Angular displacement is usually express in units ofn3yh)griv /5 ,ie zgr6

  Angular velocity is e6bl,hr4wcqr 2xpressed in units of

  Angular acceleration is expressed in units oxr0tcmmh aot55dd6+ (f

  A boy and a girl are riding on a merry-go-round wqm .pjpb7 0nxe l5,7ola; b,dehich is turning at a constant rate. The boy is near the outer edge, and the girl,l 5.p,djlx;aebp 70me7n b oq 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 at a constant 5+/v-tfsz x aerate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angulf-es5z tv/ a+xar speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constantrza z .,6+pb(xd b)+wgatwx3t rate. The boy is near the outer edge, and the girl is closer to the center. Who ba3tx+,6p dxzazr w) g.w+t (bhas the greater linear speed?

  A boy and a girl are riding a merry-go-round whicv l.yufop ;u32t.uaeja0o)ye 1t05 ka q a.(edh is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Whoy3 ;. ajp)dy qo ef1.oaa0 (leauuu5.kte2t0v has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-/vp08v4xpisq:xjvd9, yo z/fround which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to f:ypx voq4 p/, /90 xvdv8ijszthe center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the foa s j)bk;m)hj0llowing is an accurate state j;0)hbmsk j)ament?

  Rolling without slipping depends op sfv2hc26tn9(, dppcs xs7 + wkndd)0n

  Two equal forces are applied to a door. The first force is applied at the mq :)55ciihusc idpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exeqc i55si:u)c hrts the greater torque?

  Two equal forces are applied to a d tc1oabi4/(vyk 2p (e. osx1in0ry;aq oor at the doorknob. The first force is applied perpendicular to the door4i (2 anr/tysqy 1k(xav .o ;0cbiope1; 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, perpe;rf x2j7 uyr5indicular to the door. The first force is twice as large as the second force. The ratio of thyr;5i 2f 7xrjue torque of the first to the torque of the second is

  What is the quantity used to measure an obje23xo b; vunz2;c *rtt+ g-uzqmct's resistance to changes in rotati2*tun ozrc;m-v t;b2x+g zq u3on?

  Consider two uniform solid spheres where both days. ;q1i,dlu4q eo7have the same diameter, but one has twice the e7dioy;q ls1 .uq,a4dmass 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 the same mass, but one has twice th:m2d 9 bgpk8pp/ov*hke radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller so2bk / hpkp vdpg98*:mphere is

  Consider two uniform solid spheres where one has twice the mass and twice theb)idcpc (.2ed*iqo d2iny b,8 diameter of the other. The ratio of8d, inbiqbod(*epdc.)i2 c2y the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has 9jyv43ov n,u umass M and radius R. If these are increased to 2M and 3R, whaj, v4noyu3v 9ut happens to the sphere's moment of inertia about a central axis?

  If a constant net torque3zdvnzq47c8 a is applied to an object, that object will

  The moment of inertia of a solid cylinder ab5hftajq)hy*/xeh f 42out 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,bn 9niksb1. x(nqh) bjv /k11n one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels toh.)q 1 bvnsnbbk nji1/(1k9nx the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rol op2pkn4vhs:s0*z j*soayv69 ls without slipping down an inclined plane starting from rest. The linev ah s2jozp4*k*spo6 n90vsy:ar velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphedo2(1ahp. fhup 9jnf *re of mass M and radius R rolls without slipping down an inclipfju12ph (ofna 9h d*.ned plane 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 particlw2).ge(cawv2g+u2 lhcf n/e mes changes when a net external force acts on the system." This cmeh22vaglgw+ )ec2 uf./(wn statement is

  In what circumstances can the angular velocity of system of particles change25fc i i:nwxfz x; cqthz83u(k6xjw77 with : qj7xi;3 f28kc(t57wxi n6 uchzxfzwout any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whird0 o:ay hc34 no /w2-wb svucmn)7ub;ch may be present. What happens over time to the Earth's angular momentum about the S ayo r4)wocdb ;u:v2sm/3w 7n0n hbuc-un?

  The Earth moves about the Sun in an elliptical orbit. As the Earth mojke5yn2bqw 4dqa(8arx 1c+ )oves close to the Sun, then which of the follj 8a5wyek4q+a)xqn c12(rdobowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouett,u,axmh;mx sruv8. rorf:-ya wj 5d64e (a fast spin) by pulling in his outstretched arms close to his body. What happens to h5f ax avm ;x ,ro6 84sjr:hy.duum-r,wis angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstre4 rboet2ef9ax17l3qn tched tqa er4el7 x9onbf12 3arms close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouettmfx9huv.9;sf)gd6dt l* w0rte (a fast spin) by pulling in his outstretched arms close to his body. What happens tudtd.wgv 0mrxfh)l 9; *9s6fto his moment of inertia about the axis of rotation?

State the law of conservation of angv;, r.mw5/ nzp2ob)ex3)vucl-ex bu tular momentum.

  What arc length does the Earth travel in a three mongieiowk12l +l4a 5z (jth period in its nearly circular orbit about the Sun with+a5llz( 2o ewji1i4 kg a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance9-e;glpn/o1 igfy c r+atwn)2 gs:we; does the tip of the second hand sweep through in 3 minuwa g/ s;o-egwc;+ fir 91l2)t nynep:gtes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent to? /rmgq1lhf+w+

  A bicycle wheel rotates uniformly through 2zkuw +0 ya6pp,.0 revolutions in 4.0 s. What is the frequency of the whe u6p,yw0pz+ kael's rotation?

  A pulsar (a rotating neutron star) emits pulses a5/l ivhnzz74i;,zdkpokg2b3 t a frequency of 0.40 kHz. The period of its rotation ihg,5d l/3p2nk 4zizv ;ozb i7ks

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.2 +2; ijj0ft1sn*gwnj u0 su1 ;*t+n2g0sijfjnw j?

  A wheel of diameter 26 cm turns at g0r,ymmgyq87 1500 rpm. How far will a point on the outer rim moqyr g 7m0,g8myve in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revoluti 2*os3bgx xg1zons in 4.0 s. What is the average angular speed of t1s3 bogz2xx*g he wheel?

  A bicycle wheel rotates uniformly thro3,rv z+h)fu guugh 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the )zhuur+ ,g3f vcenter of the wheel?

  A cable car at a ski resort carries skiers a distance of tpx,9boly gh zbztq) :0p)5f56.8 km. The cable which moves the car ilzy9 th05q)f5,g ztxb ppb:) os 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 w0g k1gj;s kg-)mobs4constant angular speed of 2.0 rad/s. What is the links-1g) 4w b ;ks0mjoggear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If t7 29agmihv9wg+oo9iu he motor rotates at the rate of 20 rev/s, what is the approximate ling9w+va72 9iog9 iuhom ear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/ayon4ha )v46xs. What is the cyxo4) 6a4avn hentripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perime/ebuekg8h0 s +x m:-gqter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.0/0 eggsxubk8:+mhe- q 0 m/s?

  How many revolutions per minute (/bletiho367 3xdm 3rn rpm) must a circular, rotating space station (r = 1000 m) rotate to produce d3/m3 r x73 eihotlnb6an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 mu2t h1yu +j/rc with a speed of 20 m/s. The maximum centripet+ucujr2/h1 y tal 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 circul l x1u1g sdqzhjmvem6(;-6)xvar curve of radius 50 m with a speed of 20 m/s. The malzdq1 ;sh x 6xem( 1vv6m)jug-ximum centripetal 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 0.75,e+d6ip :hz bn0-m string, is whirled around in a smooth level tablebne+ ,i:zpd6 h. If the maximum tension 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 radius 9.0 cm rolls without slipping atm((b,ahp p ti w. s*/qm3nl)10 m down mitm3/l *bpntp a ),.saqh(w(a 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 constant angular acceleration of yu1eb a44w du 764v,)ksq83dpcfyzrn+nf*kc$4.5 rad/s^2$. 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 constagegpoomp8:6 *f gbd o5p/q 5d0nt 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 radius autom l-)la8ymqquu9 8fi8nobile tire rotate after starting from rest and 8aynfqul9 iqm8) 8 u-laccelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and haqpjzz 2 -kf9vz4i7uh ;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 raw4 th+re b ak.yl-n.2nd/s decelerates with a constant angular acceleration ofl+. h nb nek-ytrwa24. $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an a t l;xk*o4xt+ju-b-e +k 4qykengular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accelkx+ ktkj-e4 4 qx*louyteb;+-eration of the wheel?

  A wheel of diameter of 68.0 cm./6b wbkmpzk8 slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheeb k. mkb6p8/wzl rotates in coming to rest?

  A wheel of diameter of 68.0 cm slowa+ bf vso2n,m2s down uniformly from 8.40 m/s to rest over a distancevsa+22 fn bm,o of 115 m. What is the angular acceleration?

  A wheel of diameter of 68l8 mrows6wwg 5x 5;yk7.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 1o6s gwy5km8wr57 ;wxl15 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at ala;duq43 4w 6vqfbkk,5r drsz b-6 fg0 rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant ad;,5v b6ds4-0fu6k3 bzark4qg l wfrq ngular 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 whucv qj xkgy94t4.i23 ceel 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 ixc3kvg9 jqu yi.2 t44cs perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 9077ayzuk bxjgf6 sz .-9y(u3ew Nm. If a 30 cm long wrench is used, wh7.e fyzy6ubx9gk zs3a(wj 7-uat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of )g- d a web4jqe;4. ij8+ddyyiinertia $3.00 \; kgm^{2}$ 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 origin, mass 2mv ) f52cwfl6ks is at x = a, and, mass 3m is at x = 2a. What is the momsk)f 25v6 cwflent of inertia about the origin?

  A solid cylinder of mass 10 kg is pivotednyk)iln hgdqce e t3697xj z3*t1x1h 6 about a frictionless axis thought the center O. A rope wrapped around the outer radius h1l 6xnj93hee1 3 qngtd 6 *ixc7y)zkt$R_1$ = 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 frictionlexw3hrqq :0z u-ss axis thought the center O. A rope wrapped aro 3u:x-hr w0qqzund 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 held in the horizo r vlvi6iw8;6/i bxg5 i2pphy.ntal position, and then released vvy6682;irwig .5pi/p ihbx las 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 toyn3r2bije9; b 5c4azzs-lp (n be a ring of radius 30 cm 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 achieve, assuming icb9zsn n 5 zp24;a3b-(ylirej t rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionl1y3o utky 5 /:ha+6t mr9npwnjess disk pulley of mass 7.07 kg and radius 66.0 ct6j y+ ak n9o:wp5y1r /thmu3nm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aro/jaszs8 vdy4y jq +ixlw,;) 6dund a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What iszdj)+ jqlvsyiy/6x8wad4, ; s the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to s;a-jvn g*ek q0f: phv:tore $1.00 \times 10^{6} \; J$ 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 ine58y+tlvlzff r -x .g8brtia 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 3)dpx tcpz 2;xpqp(4uwza zy.p zf )-;without slipping down a 1.0-m high ppt x3u)cppyw).-z zf; xaqzp(2 zd;4inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mas oyz: vmh2b0x*pwk t.6n 47qdrs 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming tt zvqdw.p6o:7mxbkh yr*4 0n2o rest?

  A hoop of radius 0.50 m and a mas;j is oo8 9v3ozyw7hl,s of 0.20 kg is released from rest and allowed to roll down an inclined plane. H83h s,oz; jiyv7lo9woow fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without 46 ,a(xp)ym-ga,zfg18j- tgd6ao mjqbn2 ele slipping down a 35e incline that yj)jf4 -1pbo,6l (xgmn 8a ,gzq2-da tee a6mgis 7.0 m long. 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 momelj:a + s 9dxpsf: fa/q6v*gt4intum 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 mombsn8hr3l i /3sent 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 5.00 rad/s with arms e *ul6uyx:1 ,8deqokgxxtended has a moment of inertia8dq6uk1,: lxxugoy* e 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?