Angular displacement is usuallyg-r t h:i d8ni.xhsg:+ express in units of

  Angular velocity is expre). 5w(by j y-h2 npllqcju+:f6ksv6edssed in units of

  Angular acceleration is expresl3/pps* t:m7l pfcke1b czm61sed in units of

  A boy and a girl are riding on a merr -5xd ;wj+2d-kh-p4o)h07f hunhx b1ewzxlsd y-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the centkd jfd5z- ;xhshx4n -xhl h+7b2w d0u1p) wo-eer. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round lpo. akva-ukz-tkpfe jar)0sk,5b8s- 1*y 4fwhich is turning at a constant rate. The boy is near the outer edge, and the gir.ku8 )k1 rzv* 5jfe-k-fs,p4pbt-0 ol kyasaal 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 conuv24gf kgt lz*p ta; z 8asqm105/;feystant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the g qgta gz1pm zlu02;; 8se *y5v/akff4treater linear speed?

  A boy and a girl are riding a merry-go-round which is turnin;e wj nc*meiwxdq, 10d/(d2bbg at a constant rate. The boy is near the outer edge, while the girl is closer to t(0c;*b /dmdeeqw wn ij,1b xd2he center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is bvev9eb31h *+xcatqmc qs,y 8/s7gl ,turning at a constant rate. The boy *es9b8 y1qchlem /x+qg3bs,7t ,vav cis near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of /sb+ g-hxs3qgvn*zz05. hz 4rs j/a izthe following is an accurate statementrs*bqs/i. hj+z vzxg as n-h35 /0gzz4?

  Rolling without slipping dj +*ifs,f 0vhv* x4iaoepends on

  Two equal forces are applied to a door. The fidhebyy:p y/ v)f92 9gnrst force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces9nhgdybvy)/ f:p9 y2e are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at wm4yw,v mubwq0l::s8 lf 81fxthe doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to th81f qmb:wm,v84x wf sy ulw:l0e plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the dug9 9pv4eve,i oor. The first force is twice as large as the second force.evgu9 , ei4vp9 The ratio of the torque of the first to the torque of the second is

  What is the quantity used to meg7bjn:k v9vyxyn*p7 qp,.5. t uuz im2h zu9)gasure an object's resistance to changes in rotatiqv7y .x 2z.nzkpug*up vbiyh5n:m 9tju7g)9,on?

  Consider two uniform solid spheres where both have the same diblr5j :cv2y (wpx7b w8ameter, but one has twicv7:xp2w(r byc5jlw 8b e the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have thkx6.zxewg:5y1ahmw+1r p ja- e same mass, but one has twice the radius of the other. The ratio of the larger sphere's mo11gr. - ha xkw6azpe:5+mxy wjment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice ed,i3jb /k3e c7y mp6jthe diameter of the other. The ratio of the larger moment of inertia to that of the smaller6die7j ype33k /,mbc j moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased tox ayau8:j+6 ,t2rr(udpsm ; pl 2M and 3R, what happens to the sphere's moment of inertia aboutr8s2t6:(rmu+x aalj ,uy pp d; a central axis?

  If a constant net torque is appliedr5 qx3fp t9t+zd1t6wht7d*se to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by3l l3y,;m/ow* rpi 5r ga;zhrv $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of.w+b0* 1kdq kcef+j v hcmcu8,si2 tm4 which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of thsiq1 fk2 ctd cce4vw+ h*kj0.bmu8m+,e wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of madk cv/zyk*( u)ss M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline dv(u zyk*c k)/depends on

  Suppose a solid sphere of mass M and radius R rollsz)ig 2nct4je .tcvpvz4 -0zt) without slipping down an inclined plane stavcpztcgzn ze 2ti) v4).0-t j4rting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular mome8 :5gmgvt-6el*rj bg cdnvj:0ntum of a system of particles changes when a net external force act ltc0vbm6gj 5g *gdnrv:8: j-es on the system." This statement is

  In what circumstances can the angular velocity of system of particles ch8* )ta a6yeh.xp4 k skt9jryl9ange without anyy*y)tsl96 kat.arx ph98j k4 e change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. 5v*-krm vk 832y7nrpm npufl8 Ignore any friction which may be present. What happens over time to the Earth's angul 2pk3rnl v8vu5mmf 8 k*-rp7nyar momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earthj 3si.ek0q gg/rd xqe:2/8/amvcl4 ms moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about q3siek / l4r/8dgaqs2 x gj/.mc:e0vm the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in gc2zj,( xzuu)my d5jlz27 fn: his outstretched arms close to his bodyygn fz:,dzl2ucjxm2z 5()ju 7. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spinytl;ojsvsj03:6 mo. t) by pulling in his outstretched arms close to ho:s.vtm 360j yt;ljos is body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a opv 60(+scylhbw lu604lgd4xf- h+ owfast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the o ho6-c(+hlx wsu b0p gy6dwl+vlf404axis of rotation?

State the law of conserntk3h4nvvk9v:rl+ ; o vation of angular momentum.

  What arc length does the Earth travel in a three month pd .gvlarv)b 75eriod in its nearly circular orbib)vadvr5 l.g7t 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 m. What dist .elt 2crvou/,ance does the tip of the second hand sweep through in 3 minutes and 45 uv ro.l, c2t/eseconds?

  How many rad/s is 25 revolutions per minute r(ct; zskjy772 xwuz u3, muj5equivalent to?

  A bicycle wheel rotates uni jsy+n 0 j*q9pn33or gpx5o6bnformly through 2.0 revolutions in 4.0 s. What is the frequency of tb*p6o3s53yx9jn rnjq+gon 0phe wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a f9j8; sspnq:z9r* u nnirequency of 0.40 kHz. The period of its rotatin9rj9 z8:u psnq *sn;ion is

  A phonograph record rxson) ,ww0xt6 otates at 45 rpm. Through what angle does it turn in 0.20 ox 6xw,n0)stw s?

  A wheel of diameter 26 cm turns at itte y3+ *uoj;1500 rpm. How far will a point on the outer rim move in 2.t3 ij;e*uo+y t1 s?

  A bicycle wheel rotates uniformly throug fu +jw+q 3np8/,q*d(ot *dz bbnnbn7wh 2.0 revolutions in 4.0 s. What is the average angular speed of the w+bj+*w*7w/(pd8onq,nbn tfb qun 3d zheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ise ok,)vicj( 1ft+k5nn the linear speed of a point 0.10 m from the center of (ve+o5t1cikfj knn,) the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whic,q7 .ow9 7/ pysvdz.icnb5tleh moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable 7tsbcl7 vp dyi,..z95ne/woqcar to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0*ay7k:dld jl5 rad/s. What is the linear speed of a point on the wheel's akl*dly5: dj7rim?

  The cutting cord on a gas-powered weed atz xdvj5ts- +r2 s7eqv0,p5h cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev5sr jqd-p7 0v h2xvsatz ,5t+e/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of-kdursm-ygnqxr38z/* ( :pmn + gq( nd 2.0 rad/s. What is the centripetal acceleration of a point on the wheel'rmn mx :3-n(g8(kzp*dg/uqqsd- nyr+s rim?

  What is the centripetal acceleration of a point on the pea f/9hw:-eags2hu 8b rv8snf0rimeter of a bicycle wheel of diameter 70.0 cm when theha -/2vw98ug0f rn f8a:eshb s bike is moving 8.00 m/s?

  How many revolutions per mi q w3-kwh-gs3knute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificia -k3 gwkw3q-shl gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speeliu* p*0mb 9gxd of 20 m/s. The maximum centripetal force (provided by static friction) is**guxml9bi p 0 $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circuqor2/ugh,b c 1lar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction/qguh, o rb2c1) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attacy.b2mh hnmn:e- v7, athed to the 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 etb: .yh,m-m7hnva n2250 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 s9 l eu+(is enp (qx),n/rhwade01i+sslipping 10 m down a lanehiuw +1 ss / s9(nneiq)0(la d,+xrepe 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 a6lx:-k -h :jt2hxhba z constant 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 w69js o1 m-ho, pus1 q 4i:s.lj2kfnkiv;h)nxvith a constant 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 *: +6 )0m nfsemdkv5qnjnyaj /0.300-m radius automobile tire rotate after starting from rest and acceleratinj6:e0q+ yfv nj5nnma)m /ksd*g at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, (tm ln3rrvi z*+ puu p8mmc53f)0kpq (and has an 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 co9:7jtt8 hltujn ku 3ti- s4f9bj+/ytpnstant angular acceleration of tjt 7+u:3j t 89hitls9kfpt- n/u4byj $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and renwb tth)k5z -3aches an angular speed of 6.0 rad/s while turning througtht -3 wnb5z)kh 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly fd yd7l5 ,fq/*x/d61 k5dhpikoaqjym 3rom 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in f1 kl yqddi d3xjy/o,p*6 55kdhm7 q/acoming to rest?

  A wheel of diameter of 6zlw:0v(hfd ( n8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of fnhl d(:0zvw (115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fro ;wjze5tf *4 uoarq: 8don43sgm 8.40 m/s to rest over a distance of 115 m. How long does it taqa*fuero4 z 843jsg;t :w5no dke for the wheel to come to the stop?

  A centrifuge in a mediqd47a 4swt;:(k ,ij)zyf zvpscal 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 to restk (js4,q)wtf4d:p; 7z vsaiyz.
(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 a 30 psimseqx26k /: txh3;cm long wrench is/stehsqpm 3 ;xi6:k2x used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightenpk; f(kr, es ,u8+ l,uhfw o7sfvwn,r-ing to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the fvleosuu,kk +fpr,n(,f ww8-r;s h,f7 orce applied at $53^{\circ}$ to the wrench?

  A wheel with moment .xn32d2*)m2ygj tij(+ f xmrods0x;evaca i 7of 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 is at the origin, vv y*l47tl0hamass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment yt0lv4av *hl 7of inertia about the origin?

  A solid cylinder of mass 10 kg is tr48oc q wo7um nr7;x8z *+tizpivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius uxzc8z4iqo7tr 7wmr;*n+8 to $R_1$ = 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 gxgu4q 942q amkg is pivoted about a frictionless axis thought the center O. A rope g294 qqamu4g xwrapped 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 rynop6 m5 5dfkl+9 r z3gw6 oww)rge;0is initially held in the horizontal position, and then release5fo r0yde;zrgr3 p w)ww m lg5n+o9k66d as the free 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 wheel to be a ring of radius 30 cm and mass 1.5 kg. Nexeg5*4,) t * ojsztuvcglect 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 rollzsg) teto5,*c v*j xu4s without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pull6ohk:2/s wdtk ey of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulk s/twhd2 k6o:ley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless dis4t*,7q;k(squkryhj n k pulley of mass 7.07 kg and radius 66.0 cm. What is the ac(tuq 4;*qhk,y7kjr nsceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to stor)9- ghxt ua7 /g ti7c4vylwgk/e $1.00 \times 10^{6} \; J$ 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 iner;i sqvx41 /f;*byunqk56pd z dtia 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 1q kxp8w8eu,/t -rn r7q.0 kg 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 of the inclinedpeu-/qrwt 7 kn 8,x8rq plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls witha .+de6q)srwbp c cz1)-sec; r a speed of 10 m/s. How high up an inclined plane can )ac6.w) -b+czp1esrcd ; s qreit climb before coming to rest?

  A hoop of radius 0.50 m and a mav,1c ephz9 (ewss 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 distanc(h9we ec 1vp,ze of 3.0 m?

A solid sphere of mass 1.5e5v;srj0m-csfghq-c7uy1opy 5z /ci)m0u/ u kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m 05-qzum;)f umughy5yij 0rs7o/c e1v/c-s pclong. 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 changec*v+jhr6 dbgcsv)1 sn*3sk v(p*x3ozs 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 moo.bmc1ub: x (ument 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 a moment o: :f-6 k y5tvqwm0xusof inertiw650tu:xs oy fmv:k -qa 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?