Angular displacement ih hg3z8+ xrdi.wijxm r/:/mq4 s usually express in units of

  Angular velocity is (bb5b3bqx:arho: a9bexpressed in units of

  Angular acceleration 8gxowv 83 yxu,is expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant r *a;7b;gxdqahate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?hqad ;7x *ag;b

  A boy and a girl are riding on a merry-go-round 6p5lq+iu 7wi: /nlcxiwhich 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 speedi+i5u/x lw 7:pqnilc6?

  A boy and a girl are riding on a mnyjlvf oyd.cse;z 0 8)6p9bw 4erry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the cenyepcyj f 60w;ozbl).v s9 48ndter. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which zf,xld*55 axq5vnx0 gis turning at a constant rate. The boy is nen,a 5gxx0qlx 5zfd* 5var the outer 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 a congrta,x;8leg dvn,8 kxe ko; le4+5gt7stant rate. The boy is near the outer edgeg4 evn,l;ro t 5,8dtagx7g xe8+ekl;k, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of 5i/wxshp/ gt1 0chx,kk p 69lr6y0bjk the following is an accurate state15 ps6h/jct9k0pl,xwbxg0h ki 6ryk /ment?

  Rolling without slippin 1sy(5 ljgv8i huq zkbo73s h8w9-gh)vg depends on

  Two equal forces are applied to a door. Ti6hmg t k,rs88he first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Whicst8kh,i8 6mg rh force exerts the greater torque?

  Two equal forces are applied to a door atqm*,e idgn)89r5 ct .grfj,hao (ng/ a the doorknob. The first force is applied perpendicular to the door; the second force is app9 c, fgitg(g5qrha,rn/ade*jm 8o).n lied 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 ;xpcr dos 2en)e/,sepr*j (;b. The first force is twice as large as the second force. The ratio of th,)c2r/ e r sp;enxd(jpso;be* e torque of the first to the torque of the second is

  What is the quantity used to measure an object's c2 ibuf7;w/7tt gvk8a resistance to changes in rotatiov77twcik; t8abu/ g2fn?

  Consider two uniform solid sphpko ;9*u; fgjxjvr9 ke7ll;,q eres where both have 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 ofk;p;gj7rq , ;ul9l vk*f9ejxo inertia is

  Two uniform solid spheres have the same mass, but one hab7q1 l3h,jop/r o(phd s twice the radius of the other. The ratio of the larger sph7, h1hpd3( lbqrojp o/ere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid sp)xt) d+k phxw.heres where one has twice the mass and twice the diameter of the other. The ratio of the larger mome)+)x xhwdkp t.nt of inertia to that of the smaller moment of inertia is

  A uniform solid sphere h 9zykgl jjvs a6m5t,.7as mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a .yat szv7l9 65jjmk,gcentral axis?

  If a constant net torque is applied to an object, that object wilhl0 v* nlat.6yl

  The moment of inertia of a solid cylinder about mfkn1* 2,52q6 m3cynquhdhf a its axis is given by 0.5 MR2. If this cylinder rolls without sl d6 53 ymqh,2fma nq1kfnhu*2cipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of w3y)iu 27vc a6 5sc4 0hvueibathich has a mass of 10 kg and a radius hu )5ba 4i3c6va0ci2y vets7u 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 radius R rolls without slipping do kdt+ gos 0 wq:i (v,qo0dwhq;,p)t.qown an inclined plane starting from rest. The linear velocity of the sph qoq(h0 kosi p,t):d.d;v0gwq,ot+qwere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippli)0 n l+l9hltef0n 19rquj c*ing down an inclined plane starting from rest.lun e )1 qrllc*n0+h99lfj0it The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular mom7 mftws7o2/; fur*jruentum of a system of particles changes when a net external force acts on the system." This statement is/2sf77;rur m*uwot f j

  In what circumstances can the angular velocity of system of particles chmu pdns8j .g oqf,l0)-7r2di7h d;js hange without any change in the system's an2do)pmnrjs fli 7j70hd.;hs dq,u8 g-gular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whicrwh 72peb74az; s6gdah may be present. What happens over time to the Earth's angular momentum about the dp g7ar64bhs2 ;7wzae Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movix;6q5e (in kues close to th ikeix5( n6q;ue Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater perford(h6xr) 0ylxhms a pirouette (a fast spin) by pulling in his outstretched arms)h lhx( 6yxrd0 close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in h o9upw/ byu8yyq7 cv ;e- er2hoc2gc0(is outstretched arms close to his body. What happens to his rotational kinetic energy about tye/2 pvc2y;r9u w ybq ucoco0(-8hg7ehe axis of rotation?

  An ice skater performs a piroue w2hp:2mo qf+7it3w lxtte (a fast spin) by pulling in his outstretched arms close to his body. Wh2ix+72 qhl3 wp ow:fmtat happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentghoji12u89 gapy+z +b6ts1a 5h w+nyzum.

  What arc length does the Earth travel in a three month perit/nc4 3x9hn ua 8aduv7od in its nearly circular orbit about the Sun with a radiux cva7d n/3h4at8unu9s of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does tvd,oc4mmy s3* he tip of the second hand sweep through in 3 minutesod,m 3c s*vmy4 and 45 seconds?

  How many rad/s is 25 revolutions p5vx-hr8 8dg us3s4w tyer minute equivalent to?

  A bicycle wheel rotates uniformly through*mnc78y vz ky; 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotat8;zn7myv *yck ion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. fy /+r2rmgs 8h The perioyrr+8g m2f h/sd of its rotation is

  A phonograph record rotates at 45 rpm. Through whatx z,* nqwikz+)h;8trq angle does it turn in 0.20 s+*kzwi h8);x qtz ,nrq?

  A wheel of diameter 26 cm turns at 1500 rpm. How far wvya,q z)h*6of8 5mu vgill a point on the outer rim move *hm of v,6vaqg85) zuyin 2.1 s?

  A bicycle wheel rotatesstl0) ) wanvx- uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of the wx-wn )tls av0)heel?

  A bicycle wheel rotates uniformly through 2.0 revolutiy7 rmneu)i9qj b 4j(+vons in 4.0 s. What is the linearrqn79+ibvm)j e4(u yj speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resorthso 7 1wf:b5xi carries 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 slish5:xfoi71bw ppage, 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 lx y )q1(66tigi8dcmm a constant angular speed of 2.0 rad/s. What is them6dxilt1g i6q mc8 (y) linear speed of a point on the wheel's rim?

  The cutting cord on pvzul ci 9es(7h5+sdf+ay6h+ a gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the en(i+ deph u+ 76a9sys+hf5zlcv d of the cord?

  A wheel of radius 1.0 m is rotatinxuv( yi3- aq. .b e(lu tsob5lo/z(6irg with a constant angular speed of 2.0 rad/s. What is the centripetal accele(v..(l bi bozi3t (quayxo- r6l/5esuration of a point on the wheel's rim?

  What is the centripetal acceleration of a point w pz,myjygxah,l2m 2,m8vg *ezn82c7 on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike isze*vh2ay7 gg nz,x2pmj8wm 2 cmy8,l , moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space sta,ys s1rfo6f 0ea,/fgr tion (r = 1000 m) rota/,rayffsfo06,ge sr1 te to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with e5riu: z1y-uta speed of 20 m/s. The urt5 zueiy:1-maximum 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 circular curve of radqp0i76/ey*b 3 y,o:iys ale pvius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by statici7pyb0 eq* ls/vo,3a:yie6 p y friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to tr6,a4 7aawwf:u3w9yc a y1/zv- ndyorhe end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speeu 7a wwfc 3zwoyar: rdna1-/,4ayy96vd 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 withnse7q-: dx -gsout slipping 10 m down a lane at 4ss dq-7 nexg-:.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 4j7zc*w +x cb56s soxdv 9sp1v$4.5 rad/s^2$. 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 acld 0c57pcwe u)f bprl;kjde0n,(3 ow5celeration 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 0.35*vcov buu-f 200-m radius automobile tire rotate after starting from rest and accelerating at a constant angu- c*uvfbu2 o5vlar acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerasns ;hv7/:gn 4y :jfhdtion 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 constant angular acc-j; y0(jewygq +ftt4qelerat+ge(fq;qwyjj y0tt 4- ion 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/s7h3sby0m n+zp while turning through 2.0 revolutions. What is the averaz+ h0yp7b s3mnge angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows downy46ou ba55rok uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to r oour645ay k5best?

  A wheel of diameter of 68.0 cm slows doeaypd2 jen:b:x ,n t;)wn uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleratiy,): anxej ;de pb2nt:on?

  A wheel of diameter of 68.0 cm slows d e71fbfs. 1ntaown uniformly from 8.40 m/s to rest over a distance of 115 m. How long does if7.ns1 1tb efat take for the wheel to come to the stop?

  A centrifuge in a mep. +8v3l7uruklkb(mikn98e fdical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming 387+(ivfk8 eu lrkubm9 p. lnkto 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 to,li), ,/b06m l)om kvodd 4ato7szmq trque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the forceq/,ammdo) 7, lzok)iv,ot6 0sldt4 mb required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightenin 8xsxje b/q unz/-)if6g to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forc xin/ufzb- xj6es/ )8qe applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i /(dbr14ssz axnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: ma hh+ xowh6y.r0m/d+y wss m is at the origin, mass 2m is at x = a, and, mass 3m xh m. +w6oy0hw/hr d+yis at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 1spx 5//occh0 n *ncdzkg 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 dow/o1ncc 0*hn zdxp cs/5nward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about amh34(ax;yfdbhl(nf 7 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. mxhd((hflf 4;b 7 ayn3A 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 wyv 0+ob m. ,rwo97smtend. The rod is initially held in the horizontal position, and then released as the 0 v w7osr.+oytm,wmb9free 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 wheesya(4;l nac- uob /k7yl to 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 do nsk la/;bya(74o-ucyes the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless di 9sof0z2pn/ 03xfqobesk pulley of mass 7.07 kg and radius 66.0 cm. Who s f/qop23nfzb00 e9xat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aro/;+u0za +ibdhwtn2 6 1d 2cb*z vhagqlund a frictionless disk pulley of mass 7.07 kg and ra6d2 ;*ahb+l1g v2bwda ciu nq0+thz/zdius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be use i1 1vcv a5g x,2io-v7ceei3qmd to 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 inertia of u6l fki y9l*9;s r2-zuttdw- b$5.00 \; kgm^{2}$ 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 0.010m- c:gric8*czo7v h;u m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of tcio8 uh*zg mrcc7:v -;he inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with av+y t(xq q ob4+yg9 rqk+-t1pv speed of 10 m/s. Hoqvpvyk4+y+1+xrt b -gotq9 q (w high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a massb7)an)hz k*u +oyu lt8 of 0.20 kg is released from rest and allowed ty8u)*k azonu)h7+ b lto roll down an inclined plane. How 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 slimxif8r7t*ir +m03 rvht81w k.2h bpvxpping down a 35e incline that is 7.0 m long.t+p8xw8 . 7hvb*k ir0himrf 2m1rv3tx 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 cd os*ue.4e8k tbe8p/ynwq o9z 6t63tchanges 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 inenva6v ;pho)1 qua4t;ertia 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 rotatielqfv2lj) -x3ng at 5.00 rad/s with arms extended has a moment of inertia o lxl2)j-3 fevqf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?