Angular displacement is usually7p 4qn9z8c:3gwjs fku express in units of

  Angular velocity is ej+*f3.hw/l 2gt:o xrn ifcq9fxpressed in units of

  Angular acceleration is expresserfio8avqb*0ze 6 92 xsd in units of

  A boy and a girl are rid:kuyc uz)9mi*ing on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girlyuc 9uz*m)i k: 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 constant4ghkwlw4y2 zsf lf42sgd.99 i rate. The boy is near t942s2 ls fg.wg9w4 h4klyzfdihe 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 at a constant r 8l,/g z3tnw+wcv*2p noxe a.uat/gz 3cw.x vo8+2*n eup,wltnae. 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-round whic 7ux4 .b wu4l;2rqffjyh is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the c.l4u7 rf4u bqw yj;fx2enter. Who has the greater centripetal acceleration?

  A boy and a girl aren.gwd.g vqm98d6k b,o riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the gdd,b 6g.w.8nok mqgv 9irl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatiunlm,*o r d4:png. Which of the following is an accurate sudr* ml,4nop: tatement?

  Rolling without slipping ykqyt) 3ciql6v0 z9.bvki9,5otdty0 depends on

  Two equal forces are quq6+:o,ylemt)(ya 2b s j7af applied to a door. The first force is applied at the midpoint of the door; the second forc2q qb:+7a (y)elasmt6uy,ofj e 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 am .-b q5jerw)et the doorknob. The first force is applied per.jemqw5b) e -rpendicular to the door; 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. The 8lkf,.jt ge3sr1*vla96b x iqfirst force is twice as large as the second force. The ratiokl et6 98ij1v ,3aslqfrg *bx. of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resist +k 5m+v/+toy p rvae5/u)qjopance to changes in rotati5vj+t vrqo) eum+p+ a5/o/ykp on?

  Consider two uniform solid spherhydfb:*1) ed6*,ohix kkpe)7b ,rgs9rp l9 s ves 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 sry6*lo1 pd bkr )h9sp kib:ds*fevh7 )e,x9,gmaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice therd:q5b2 8c48 vsufhmo radius of the other. The ratio of 8shvb:q8c45rom u f2dthe 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 twhl bi -z0 c:upp0gt5 59i+colu;sftb8ice the diameter o0-h fbbi :gp9ztos+cul ut5i p085cl;f 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 eq i9r79n1/tcz2tar i and radius R. If these are increased to 2M and 3R, what happens to trq919ce2i ntzti r7/ahe sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that ovfwh*n)*dw x;xb6h c:bject will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 exdn7:+yj;ofk2: s(hx0vxo sMR2. If this cylinder rolls without sli0:ve ysj:ox n2x ;(+khd7xfsopping, 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 mav0:c9 )qblhx:e7kzp j ss of 10 kg and a radius of 30 cm. What is the ratio of the rotatikv b7e)9 lx jpqhzc0::onal 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 rolladp/ 2a.+)wm6m k uvcks without slipping down an inclinedda ku vw/cmkmp)+a 62. plane 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 rolls oal(krmk s,2:5yr(af without slipping down an inclined plane starting from re2(k a5m,s:kyf rl(roast. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of partic6fz4p)qh-jzpp(tymp 9 v9-cxv4 -h p rles changes when a net external force acts on the m z9h9vpt-ph(x6jf)q4vzc-p-r y p4p system." This statement is

  In what circumstances can the angular veloc2.onxsm*aemf( 9o9(ded x 7wt ity of system of particles change without any change in the system's angular moment odw7. tfoe(x9a2(*mnexsmd9um?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whw9c*dv sg 0x(zich may be(cdz9x s0*vgw present. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As.jf-3c 1s5zuisp x4l n the Earth moves close to the Sun, thec z1jsilx 5.3sfup- n4n which of the 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 outj,, z4g, u ,vdq;11 hvy( buv*oosleuq7fff 8xstretched arms close to his body. Who,fxjlhvv u( sodvq, , ffg8 ubz7ey41*u1;q, at happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette o i/x :z i:s(ra*oep-bg:m3uo(a fast spin) by pulling in his outstretched :uxzpe::im* 3bo-ri/ ( o gsaoarms close 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 pulling6g ; iy)ykwt/v in his outstretched arms close to hi/ykwi)tyg 6;vs body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation v 6l k4qnlqk7u5aw57yof angular momentum.

  What arc length does the Earth travel in a three month period in its nearllv(z.q+t f7 fdy circular orbit about the Sun with a r.+ t7 lff(dqvzadius of $1.5 \times 10^{11} \; m$?

  The second hand of a clockbrtq6p)vqq s8.l /vu2 has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 second qrvpbslq) qu6t./v82s?

  How many rad/s is 25 revolutions per minute equivalent tou 80b3 /cx t8 e6 k;h-pcjra7e9 g+zgqxanppv/?

  A bicycle wheel rotates uniformly through 2.ed6av j2b73g f0 revolutions in 4.0 s. What is the frequency of the wheelf2agjb 6v37de's rotation?

  A pulsar (a rotating neutrpwz6q() o rc pp8ue)k6on star) emits pulses at a frequency of 0.40 kHz. The pep)8)6pqw(kpuor 6cz eriod of its rotation is

  A phonograph record rotatescqd1ti- 1qbcpa0 g;tmm aoda v+9p5 )9 at 45 rpm. Through what angle does it turn in 0.20 s?t mqv-ba aa09t+p;io c1 qdc)pg19md 5

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point o0 v: *.m)bv(bnqvy *w hv-aymhn the outer rim move in yvhh* y0 )qwvv .n:mv(*bamb- 2.1 s?

  A bicycle wheel rotates0rli9 vba s7k* uniformly through 2.0 revolutions in 4.0 s. What is the average an l*s0rvki7ba 9gular speed of the wheel?

  A bicycle wheel rotam8b x*q4g+gpjz l.o6ltes uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center ofq j +ol86gl4mbxg.z*p the wheel?

  A cable car at a ski resort carries skiers a distance of unvr762al);z l:w sb(xw elc56.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pu csb );vll(5ulr:w6 z7an2wxelley 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 rad/s.-qk s yj,+ wg9 di5ozm,t+pg.s What is the linear speed of a point on the wheel' opqz id.+jkwsg9-s +y ,m,t5gs rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the moqb/1zo myq g01tor rotates at the rate of 20 rev/s, what is the approximate ogzq1by1 m 0/qlinear speed of the end of the cord?

  A wheel of radius 1.uwp8jw rl.y 4lir,9 g5c-p5uo0 m is rotating with a constant angular speed of 2.0 rad/s. 5u 9ijww- ,.rcp 584rop uyllg What is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of 0d5q0e3 wrn mh/ -o.amm taz,ua bicycle wh e0 3w.5d0zqrm,mnha moa tu/-eel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, st 3 pcs61as;drotating space station (r = 1000csa3 1s;pst d6 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating aw3qtqd;o u2or +c*a*o flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) is 2ra ;q uo3c*do+q w*to$1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flau6 z 3ybq 1jvwkgte61r*(ck1 at circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal fo w ze6*c 1v1 j3btygua1kk6(rqrce (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 sthu(pexz5q d ,2 sp0.xzring, is whirled around in a smooth level table. If the maximum tension that the string can 5hx2,u q.s(dxzezp0 p 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 ruiw,5jov w9 -holls without slipping 10 m down a lane at 4.ow wjuvi59- ,h3 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 an1 6ymxl:5vysfeb4 5 cogular 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 cons7p(5n ,wakzy- mk+pqj tant 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 +b:h3g s y9sas*veu,t automobile tire rotate after starting from rest and accelerstvabs+3h,9 usg:y*e ating 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 acceleration oi,kt t)f:d u1;gk4lk+z/ qk pyu86ozsf $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a consta.(b,hw qa2sn bxa1u04b 2e gvrnt angular acceleratira.sb aq euv(b,w224 0hn1xbgon 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 rp.: +jp cs-5kp neo/ r*3tbpyaad/s while turning tkj5*pro s. 3 +apy-:nppbt/ec 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 resr-mx4g9e( dq4 n pn*ixt over a distance of 115 m. What is the total number of revolutions the wheel rotm xn4xin9qd *g-4r(pe ates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unpey2 fjpo-g1 x-s70 0;vtcyk flyj;m( iformly from 8.40 m/s to rest over a distance of 115 m. What is the ans 7cx- gp1tl0 mj(oy;y e-j;2fpy0vkfgular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly frcvs 8 .us0 9k0d lyaqh*a:0oyrom 8.40 m/s to rest over a distance of 115 m. How long does i0c 0s.o:rk0vsydluhay*q 98 a t take for the wheel to come to the stop?

  A centrifuge in a medical laboratory 4gxi stj6hb,7 7 zvvc.8lrxi*rotates at a rotational speed of 3600 rev/min.7c*xh bs6gv.z v j74tix 8i,rl When switched off, it rotates 50.0 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 t/.i (g v:;lz hq0oukmvo a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is iv: (vozgq;0h.muk /l perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a5fqi u. n0fwb4 30 cm long wrench is used, what is the magnitude of the force required when the force n.uf f4iwbq 50applied at $53^{\circ}$ to the wrench?

  A wheel with moment of incd9t vc)2 *qkbertia $3.00 \; kgm^{2}$ 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 v tu-z/5rc/e5g5x2 gj m1dtipat the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about t e1 /gdm5g2tp5vux/5zi tcj -rhe origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoughty.m6 76 + rwlziyya3dc 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 anotheryrazc6iyy3+.m d7 w6l 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 thoughtrlieoctml)36k8;,izfs 5 / rj the center O. A rope wrapped ,)ljzkotr fi/; msir6 58e3cl 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. 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. T tsa:y0n1dque+h2ymggp64 4ihe rod is 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 n g+mqgstd :4i4p 0ae21hy yu6of a rod about one end is ML2/3.)

  Consider a bicycle whexvgi53i jcw)7 el to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sp3ii7g) cj xvw5rocket. 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 it rolls without slipping?

  A 1.53-kg mass hangs on a rope w)jszb1-(j 0svjp4zt, fgjy : o8.0anfwy3ezh rapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the .h j z0z)jw(z4:0v1tespy3j8j-o n,a g sffby pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless ftux k8aph69) disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?u8hf 6px9ka )t

  A rotating flywheel can be used qj(6syu0 d)koif o5r ,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 o+tcm*lx yjr5l 5/k:b f-e9kjzf $5.00 \; kgm^{2}$ 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 kzjpx4e n (0br.rqp17l70j0a xq jz5wpg and radius 0.010 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 oj xrejq(1pj7 7znx0a.r 4p5bl w p0q0zf the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of r 9hmqi ky(/n-10 m/s. How high up an inclined plane can it climb before coming to ryk -r9(iq mhn/est?

  A hoop of radius 0.50 m and a s)h1jukc k55k pr14i7aerz g5mass 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 distanz11er 5ra i k4kjp)5ks 5u7cghce of 3.0 m?

A solid sphere of mass 1.5 kg and nfwl3i(q/ im2p9qs4al d:1 xqradius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia xn 9i1ql:2fl4 /qaqi3(m ws dpof 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 chc7v8ca4/lawp8)z ngz anges 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 inernbwp aqqv(7+23n 3 pbt gbmdk)-x(:efhas2e 4tia 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 a(knaasu/ n4.h6ss sq *t 5.00 rad/s with arms extended has a moment of inertia of sa.*/asn4h6n qkuss(
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?