Angular displacement is usually express in unitlws0xtbu3 (8nk u lz+s wi*y+9s of

  Angular velocity is expressed in uul+ :td: jft4wnits of

  Angular acceleration is e-s 7 zsndwa8z-xpressed in units of

  A boy and a girl are riding on a merry-go-round whic im +0.w4t/g 0c:spkghi ee8uqh is turning at a constant rate. The boy is near the ous tqw0:ukm4/.eh80g+iegci pter 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 turning .w z(nknej2b 8at a constant rate. knw8j.ze n(2b The boy 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 akno;z7 m3aef0tcz my 5 b**l6ut a constant rate.7mn f y3*ebtuk z6lma*c;zo50 The boy is near the outer 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-ro*g -p)8jbg wfkund which is turning at a constant rate. The boy is near the outegw pf*)-kb8jg r edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridinb(g+.* endcx vg a merry-go-round which is turning at a constant rate. The boy is near the outer edge, ndxg .+ebv(*cwhile the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the bmj 4 6gkinq,8following is an accurate st 6q4i8m bkgn,jatement?

  Rolling without slipping depo ce-j;/ y4oi )dek.vnends on

  Two equal forces are applied to a door. The first n13mcdn/, )i ps3u xmh5p+y vtforce is applied at the midpoint of vdy3hncpmsmi p1u x) 53n+/,tthe door; 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. 5jjmavc e;av5mt9jpy;ep9* - The first force is applied perpendicular to the door; the second force is applied at 30e to the pla *amvjy-; mtce v9eppj;j595ane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the4zdrs- 5g7e by door. The first force is twice as large as the second force. The ratio of the torque of the first to the torqub-5 d4z sgrye7e of the second is

  What is the quantity used to measure an objeqf 8y;fm5i i+gct's resistance to changes in rotatio5 8i yqif+;gfmn?

  Consider two uniform solidf-73x u ft9njfjso)4a spheres where both have the same diameter, but one has twice jusn-aftffo jx7)39 4the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have tq 0k/fxt,l -x hrpv;8mhe same mass, but one has twice the radius of the other. The ratio of the larger sfvpx8h/kq-l 0,x;mt r phere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres wherl0l* (i 5tjkgoe one has twice the mass and twice the diameter ofil5(gk0*ot lj the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are inc zur6 2f,l2tdi x71xz*o0qnnpreased to 2M and 3R, what happens to the sphere's moment of inertia aboutort*6x0dq 1fzn,nl2p 2u zix7 a central axis?

  If a constant net torque is applied to an object, that ob55otyfie- yq,5 bl5cq ject will

  The moment of inertia of a solid cylinder about its axis is giveg*mu,6vhuw;m 4)igvh n by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to ithvu;6,gwu*g vmi hm )4s translational kinetic energy is

  Consider a motorcycle of xj)vov4 nrvr,rsy4p ;m,n,/jmass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotation,rv yxsv mrn,/v4rjp,;jn4 )oal kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid spher6+hk3 i 5jy*dnza)4qvq *kd yqe of mass M and radius R rolls without slipping down an inclined plane startiaqkh46d5kq n+* d)jy 3zy*qving 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 rolls without slipping down an inc;k9zhm na*h yum23:ey-,ssz jdno07xlined plan: ,hnuyszax0koh 3e *92m-dj7;sym z ne starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles chanl nhc xqv;0;d:jc ln8s,xz k8w,kd9c2ges when a net external force acts on the system." kj9wqk ;nhddlz v,:n0xsxcc2, cl 8; 8 This statement is

  In what circumstances can the angular velocity of system of particles change wkg51ms3r ia7 cithout c57kr sia mg31any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which mayk/;peh3 b9yck be present. What happens over time c;pyb9/keh3k to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit.oedh3 )ebk rs.vj43, f As the Earth moves close to the Sun, then which of thsro k3je)4e .b,h3dfve following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretw q-qwp.,+y5sq1v o:-infoacched arms close to his body. What w- qi5 +s vqwanco.-o:qfyp1,happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fv l dx;zpn)8.f;mx (ewast spin) by pulling in his outstretched arms close to his mwld ;f)z;8vpne .( xxbody. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs n5rra*zu3nmpn:4v c 6a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the :rnnm63r 4czapn 5vu* axis of rotation?

State the law of cons1*c.v ady 7p4 aqa-ssq .nk-miervation of angular momentum.

  What arc length does the Earth q*9fwr9jur9u5vb4p x )85yqj smc;cd travel in a three month period in its nearly circular orbit about the Sun with a radius ; )rjq9*9 b4c8dvmcxsyqr5w 9puf5 uj of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0. xr leo7:b6o)iknj4rpwc 3g5* 30 m. What distance does the tip of the secow)g5b roc4n7lpj *ke 3xo:r6i nd hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per yr3a;i; .ep, fk: nsoeminute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.i y:1v-n.ok(3j vfeit What is the frequency of the wheel's (:feoni. vy1-tv3 jki rotation?

  A pulsar (a rotating neutron star) emitsz -ip7 inr(n w36bfl5o pulses at a frequency of 0.40 kHz. Thep5iwn -o(bzf 7nl r36i period of its rotation is

  A phonograph record rotates av u;k*r0idg b;ux:c slqb/ w79t 45 rpm. Through what angle does it turn in 0.20 s ikv x0bs/:7qrg; u*9 lubw;cd?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poi)w4,smse *y wjnt on the outer rim move in 2.1 4ejm sy*w, w)ss?

  A bicycle wheel rotates uniformly throf*pn --e8 qaf0ge9b.vv5b gppugh 2.0 revolutions in 4.0 s. What is the average angular spe5e*p gp-v08aqfbbf-vpn ge9 .ed of the wheel?

  A bicycle wheel rotates uniformly throughme 4y ,l3uso:jcmr9q y2/(v t7 uuuo.j 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.qyt:uv ( 4jl/muou sjmo2u 9,cy 3er.710 m from the center of the wheel?

  A cable car at a ski resorome g22hv;/ ;o+6yecwb;i u jnt carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley j+by ;en 2;cmg2o heuvo i;6/wwith 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 2yb v6vm5ug3 3l5 t ;jma8wx+i,hhv5xz .0 rad/s. What is the linear speed of a pxtvzy 86ghl jxvw55umi5v +3;m,h3aboint on the wheel's rim?

  The cutting cord on a gas-powered weed cutter ise aacr:vw7md( y52 zw 8oow+9u 0.16 m in length. If the motor rotates at the rate of 20 rev/s,wroza2ed79v: c8 m wy a(5uwo+ what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is ro9uc r8-59irnvg w,by0gmuw/ etating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a p -yw 9r85g9uc0u,emgvnrwbi / oint on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter3nkcbll;pu // m.;sfw of a bicycle wheel of diameter 70.0 cm when the wumkcf.l;l;n/ s/ p3bbike is moving 8.00 m/s?

  How many revolutions per minute (rpm) m zlnkykwmwtd9k/*o;+ j (7ir .ust a circular, rotating space station (r = 1000 m) rotate to pl(dm+jw * 9 o7/kzrwk.tny k;iroduce 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 20 m/seu81wu ):kohd . The maximum centripetal forceu1uhod) w 8e:k (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating arb2a4ufm7jzc: nhd-)gedi8 8 flat circular curve of radius 50 m with a speed of 20 m/s. The maximum ce87m:f z e)d gbudc2hai-8j4nrntripetal 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 end of a 0.750-m stri3c+v i(5 tk1bylplq9r ng, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear sp+p 9cly bk3iv 5tqlr1(eed 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 sldb52g- l :d,ozrcm52egd5s fp ipping 10 m down a l -pbdl5f5 gsz 2c2 :ge5,drodmane 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 uj0q:w xqqa 8nchabs8p eflk5)*60p5with 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 acco* 2nfqm34v tkeleration 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 after starti*xu*/sb: jy8 cq-k wirng from ruxji*qr: k- b/ wc*s8yest and 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 accele kjubl xsli)(c27v/v -ration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerady( rw q/ ./;nmueise7tes with a constant angular acceleratioiee/sq(u/.mrn; w7 dy n 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 while turnhri)ccw;cfdid gj7ir9qc3/ , 2 3s0hx 80ibioing through 2.0 revolutr7dqgo3/x 3icfij809sh ,0chrbcc;i i )iw 2 dions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformlypoy l3970rlk8awfal 2 from 8.40 m/s to rest over a distance of 115 m. What i2pr8w3lla o0 k9f7yals the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformlc06v e0r92u e skw*dfmy from 8.40 m/s to rest over a distance of 115 m. What is the angular accelerausmwde *69 ce 0vkfr20tion?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s totwjc,u//ef0 x;6g gsa rest over a distance of 115 m. How long does it take for the wheel to come to thcw;t e js6/a,f /xu0gge stop?

  A centrifuge in a medical laboratory rotates atjva89ks 5pd: h a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 sjhv9:p 8kd5a 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 km (+(k0acl f xvbnd:gxog3(9a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitucgx+gn b :9( (afkx(mv0kldo3de of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening majhyr gn11ys/ 6x:p 1ba9k5yto a torque of 90 Nm. If a 30 cm long wrench n95 sarma6hpy xj1:1/bg1y ykis used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine / l2dg72olgk 8/o m2xpm4lupkrtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as2j7cgi 2koemj3; y4lz follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m isjke3jm47 oil gy2;c z2 at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass74o)mxmya ek (x8c8fn 10 kg is pivoted about 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 downward. (See Fig. 8-1.) What is the a4ym78ecm)ax(fkxn o8ngular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axi0h.bipt4nbwv+ ta:bdo-rwu92 i9m4 js thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a forc9+nbb4hd i ba:up w.0trwovi24mt9-je 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. 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 he)gnt+4u uh1rbi1j;d ald in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as i1+)4 dui hbgrau1;njtt is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring o;)fc*ka a.ibm,6g wbbf radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force ofkw*cagfbm i,6 ba;).b 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 around a frictionless fhs3k1ijh:i+ yxca )6disk pulley of mass 7.07 kg and radius 66.0 cm. What is the ani+hk3cjifs x:a hy1 )6gular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aro.z6/aex kjdjj (n 3xn9+ (xk/l -a/mcm) uzylnund a frictionless disk pulley of mass 7.07 kg and radius 66.0 c/(my.-n/ nz m9+n l(ze aucj/3)kdjkxx6xjl a m. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. d x2wntqvwnv k*1:n /mz)lg* yq6n+u ytx-,o9If 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 insn +xyc4w(c x;ertia 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 rest and rolls wgc,(u/y)gydmw+uf )6 izxowa b3ki)(ithout slipping down a 1.0-m high inclined plane. What is the speed m)d ,g(z(3 bcywoy + w)ui6x kiua/fg)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 rollsi mz)a;.ynqf)u ,1 onm with a speed of 10 m/s. How high up ayon,1z) un.mfq ;i )man inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 n4/cz acb 5g55m39qosnj dm z7c /fb.fm and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m35m5bcf/a s94zd b/nncczo.gq5fj7 m?

A solid sphere of mass 1.5 p8.ak0fge* qd6td :yu iwtloi)1 iw4d(n8- uikg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of ad8f-w8ipik)l 6 u1 *ag:(tyt qi.ndw e0 4duoi 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 : .t7:x 4 k7c( a;sxne,rgmhvxibwak,momentum changes 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 mg 8a/: br.hcxkaettx ;:m 0ms1oment 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 5.00n6 :) sp(ripmi rad/s with arms extended has a moment of inertia ofmnisir(6:p ) p
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?