Angular displacement is usually express in units p2/vkk4pwm1 b of

  Angular velocity is kmd6 )e m;ybu6ekn6 (uexpressed in units of

  Angular acceleration is exu - +m0c1s.j5ctogpb jd-1lgypressed in units of

  A boy and a girl are riding on a merry-go-round which is c pkny0iwi+ ,+turning at a constant rate. The boy i ii+nw ,pk+c0ys near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl arec:sat e)ciz(uzc)3c1 riding on a merry-go-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 greatsc:)ae i1tcc()cu zz3er angular speed?

  A boy and a girl areh ,fum jyfs 1x/3-fb f.98duyk riding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. u f kffy9y3h81u.m/bxs-,j fdWho has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a 6 * 8n (ajy)k2az)bvavgquhm 3constant rate. The boy is near the outer edge, while the girl is c6n)h(a3k8b*mvq2y) a uvjzg aloser 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 consta *wl9f tyx6 *bcacr1v+nt rate. The boy is near the outer edge, while the girl is closer to the center. w1x6+*far9ylc vbct* Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of thtl/b58n esiu-ckv+*1k tnt3 be following is an accurate statem-sbbtei/ 5k3v8t k+un ln *1ctent?

  Rolling without slipqvl/pckbb j*h3 41 by av 4g6rxn,)n(xping depends on

  Two equal forces are appliew6 igo opst4*3d to a door. The 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. Which force exerts the greag otw4pios*63 ter torque?

  Two equal forces are applied to a door at the doorknob. The nx9qrcv j0o*mu n u8-6first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts tn cn0*qu6ju m8o9rx-v he greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. h(460egg8)ay2omzirxrx0 ) 1vk jl et The first force is twice as large as the second force. The rati(02a i)v 6z yr0 kj41mxgxroehle)g8to of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's rbvu pdf94yp j1x6-f. resistance to changes in rotati61uffdb-yj p.vr 49xpon?

  Consider two uniform solid spheres gl jk8fh0iq 1+where both have the same diameter, but one has twice the mass of the other. The ratio of the larger momk8jlgfq0h1 i+ent of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of v(ukl r4 3o2 1ncn1stdthe other. The ratio of the larger sphere's moment of inertia to that of the s41 312uk orsv(nntdlcmaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice tk lqjtf5j f qfu eb *eqo89(1.d-jk0xx od)f/,he diameter of the other. The ratio of the larger moment of inertia to thatq/xe1o-ofd9 ,jqfx e* )fbj0 (q 8jlktkduf5. of the smaller moment of inertia is

  A uniform solid sphere has mask ivpk;/qh6o 2s M and radius R. If these are increased to 2M and 3R, what h;voq2/i pkhk6appens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object w )kfm 2qe*gqt*ill

  The moment of inertia of a solid cylinder about its axis is given by:nz:i.+mc p tk $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150g bxlnej) 4sem 7. coon8,,;yf kg, 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 to the total translational kinetic energy of the bike? Assume the wheels are unifore7)o 48sgxfl . boy;nn,mc, ejm disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down an:aw nvr+c)-p8za 9ah q incla+ahzpn):wr8c 9 aqv -ined 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 wibxo,cuo0 gi :2thout slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incli 0:ixgo, bc2oune depends on

  "The total angular momentum of a system of particles changes when a net ex9-73dj 7h4i lr r0vx/ajlw shxternal force acts on the system." This st4ia r-xwl3hj77r s0h9vjxld /atement is

  In what circumstances can the angular velocity of system of particles c2a(n:et;w 6en-kx cgi hange without any change in the syi gx:ate26 ckwe (-;nnstem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any -vn1c*/rma m0attqav,z4 ) mj friction which may be present. What hapm4zm,nrtaq/a0*)- vj1tcvampens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit8daf thr*) mobcg6 a.3. As the Earth moves close to the Sun, then which of the following best describes the orbiting spefgdh6c)3a8* m.ra b oted of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretjxziniq5 ,; 2ag3c2xxs*.n3+nwxf y yched arms cq+ gj3ynfwxx i5a;sx i2yz2 3xnc.*,nlose 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 hi: jb. 3ov0xim urjfp-6z(o 1lus outstretched arms close to his body. What u-1oib 3zrlx fmv:o 6ju.(p j0happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his5q9bu*ut 4pyz s5b,om outstretched armsub5q ,*4ompts9uz yb 5 close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conse y+2tf,kwoq3q7 8l apmrvation of angular momentum.

  What arc length does the Earth travel in( n,kb.aemcu9h bp8 ebbi/6r. a three month period in its nearly circular orbit about the Sun wi.ra m ,b /beh8.pcbbk9nu6ie(th a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length ww 13yjrs bp 5eu3rb05of 0.30 m. What distance does the tip of the second hand sweep throug3se0yb5wrw1ujbr3p 5 h in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equm ;l n6 tusk2w)7cw4:vlg3aynivalent to?

  A bicycle wheel rotates uniformly through 2w)7tg kxw r(a+.0 revolutions in 4.0 s. What is the freque+kgtr aw (7x)wncy of the wheel's rotation?

  A pulsar (a rotating neutron star) emitsh+ jooco ,+gfw58c9et pulses at a frequency of 0.40 kHz. The period f5w coh8+,tecjo9o g+of its rotation is

  A phonograph record rotates at 45 rpm. Through what ang;yf ;2p;wswuk p.:mti le does it turn in 0.20 ss. p; tw:2umkfwi ;yp;?

  A wheel of diameter 26 cm turns atb -to(w;bp, +e d:dhlo 1500 rpm. How far will a point on the outer rim et ;d lpb,d-o+wh(:o bmove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.s0t z3pq 3*o0 rqu4d ;,bit cea(x8phiak;jx7 What is the average angular speed of the whe* tuqqt k;bsajxp c07zdah;( 4 epxr383o,i0iel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4+t(kr2sb f1df9 mjqz5; zmpv 1.0 s. What is the sztb51 r2j+f p(1v9q;fkmdmzlinear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resortcasrr uv: ;rxn*vn+y) e9 78zj 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 slippage, how fast must the pulley rotate for tr+:u)e aryj* ;8nrvnv 97szxc he cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotaz /b op7vw+1etting with a constant angular speed of 2.0 rad/s. What is the linear speed of a poinz7t/1ev+ pbowt on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If thel u h+u; h4yl.sim92s;(qffm pz16ued motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the co6lyud2upmmq .4(suf 9hlfes ;1+ih ;z rd?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s.9of et(v*44fcsi* wm/pps+iy What is the centripetal acceleration of a point on the whesy4/9 sfiepi*f (c+w m 4opv*tel's rim?

  What is the centripetal accelerationif*6dgi8f ad a,9 wdf(f5kwe 1 of a point on the perimeter of a bicycle wheel of diameter 70.0 cm www8 igfak9 1*(aed 5ifddff6,hen the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space st3 wb9uhfz-t41l) nao hation (r = 1000 m) rotate to produce an artifiw4fth b zau on3)91-hlcial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat u 1ms9:u+1tf(;vmx5 otrkte6 yv p f7mcircular curve of radius 50 m with a speed of 20 m/s. The mavm6+y5tu9fvmmfpx(7:u; e1 ttr1 skoximum 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 circul* s,7 dw9ngrv db:jd+war curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (prov w+d7vb s*gwnj9r ,d:dided 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 e 59 omnsvq+pudc* zb:6nd 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+zb*9 mop5:qncsdu v6, 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-, fxve4h1fr m 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s. mxfvh-1er4 ,f
(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 cons od 69w /.nkhey0inv5qtant 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 constanzuv;mgxpz)x.xpyk, 6 fs/ z* 53ni)kkt 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 auto/x,cxpt l9wmp z. 70khmobile tire rotate after starting from rest and accelerating at a consp/hxl x0km zwt9,c.7ptant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an60.nigl /1.yunaw,nqz4h nba 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 decelerates with a consi/fmh3-bw o3 )uvgsa4 tant angular acceleration of u3/avws b 3go)mihf-4$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angulat0)ee 2b.iics- l fye0r speed of 6.0 rad/s while turning through 2.0 rei 0eb0e et .is)cfl-2yvolutions. 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 rjx )f;n0;(sk n-hllz aest over a distance of 115 m. What is the total number of revolutionl0l;x-)(j nfaz;h ks ns the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly froz +bwn-5z*ur i6x ctq1m 8.40 m/s to rest over a distance of 115 m. What is the angular a5 zr1ztnc6u q +w-x*ibcceleration?

  A wheel of diameter of 68.0 cm slows down unif zg7 ,6lf5nryn./lg shormly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to comenhlry/ lsf7ng. g,5 z6 to the stop?

  A centrifuge in a medical laboratory rotates at a rota:/ab03qkbl .:5 tkxhwvazr .dtional speed of 3600 rev/min. When switche. a3v/ztxlk.r0d:b kb qa:5hwd 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 tightenix jaz.aeg: 6r1m ci:0qng 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 is perpendicular to the wrenchr6zje:1c g0 mi:.qaxa?

  The bolts on a car wheel requirzly5n.wr4 .j1o 7cx 7bn:nbk jc9jdt3 e tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the z13db7 .c j7rjtyxw9j.nn: 5lobcnk4magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia + inhfc,+6di l$3.00 \; kgm^{2}$ 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 th)xl 0hp w-qsiyw j,g(/e origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin)jh p/ix s gw-0,lqy(w?

  A solid cylinder of mass 10 kg is pivoted about xtfi . )q2tlh6a frictionless axis thought the center O. A rope wrapped around the outx 2q.thf til6)er 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 pivoted about a frictionless axis thou zhy*c, exnp7/ght the center O. A rope wrapped around the oyh,z* nxec/p7 uter 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. jwz( t+yf(ftij e-12d4pp 7ir ty5q /l The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. Whatyf4tplit2-i1/((f 7yrz ej tjpq+w5d 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 to be a ring of radius 30 cm and mass4nia2 8 dvarkxu q6z)3 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentiallui864 dv2aark qznx )3y 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 ok;f/,fl yed -jr7xv,oyw l- :mass 7.07 kg and radius 66.0 cm. What is the anj y ,:-offwke-; r ld,ox/lvy7gular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of masfkye-xyw8/dyw14q;r c.hx( x s 7.07 kg and radius 66.0 cm. Whatreq xwcdxw f 1/yy4yh(x-;k8. is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is ml)n.6i/stv l7 iys0wp d;7vz(vgfev-v m4 ,w 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 i 4cjl) ,-uwsu ;k 7w-fx cln0,t8j n7.lqyqkuqnertia 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 res:fyy34/uzmu9 k8:2 gbwvai j:w-b epwt and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches:j2 :evi/w:yfug8aku4 b yww93b -mzp the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s.t2qt/z8jf uq mxe31: m How high up aqequ j1/28mxf : t3tmzn inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is reldjxoy 8y*)r(5yyb-0q l0ac/ -xs fawyeased from rest and allowed to roll down an inclined plane. How fasyoj dc0x-s)yb5yx/ *a(a- yr8ql yw0 ft is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 10 c ij .1-; yky6ehwl,eel(akhmdrt1,j: cza/ 5 cm rolls without slipping down a 35e incline that is 7.0 m long. 1idh6 y wj -lr,aj/c kyle(z1ae ,.h kc;te:m0Assume 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 momenn o-7lg- gkih,tum 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 moment of inertia fh+ : m+j.a-m11+pd mm eb-/krgsevbfof $5.0 \; kgm^{2}$ 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 extended has a moment ew:kv /-wqhc-o2,w3ds ) yksk,tbs t,of inertia ho,bkcwktsvd,s-:3/w-qytw s) e2k , 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?