Angular displacement is usually exprf2:-rozqsbfxe 8oi29 ma* wj;ess in units of

  Angular velocity is expressed in units on *9g:ub4gxv**nepp wc-ln ;sf

  Angular accelerationtlbtu p,y8 f :7z3r53-hzkxdd is expressed in units of

  A boy and a girl are riding on a merryns /*vjqx7wz6j0e 9jrrkp1b4sn :mh 4-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 greater angular *r0nhwsn4r 7j:x mej /96 jvpz4kq1 sbdisplacement?

  A boy and a girl are riding on a merry-go-round whicb av+1/jdd kj7h is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greatkd/jj7 a1dbv+ er angular speed?

  A boy and a girl are g m 2aikwy.,d 3x6o0az.m- sxk(dar5iriding on a merry-go-round which is turning at a constant rate. The boym26 z riy3 .ogk.( ad,kxaawm0 x-di5s 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 which is turning at a constacy+p ol.,vj)p ytfx87bz 7xt(nt rate. The boy is near the outer edge t+jb )lfxv .otpx7y,c(7zy8p, 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 constanpfuf)0kti 6*lt rate. The boy is near the outer edge, while the 6 ukffl0 tp)i*girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that ckd 5oqg acjgc)(c((.p 8h fint: -ml-is rotating. Which of the following is an accurate sto(i kgcmc8dhj.n ( 5f cp(g )c:a-lqt-atement?

  Rolling without slipping depends q 4v9y, (k3w8kyi tdwlon

  Two equal forces are applied5 w p4w;hc) /njh zw;xm(wqsu/ 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 greatern /5 p)us h xwqwc4;mw;w/jz(h torque?

  Two equal forces are applied to a door at the doorknob. / l-h4. ez(rh2iqdc bl The first force is applied perpendiculr.4z /i (dhlcq2eb-lh ar 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 appliedq2/zxejt hg( h3*i7rq to a doorknob, perpendicular to the door. The first force is twice as large j/7rqh2gqti *3h exz(as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resist 9h,7sa ;sitklance to changes in rotati ;is ak,9t7lhson?

  Consider two uniform solid spheres where both have the same diameter,a5fccd()e.qhtwx;d2 (y;bjf but one has twice the mass of the other. The ratio of th(fb;dh xt2;aey.cdcwq()5 fje larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twi*ymlue) 63a gice the radius of the other. The ratio of the larger spherl6g)m iya 3eu*e's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass andwacm hap;d 928 twice the diameter of the other. The ratio of the larger moment of inertia to tdap;9aw8m2hc hat of the smaller moment of inertia is

  A uniform solid sphere has mass M and radio7glnfs1p b,o 0 fi7l0dw9, gkus R. If these are increased to 2M and 3R, what0 lo1og,0n9l7i d7fws ,f gkbp happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to a/ba am /,hfy.vpzl+- 4yi gez*n object, that object will

  The moment of inertia of a solid cylinder about its axi+fz-fkyg+wmar5eo0v i gf 69c . a)4qbs 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 of5mvw5cd ckn:i 56v,n b /1wuifhmg /j( 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 total translational kinetic energy of the bike? Assume the wheels are uniform diskk: buj6/ngii55 vf mdmh1n5w,/w v(c cs.

  Suppose a solid sphere of mass M ad 6; yedhq;tep z2*vh2nd radius R rolls without slipping down an incz h2*dvhpyq;;6e2td e lined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere 5sxy(ld;p1xj of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity dy1pj 5;sxxl(of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a netivataq+v: 7rl6e1 +om external force acts oni6vr : aoqla1+ 7evt+m the system." This statement is

  In what circumstances can the angula -: bt61kwlgsbr velocity of system of particles change witw1b6gt- ls:k bhout any change in the system's angular momentum?

  The Earth orbits the Sun in an el9:ji ebcbntttl-j/pkp,hl )w 5-j(h) liptical orbit. Ignore any friction which may be present. What happens over time to the/ lej-)hptlw:bc-ijkt,( p jn5tb9h) Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit.b p7v8 swbbl w5o++0fega .+qj As the Earth moves close to the Sun, then which of the following best descris v w07qbeg8lo.+ afbb+jw5 +pbes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulls nv .y:6kd79 ft6gixrkk 9yn8ing in his outstretched arms close to his body. What happens to his angular momentum abou.n6i d998vtxkf kysgk :y6n r7t the axis of rotation?

  An ice skater performs a pirouette (,- r8gn r0zsv0wokp.y a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational k0.8vo s kp,-gnwyrr0zinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling igg*fo ;u4xv,8q xvh *dn his outstretched arms close to his body. What happens 4*8xg;oqughvv x d,f*to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum. ha2l*s 2ltccj-jjcyl9 . u74o

  What arc length does the Earth travel in a to.+o+s2 h jwwthree month period in its nearly circularhwo +s 2+twjo. orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 u(8/bya-xb2nlq 5m lam. What distance does the tip of the second hand sweep through in 3 minutesaxy 5q8lbl( nm-/ab2u and 45 seconds?

  How many rad/s is 25 revolutii)0to:2jz oyjons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 p1y+ ;nj 8h1x5iq tpiprevolutions in 4.0 s. What is the frequency of the wheel's rotp ;p +i1jht81pqnx5y iation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.4;c m0/f ykih;)s/h2v;im r, xx4j6xphjj /rxp0 kHz. The perioj rrj mp xyxhfpj2xi/h4kc)hm;i;/, 6 s0x/v;d of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0. cjvq0eu7 q0.jqpb6x(iya)02o i cm1 k20 y0e7p2uq1c 0q jk x(ii ov j0m).aq6bcs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the 4wh 4s)sgeg x*outer rim move in 2.1 x 4hgeg* sw)s4s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thl. hw9n-o ct 3t ruw0,yr2g*zje averag,cow.h*-r w 2yn rjt9zl3gt0u e angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is t59i e2 kp*,cpfkvyrv) he linear speed of a point 0.10 m from t5 9)pk ,*p2ivevcrkfy he center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cablxc39 /q3 ;1icm+aegxtjkln7 re which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast muc; 7jxgl1ti ex/n9ar+ 3cqm3 kst 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 angular speed of 2w,l2jkbsso(-36 g9t+v v(-z ossac sb.0 rad/s. What is the linso,2-a s+ -wbtvl(bj3k6cs (ov zsgs9ear speed of a point on the wheel's rim?

  The cutting cord on a gas-poweredi gbovquj05 p+u;k8b aln7rwnl;6cxs- k2a1- weed cutter is 0.16 m in length. If the motor rotaterb; kl-n5bculaux+oan8ivj1spk0 7g6;-q w2 s at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is roi4,wdzd5+8.ewqx ra;,e obol ).v8nc,vkejttating with a constant angular speed of 2.0 rad/s. What is the centjed;t5 a8k,ln vir+4),. vde ,bwz8xcqweo .oripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyxvd,o q+*za;kc js:m **/d 9vzabx/ vscle wheel of diameter z b+vs /xkcam jsda9;q***, :vdvoxz/ 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rot-y afg1in/zu v+ji nybun5j oc+f ))3xq,2kj;ating space station (r = 1000 m) rotate to produce an artificial gry;jgb+x5y n-jz +) j )qif aok 2,ufunc31n/ivavity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wkl(jr-8v;;q fi,iq*d /q.:ictzma ym ith a speed of 20 m/s. The maximum centripetal force (provided by staticdj (zfta -m*:c/ q ,imlr.ikiqvq;y ;8 friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circuzjnlatn47oj,:. 3mz dk, xslz7.pe4m lar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by staticl43,js nm k zzn,d xl4t7zj.e7o: pam. friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end oxop3x*vb 8v 8 cj3la;zg, ixnjy46po +f 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 speed can the maspyi;cvn36 o4jx 8*z8v, ob ljxag+p3xs have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cmu t); d )qabtv0ocjf6vctni22,vn+b3 rolls without slipping 10 m down a lantnfun2vd;6i) 32vtvb0cc)b, t qao+ je 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 ot+y 0ao6g*y1oplp v y-f $4.5 rad/s^2$. 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 v8;m gvf6(mcxapy4cm/mf;e:0xg9jaconstant 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 aft pbdjpuzvn736fg t,wf-h: .6w er starting from rest and accelerating at a constant angular acc.36 :ub,gd-p zf6fjphwv7n wteleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angularsg6ared7i 2jr/3k d.r acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceleraony )uv25aj +xua+ :intes with a constant angular acceleratio+xnya n uu5oi :a)vj2+n 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/s psrw(ga), i/9nr uh/j;x0nrhwhile turning through 2.0 revolutions. What is t9ar unw/g );,/ (nijrr h0xhsphe average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest o;ig,ku,i t*g iver a distance ki i;, *tgiu,gof 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter ofdia )): kt myhn8c/na8 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What ism)8k/ntan)d a:8yih c the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 mqk*bzlej6, 9/yx)-r sf6m kj m/s to rest over a distance of 115 m. How long doe 6kmqez/lsmjykx-rf6, *)j b9s it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory j2cmgmth7 u+x:7lrf7 rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constarl 2j7cx hm7gu tm7:f+nt 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 to a todky/)rii+33sg/fw xmf lf41 r ws/,urrque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the r s f/wfy/wxd3s+u4i)ifm,r lkr/3g1 force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening t ;uqo rtxe/*-no a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude otxrque;no-* /f the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of : cx-:5c,al)z;(mr3me2z mbuh p brob inertia $3.00 \; kgm^{2}$ 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 isx 70.rx+daqnxm e 4-ap:6tjijprh. 9n at the origin, mass 2m is at x = a, :.prtian9 qph +4r-j0ax xm.7dj e nx6and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thouy w/e sw6hoc/;ght the centerw;/hesoy6/ cw O. 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis th (*lz 16hn k)i ep1udjnkwcj*(ought the center O. A rope wrapjenw zpd*k)hjcn((16kl 1 i*uped 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 *ie lsz(1rst -2 xxt2eone end. The rod is initially held in the horizontal position, and then released as the free end is allowed tis etx( 2-xl1rezs*2to 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 to be a ring of radius 30 cm and masek;7m g qr/pe4f+*4a1n:7c yrxwne vus 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 it rolls without qp:+/ewfr7;x uc7nk4r4m1 neav e*yg slipping?

  A 1.53-kg mass hangs on a rope 52o jkqu )rh44y fq-tcsn2 i7ehf28fb wrapped around a frictionless disk pulley of mass 7.07 kg andf2sn4 fr7 5)htjk qbich8o4qy e- 22uf radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk fr3ev-p2 o ,k)xqjt-r pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the maprq-rxk)3,-jf 2 veto ss?

  A rotating flywheel can be used to store energy. If it is 2+ r eadoxy;)frequired 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 ofv;17(d*nysi -bf i8 htoczt.a inertia 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 0.01jsiq3w t, ,r4ftlg5otlh5h(zn.fv so :s/ d7 (0 m starts from rest and rolls without slipping down a 1.0-m vtn(5/f4q5ijrsshl:w, 73o.thltog fzs , (d high inclined plane. 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 r6 o/(xxh ha3yq ntzs,;olls with a speed of 10 m/s. How high up an inclined plane can it climb before coy;/,xzo (xhtnh3aq s6ming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releau1mg3ge9 z0 6q2lp w 7ys,lcqwsed from rest and allowed to ,l 2 w690czsuwqmeg7 yql pg13roll 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 withocn8 qzb4/:emuzxj+a .ut slipping down a 35e incline that is 7.0 m long. m/u je :z+ nbqzax8.4c 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 mo,8+i wbee:dl umentum 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 rf8h 2hk-y7yhz e0rd:26 l bgk;ns*j9v u juh7of $5.0 \; kgm^{2}$ 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 t3fb;46amba uhas a moment of inertia3tm 4b6ubaa ;f 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?