Angular displacement is usually express i u*nvm4f3 ,/t+av mgrcn units of

  Angular velocity is expres to)whq euog../8ze1hzzyir5*ar4p 1 sed in units of

  Angular acceleration is cas goa15 a)7fexpressed in units of

  A boy and a girl are riding on5 n:-nuem ,rk4rne7cp a merry-go-round which is turning at a constant rate. The boy is near the outer edge ,p:nemn-ru ecr4n75k, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-g kwme:,3;i pnro-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 greatn,pkr;me :3i wer angular speed?

  A boy and a girl are s2cis t0*c/+o7 bakktriding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closa0 cs +k2cs ibot*k/7ter to the center. Who has the greater linear speed?

  A boy and a girl are riding a merryjxd.q6mgh 2x1wle.n , -go-round which is turning at a constant rate. The boy is near the outerq..,6glm 2hx1end xjw edge, while the 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 turning at a5 pxj/z)) kmysmne xj6.zv59m constant rate. The boy is near the outer edge, while the girl is closer to the center. Who hnzexmv)jmkymp5)9j 5 z. x/s6 as the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an1cts8 zdwh,0 z accurate statement0hzc ,ztd sw18?

  Rolling without slipping u f ci:w4 bo:wez-ij)dy;o*-g depends on

  Two equal forces are applied to a door. The first force is -8zzg7trc2r oapplied at the midpoint of the door; the second force is applied at the doocrz7-t z2g r8orknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at d**e bi+l cz8lnrl. 9 wq,qby9the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the8ne*+bz q9.9*b r, ylldwq ilc door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to thmg6 5 0ph fqtml esl*;3jj;o3xe door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second33gxt mo0me; *hsj q 5pl;6fjl is

  What is the quantity used to mease3o - h6ytjo2hure an object's resistance to changes in rotatihej -3y o2h6oton?

  Consider two uniform solid spheres where both have sp+h;j8 s o,x5zoqmw- the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia5xoq+s8, op h;mzswj- is

  Two uniform solid spheres have the same mass, but one has twice the radius of *mn4p)zs vm oa2g t g1uj6*z *pzxs(u.the other. The ratio of the larger sphere's moment of inertia t*upm()az*p.uxgn 61zos zvtj2g 4sm*o that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mas . d-ncz:6ao)uitcpk7y8 h1tis and twice the diameter of the other. The ratio of thc.z-npy a)id 1otk:6ic8h7 ute larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has ma9wjwug.7w )q ess M and radius R. If these are increased to 2M and 3R, what happens 97q gu)ewjww.to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied -9nf67x i wbeb/fe/xpto an object, that object will

  The moment of inerti x1h(4)/lcga hv6casma of a solid cylinder 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 of g; mhlg*5b0y mbk8hsz, dv )ca(np6e510 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? Assumv,;mz*y n5lk m0 (ag p6sb8h5bh ceg)de the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippingg+naiyk2a icrd+z;zy dm/ 4 :: down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline dz; z/gai:: m2k c+nrdayy4+diepends on

  Suppose a solid sphere of mass M and radius R ro (xlqf,d-blgy ba 7q6:lls without slipping down an inclined plane starting from rest. The angular velocity of th q:7da-(flglbyb q6,xe sphere at the bottom of the incline depends on

  "The total angular momentum of a system ofhx32 szkkbj*6k/aqx: g+au5k particles changes when a net external force acts on the system." This statemj*3h6/u:k5 kxa+ xkqg2azkbs ent is

  In what circumstances can the angular velocity of system of particlesuw -: dz6ol2x+hzxb6it z4(yo change without any change in t -(wx6uo2+bzt dizo z6ly :4hxhe system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which mav;e/rj+ dcck) w ),imly be present. What happens over time tkvrl;j c )dc/ e+,m)iwo the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earthuij--x +bqelbi 8(aa3 moves close to the Sun, then which of the following best describes the orbiting speedi8iaqae3 -b l(ju-+xb of the Earth about the Sun?

  An ice skater performs a pirouette (a fastzem*ztlvn109o ph+o. spin) by pulling in his outstretched arms close to his body. . n0m1*t eo9z l+phvzoWhat happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouettxbi+10u dtiy9 e (a fast spin) by pulling in his outstretched arms clost1 xi9+d yi0bue to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pu:swavoe7 k(9slling in his outstretched arms close to his body. What happens to his momentw9svsea7o:k( of inertia about the axis of rotation?

State the law of conservation of angular momen3dwk)6ira)v v tum.

  What arc length does the Earth travel in a three month period in its 2ar-2psizjv + nearly circular orbit about the Sun withsa 2+i-2 jpzvr a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What )n:qs8 u-.t+2lzco1 rgyi/b xcvu1 wvdistance does the tip of the second hand sweep th.vx2 +wub1qltvu8 g nior-1c )s/yz:crough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions phjlga,6yizu 0k+u t 62h,s9r: c)jnv der minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutionsbyfxel .n.a- + in 4.0 s. What is the frequency of the lany+..f xb- ewheel's rotation?

  A pulsar (a rotating neutron star+f;)zn55q1rrik z hk u)qm: ym) emits pulses at a frequency of 0.40 kHz. The period of it5)qry1ih z ;n5:q+zmk mrf)kus rotation is

  A phonograph record rotates -hvn;g -lnte7 zr,7riat 45 rpm. Through what angle does it turn in 0.20 nr-n lh;z,v 7et7g-ris?

  A wheel of diameter 26 cm turnv g)0:nmuc; 8dqilu/ eirjv 39s at 1500 rpm. How far will a point on the outer rim move in 2.1 sn gv/93)q0u:dir vi;je c m8lu?

  A bicycle wheel rotates uniformly through 2.0 revsym).lcd05sea l ztxz5b 1e41bs 8ww+olutions in 4.0 s. What is the average a +zwcswb01dlm8 l1xes5s)b ta5 .4 zeyngular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutionvjje68,jaz o d ,ma-s3s in 4.0 s. What is the linear speed of a point 0.1ajm-j dv,3z, o 6easj80 m from the center of the wheel?

  A cable car at a ski resort carries skier o2h7b5ffjl-a s 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 pulley rotate fjboaf7h -l5 f2or the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatino;gy sga6f a)3g with a constant angular speed of 2.0 rad/s. What is the linear speed of a pointsg 6fo3 ygaa); on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motof i 6 lhdc,c3-ow* /qc.ua.uutxr6p w0r rotates at the rate of 20 rev/s, what is the approh .-wad36rl ,upx*c.oiqc0/ u twuf 6cximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotatin(l kfyj 3hb7h/g with a constant angular speed of 2.0 rad/s. ( kjyh/b 7lhf3 What is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal accelerix51ziu(2 x:sut dl3 lation of a point on the perimeter of a bicycle wheelx23:iu 5xdzsl1 l( tui of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circulara lmt4g/l/ysr. 7qhg*, rotating space station (r = 1000 m) rotate to produce an artificial htsq7g .mg4ayl//*r lgravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of ra17epxxr0.b;scw/ nk 7bpf 4 crdius 50 m with a speed of 20 m/s. The maximum cckx;sr/f e.b1 77pwrnc40p bx entripetal 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 fl6 6h) auu5xi0gf i1gtpat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stgif0aup6i hu x16t)g5 atic 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 :+c:u)g bd vysaround in a smooth level table. If the maximum tension that the string can sygc)u:+db:v 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 kgejlrb+p .(wcl v2iqo8 .d ,op3 and radius 9.0 cm rolls without slipping 10 m down a lane at 48e ,(3p. woi+db .qlcvrl 2pjo.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 constant angux0 ual:nix/- glar 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 anx 4hzp m 97vyol2)xf*p 5j;khjgular 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 tire rotate aftert079nt 0sumf((i yfp)k1bd+wu 2fb cj starting from rest an) 2f cwbu0yk9 m(+(bnfs1fijt 7d0ptu d accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hi que2ya :lw5+as 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 decelerate4suc jip km/+.a0bo2qrv -8 vks with a constant angular acceleration s-.2vjpa/ kb4 i +8mo r0ukcvqof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches yvd6xc +ln b3.yv5hk+me 5z 3fan angular speed of 6.0 rad/s while turning tk5v+v enx6bm3d.hl5+ycfzy3 hrough 2.0 revolutions. 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 to rest ov8th5rgk3u pkov)9zk k36 .utb er a distance of 115 m. What is the total number of revo ) h3k ukt.gkk3u6r8pzo5btv 9lutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8zdb03v *l9z8g6qg y 5owbh)brv du5+x.40 m/s to rest over a distance of 115 m. What ishzydb8u9vvg5r o5bd+qw g*x3b6l0 ) z the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformlckuqx h ,s*cxy3f-,i7 y from 8.40 m/s to rest over a distance of 115 m. How long does it , -ixks7hucf,*cy 3qxtake for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotatyi7m k6 r h/2i( yhxejy)0iz)hes at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a consta)e/r7h hj mikyi xiyy z02h()6nt 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 torquej4) xek8yh6w o of 90 Nm. If a 30 cm long wrench is used, what i 8oy)4ekx 6jwhs the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel r4p/uu8rdit 8 qequire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requi/tp8 uidqr4u8red when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti8b: aqwaf9ee 3a $3.00 \; kgm^{2}$ 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 origi8gy; 2ht/ ckrfn, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of i2;tkcf8 gry/ hnertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a 3bl2ogoy tsnb)g+p9( frictionless axis thought the center O. A rope wrappeb t3py9+go( sg 2o)lnbd 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 p1ox i6klut3c1 *cg3fd ivoted about a frictionless axis thought the center O. A rope wrapped arg3ck 1u* lf cd6x3i1toound 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 bbmrtv+3u,orr9 0 7 s,e(bjbr jx; dd0is initially held in the horizontal position, 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 abobo 3 rrrd;mv+db,rxsbj,t 0(7u0b ej9ut one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and 7l68 q.ib1 srybmfe ob t)c8x;mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 7fo8 ey);q68ci rs.xtb1bm l bN 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 around a frictionless disk pulley of m/r onisqj5(9eass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the puqiesn / o5(9rjlley?

  A 1.53-kg mass hangs on a rope wrappe jwz1sk0ns3ay+ e2i2nd around a frictionless disk pulley of mass 7.3nie21ys2n asj+zk0w 07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it ivr uk,qp 4l4x:s 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 ine6l6-rqr nj j9 d-ghhk.rtia 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 massbu 44tn5sn ve: 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high svt enn54u:b4 inclined plane. 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 radfkgnje5yq,7 (ls:g1x.m1 x dvius 0.010 m rolls with a speed of 10 m/s. How high up an i gxxekj5. sdyn(qvm7,: 1 1glfnclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.2u fgd c;)lk:+w0 kg is released from rest and allowed to roll down an inclined plane. How fastkdl ) wg+f;c:u is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radiu 5z- iuj*fkuz/s 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest ufz5ju*-/ izk. 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 change(k5o 6g;q vepds 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 mom2e5+(aqzc5kvj x *: yvow+bdi ent 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 hlw+hnp:jt pnra jr op6-t; / f1i87c*at 5.00 rad/s with arms extended has a moment of inertia of *+on:/hrhjf-ln aw1pj6 c7pt8p;tir
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?