Angular displacement is usually express in units o+cu r-zh ua03gf

  Angular velocity is expressedj ;q03ps2l* o mol2gvy in units of

  Angular acceleration is expressed in us*52c*xchukru1d / c lnits of

  A boy and a girl are riding on a merry-go-round which is tum* t adsa-a1d;g ,wdkl:t4dlgh e1 3*erning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular di1:tk-ds,gm dd1walehad*4 gl t3*e;a splacement?

  A boy and a girl are riding on a merry-go-ro (qsvo; )lllm3und which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has t m(;l3)qsl volhe greater angular speed?

  A boy and a girl are riding on a merry-go-round which-o wbxq 1rum2bud 7x 5ks165gh is turning at a constant rate. The boy is near thexrmbbo 565su2qd1x7 h - 1ugkw 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 which is turning af4x dm8z; b-ytt a constant rate. The boy is neazd4fm;b y 8-txr 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 constant.ec5t hy7by)k rate. The boy is near the outer .y7 )bkht5ec yedge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body thi(j,3vlyf r79j2y v glat is rotating. Which of the following is an accurate sta i2ljvv9 (rg,3ly7yf jtement?

  Rolling without slipping depends-nctarbp;v3dbg5 :vu 0 gwx,4 on

  Two equal forces are applied to a door. b6ted 5ib8x2 f1iqtf1 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 greater 2ffqex8b b6tt1i d1i 5torque?

  Two equal forces are applied to a door at the doorknob. The first fkg6d8yc d*f x y4 uui2kqqh*99m+, iylorce is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greaf6yc 2k9dqq*hix8 9iy4y dgm*l,uk+uter torque?

  Two forces are applied to a doorknob, perpendicular to the door. xke3 f -attv0 qqx .azrf/92*cThe first force is twice as large as the second force. The ratio of the torque of the t 09.eq*fkvca2a3x-f q z/ xtrfirst to the torque of the second is

  What is the quantity used to measure an object's reozu:8erl +4.qbrkmk h+y h1e)sistance to changes in rotatio)z.8ryebl hh+:k +1r emqkuo4 n?

  Consider two uniform solid spheres w*lv wo*ql4 asyi d 58:*0e;jp*hkclsjhere both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia t wc 5ljlkv*4aloqs*i*s;jped : h0y*8o that of the smaller moment of inertia is

  Two uniform solid spheres havlz9ip 9mo67f.alf)y qe the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertiaf 9a96llz m.i7f)y qpo to that of the smaller sphere is

  Consider two uniform solid spheres where one ha09:3tdu pt5t:rac q v2du em8is twice the mass and twice the dia2 tt:du 83t:0ud a5 ce9qripmvmeter of 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 increaof9 )mw. h0v i3:a*x)xelfqaz sed to 2M and 3R, what happens to the) i: v93ham.ffqleaw x*xo)z 0 sphere's moment of inertia about a central axis?

  If a constant net torque is applied to anu-g,rxm khl 7xhxy1i( 2sm w7.k4hsb* object, that object will

  The moment of inertia of a solid cyli1ti1pm x mze0v tf6yj8t0qo)kf* rq8-nder about 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 w2i r+ l*wp6ptn+ +mauof mass 150 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 toa*ir++upw 6+2pl t nwmtal translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of lc-ue6z4*muz8nkw.v . w0ieqmass M and radius R rolls without slipping down an inclin-ekw.uul68z4m iczv*q w 0.ne ed 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 without slipf )12 tz,gepprping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends21 zepf p)rgt, on

  "The total angular momentzwm/ c o-j3xavgy75+ hvk)uh:um of a system of particles changes when a net external fo3+x-hw:agju5k vhov7 c/zym)rce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles *jv ccs4).kja change without any chav)*4cjkc. aj snge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frisxikwkbq5r6 :1uoo/sp 4 7w- )pqm 86dpepw0jction which may be present. What happens over time to the o:8wmkpe5bk/) w1s0pxsi u po6rjqq476dw -pEarth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves cl: e94z/6a n onndwx0jjose to the Sun, then which of thed6 annoj0 ew:4x/ 9zjn following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast s pg.s.jn 62.c7(koa/k hhu gu 3vuge1epin) by pulling in his outstretched arms close to his body. What happens to his angular mok vh6 .nhu7p/ueo.g 23agjcegks(.u 1mentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretc))- u, d ndzor)ymq)vnhed arms close to his body. What happens to his rotational kinetic energy about the axis of rotatiou))-y)n z vo)qnr,mddn?

  An ice skater performs a pirouette (a fast spin) by pull2( 08kbvhijy98 oiyippd( tw/ing in his outstretched arms/wh vod y9 p0t2kb(8i ip(ji8y close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation om;i.wrgb 3;f8x c8i hff angular momentum.

  What arc length does tb0s;o i0)h5tgr8m ol jhe Earth travel in a three month period in its nearly circular orbit about the Sun with a radius of 0o8ls;5)grtm jhi 0ob$1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lengr ;)k8pmoz z+jth of 0.30 m. What distance does the tip of the second hand )pkj 8;mzr+o zsweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 rvelt 4iht.d:x ;mxm,eg 4wp97k((b fgevolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolykllimn*qz.9242wr i)t ve k0utions in 4.0 s. What is the frequency of the wheel's rotation?rk2 )ilzim24vkly*en9q0 . tw

  A pulsar (a rotating neutron s pulutb1(; jevtfsp2u0 ,, ys,tar) emits pulses at a frequency of 0.40 kHz. The period of its rotation0,2u utlf sev(usjby,pt,p1; is

  A phonograph record rotates at 45 rpm. Through what angle does it tjky(d )43 takwurn in 0.20 st yk3(a4dwkj )?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the out;zps ;;sdj 2wber r;s;sdj;z bwp2im move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolut2ivdyh/l3zg)7pd4 pv ions in 4.0 s. What is the average angular speed of th7gy )32zdi 4/hvpd lvpe wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. x3 f,,wry /xjg What is the linear speed of a point 0.10 m from the center off,/3,x g yrwxj the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cabler ifmo vll -95*brcf.k0 e0zi, which moves the car is driven by a pulley with df lzcmikfv.b *9 ie-5l0r,o0 riameter 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 angulsai+q tcldd)/ x,o:p/ ar speed of 2.0 rad/s. What is the linear speed of a si)xdo/ld, :/ +tcqpapoint on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the mil 3-2hoi6dbf (bo ju6otor rotates at the rate of 20 rev/s, what is th fuh ol3ib ji2(6b6do-e approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angux)2 mc31u nzs7v0nvcs lar speed of 2.0 rad/s. What is the1 23 )uxv7csvn0nmzsc centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point ;ov 7j0wp9i xlon the perimeter of a bicycle wheel of diameter 70.0 cm wh07 piw;oxlv9 jen the bike is moving 8.00 m/s?

  How many revolutions per minutpz3hg.g3 1 b9sdb9w* g oiue:ze (rpm) must a circular, rotating space station (r = 1000 m) rotg1zp bu 9w.eoh93dzg isg :*b3ate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed;cj5xc- jzz5k of 20 m/s. The maximum zj5 jc-x5zck;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 r 0bciwxb26 u0klli8 mpr ;:7qch (sso)adius 50 m with a speed of 20 m/s. The maximum centripe0s 6:0 qp ) bluxi7ilc 8hb;wrko2(cmstal 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 string, is whirled 2nyf8;i w ad4a80.7figooebcsp y,n6 around in a smooth level table. e c , f6o;dan n8io4. g80i72ysbfpwyaIf 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 10 m djasfvv), h *+lown a lane a,)sa hv*vj f+lt 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 accelerati8, ug.n1 osp:i ksc)ejon 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 constay e4x3:f.q4lphex h+y nt 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 automobile tire rotate aftsuo bd2n6jip3qo1 42ter starting from rest and acceler1sn322dtpi4 6jo uq boating 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 atwt fi,9wm(.m efag* ,f 2jxb/cceleration 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 et1n bgso:e.)angular acceleration s1:n e.beot)gof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6. a vgp6n6kw1m* 77e1:pw glamb0 rad/s while turning through 2.0 revolutions. What is the average angular acceler6m gg pn:e767aabwwk1lv *pm1 ation of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m8ga(1a8vs2fm c(ilcb r.ob )q/s to rest over a distance of 115 m. What is the total number of revolutions the wheel gc(8c )(.l8qasfr b b2moiv1a rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to ut7hd.*f +a;iwejy4e rest over au j* e;fhe.i7y4 wta+d distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uni+vbkqlvj6t o *:;-84ia1ltm hxk0jw aformly from 8.40 m/s to rest over a distance of 115 m. How long does w+1xi o8:a vtl6hvaktlk qb0-j;m4 j* it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationalidn o(le;j*+o5: med3q 8cqrc speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular 3od:q8lcn+jc *m de;qe5i (o racceleration 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 a torque of 90 Nm. If j/.k ypl4 rta(vh vt8/se,po,a 30 cm long wren84/rvjky.eta/ p h opstv,(l,ch is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel requireu v(6(oo)aiafp s:)s ,1 uu38qulcuufi 08qcz 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 appl(f 0iz6, 8uu3 oa) as (u8lsufvui1qq)u:cpcoied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertavpwg 8eb /qgn4,v; (ria $3.00 \; kgm^{2}$ 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,hg)br4bd 34j-+m ks qjq n(f2u mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the ori)s+q4 3hqgmnjbf-2 rbjku (4dgin?

  A solid cylinder of mass 10 kg is pivoted aboutwj7zb f:dzm1deu8(l3xoa 7 ; p a frictionless axis thought the center O. A rope b 3zp(azd87lumfw d7 jx: 1o;ewrapped around 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless a i*xf(i0l /vxlxis thought the center O/ (x*xl0i ifvl. A rope wrapped around 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 horizqgyokp3/(4np,ek 7lasx- -xd*o ew6montal position, and then released as the free end is allowed to fall. What is the angular accel n-s3pewk/*m xkoq-ld7poa( ,y64 x geeration 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 radius18btxg o ltu r:+,vpk,v pizmp7.g b.6elmh-* 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 radiusk : -.evzu,vgp*bpx,1i. t67r ml+ mp8gbthol 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 may rx1ge,k: t7qss 7.07 kg and radius g1,y :r7 txqke66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped arou:hk6:vc g/ y-gk q(lnynd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration ovkcg/ylyhng(: qk6 :- f the mass?

  A rotating flywheel can be used to store energy. If i b8m/kvmf3g y2t 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 inertl/m t-q o2z)v hdm)-wcia 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 massmgjd4cn 0eu) .xlks-; 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined pla4nje.d0kg-l )cs mux;ne. What is the speed 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 ro g*0gfbk +rqh2lls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to*ghf qb+rk20g rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from o (4i tnk199d didrk(2xruonq* ,hwx6 rest and allowed to roll down an inclined plane. How fast is it moving after dropping*9r(4ndd hktqoxn1oi 6k,2 r(xdwui9 a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls w.xk.6q y sxx5qithout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sp.qk6s xy 5xqx.here 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 momeqz4)eyo zy6c:ntum 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 momen: 0e/xi-3wxhm+r rqxst 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 extended has hey 3 w*wc0n, hqjm 4(vbrm0)ma moment of inertia4w)m 3(qej w ,mh0vhnry0m* cb 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?