheel's rimta.2 j9rrb/ gm?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. Ig7w m *.wpyyro*7c4jqbr:z9mf the motor rotates at the rate of 20 rev/s, what is the approximat4 jp:rz7*9qb om. w w7mgy*cyre linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating witf0arc5 j: c:kgh a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel'sf:j:g ck 50rca rim?

  What is the centripetal acceleb*i yo+8ay ui:ration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when t+iiya b u:o8y*he bike is moving 8.00 m/s?

  How many revolutions per minute (rpm)pt:cy mc)32-lir b sd8 must a circular, rotating space station (r = 1000 m) rotate to produce an artificic38 bs-y2dr):ltm pcial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circularx+2h5 .p .lce+se j idd,wfi2m,8wfy e curve of radius 50 m with a speed of 20 m/s. The maipcfxsd + ed25.ewi8, eh.j+wmy, l f2ximum 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 circrabcid-q 1p4 9ular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided -r p4baq9 1cidby 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 0.750-m string, is whirled aro qcfn n ,g3r654:ci rmk)xdjbt2 )zj*tund in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what m6:rknbjt mj)z32 4ir gf*t qn5xdcc ),aximum 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 rolls without slipping 10 sz;o5qx2i6 gub m1a; um down a laa2b u61mgq xziu;os;5ne 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 wiv(o0 hly m qbhgo-(0fdg.u3hf x -1nj4th a constant 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 angular accelew: y25wu ee 8nptr;7nsration 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 automo(d* bbvrfg /;cf09rkqbile tire rotate after starting from rest and a rd*f 9;g( qb0vrfc/kbccelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rebhsdud ug-e+,3zv6:yns cli4av8o72djb 73 pst, and 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 decelerates with a constane) dya sjkc2p/9.a2 aqt angular acceleration okd9)./2a2a eqca yspj 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 rad/s while turning((9y/atc z.w wj rvf:g through 2.0 revolutions. What is the average angular acceleration of the wj 9cz . yga/((twr:fwvheel?

  A wheel of diameter of 68.0 cm sltrofp otm1j;j1 2x)6,ea4 g nuows down uniformly from 8.40 m/s to rest over a distancet6x 1nj, o1 fg epa2;r)uojm4t of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows eg0qiz/8d6rps 14bikdown uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular ap6 /b0dqrzk4igs1 8ei cceleration?

  A wheel of diameter of 68.0 cm slow7a8u9v:3 hyeh/3dfww ywp *q 3 iqd:tys down uniformly from 8.40 m/s to rest over a dist39a: wwu* wd3 y/fhyq3pd7 yh i:ev8qtance 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 rotational speed o.y35 orkjybiw+lz1qnd92 yc*f 3600 rev/min. When switched off, it rotates 50.0 times aty9 wc .+yk ozr3d1ql2n*bj5i y 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 whh3x46zwg o6r ir76ese eel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude 7rzerxe6hi 3o s64 6wgof the force required when the force is perpendicular to the wrench?

  The bolts on a car whk)7 tta;0ee fmeel 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 ap)tfk 7e; em0atplied at $53^{\circ}$ to the wrench?

  A wheel with moment of int nsu:q;io /n,8mzzjg*: os* dertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule w20-45t-y vv itxrfqh0,hftu is modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = hqt4v-tf2fx0 wt,v uh0-r i5 y2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted ab/m 2: /9b lh;gmobjbxtout 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 b2h/:gmtmo9b;x jbl / 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 the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thou:mv6c)cf /h y d dyz8rin7d/6ight 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 = dry nfcvy86i)/ d/d6c mh i:z70.50 m exerts a force F2 = 6.0 N downward. 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 rod9pk)01zbcmg7 f 2yfoxw95kwb is initially held in the horizontal position, ck f19b7 w9)m2w0fp zgyobk5x and 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 r7nbjtiy w4iin)jo4x2z-.30mb ik 0e wing of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 22i7obe0nt w i34.mib0j4yz x j-iw)kn 0 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 hangsb(pdld1(bjl y xp 6.c- on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radiux.bdj1 l(c- bpy6pdl(s 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aroul* j,llg0z4dn,9) 6opsl zvuwnd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm0losnjzvw 9dp uz*6,,4glll) . What is the acceleration of the mass?

  A rotating flywheel can be used to. eo)n6nqd .ay 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 inert ri18 3z yyz nxf9a65d9a*tujtia 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 frim 7h9p/nhn 5xx2my p7om rest and rolls without slipping down a 1.0-m high inclined plane7 imp7xpynm n2x9/h5 h. What 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 s:m qsxue rfr70( 6qb4cpeed of 10 m/s. How high up an in4:rcq7x q6bs( f urem0clined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and+ .zi1da8iupd a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is i+uipz da 1.8dit moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls wi;b h4jy 8mmur. 2c;vpn( a5fatthout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere4m 5vj fnh;8ucrbm( y2a .;tpa 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 changes bylp *sriymjz17if4n; ; $20 \; kgm^{2}/s$ 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 fo( nfsm8 )n67fsg3voinertia 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 of ixk -.h;jzlok (i94icvr sd)b/nertia o ikbi/cdzv x.r)(-9;hjk4l s 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?