Angular displacement is usually expr q7yfj.p)ju9t.g (gia ess in units of

  Angular velocity is express qr gu9ow+tk7nfgo( ;g+jr2 ,:ipt5oued in units of

  Angular acceleration is exp2(g qnjwl.eyb2n 3 wl-ressed in units of

  A boy and a girl are riding on ao/8iwrt, syq 7 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 greatoq w ,r/si87yter angular displacement?

  A boy and a girl are rilz p7 anbi2/zku)i m+7ding on a merry-go-round which is turning at a constant rate. The boy is neap7zu 7a)kn/zbi lim2+ r the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are ri)ll.jj3/l5niaivs clvo4f1,3n e5 axding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is close jv5lvo3,njc/1)s.4 ieax alnfil l53r to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whiy4xkn r,lq(ss1 w/v+a ch is turning at a constant rate. The boy is near the outer edge, while the girl is closer xsrw4yl(s kav/1q,+n 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 com howh ,,d3w*ynstant rate. The boy is near the outer edge, while the girl is closer to the center. Who wdw m*y,h oh3,has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate 6: syqfa9vd;zfil*u 1f nx )*as:dq1*a*vi)fla9n y;f ufs 6z xtatement?

  Rolling without slipping depends lgawt(8 u6g1ion

  Two equal forces are applied to a door. The first force is applied at thewtfcui/q *m, ,0ff+br midpoint of theif+*mcf ,u 0rbfq ,tw/ door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied g45 ltbdgj78gto a door at the doorknob. The first force is appli7g gtgj d854lbed perpendicular 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 doc1pn:q2g lk eo2 harsgx-+1 .wor. The first force is twice as large as the second force. The ratio of the torque of the firstn-+h koq:ls1gx pae 1 cw2g.2r to the torque of the second is

  What is the quantity used to measure an object's resistance t6 y7rgupuy; r0o changes in rotatir p0 6g;yruyu7on?

  Consider two uniform solid spheres where both have the same diameter, but one hai dhwo )):.qwwm+jd 8js twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller mo wm+wdjj. o)8)d:wqi hment of inertia is

  Two uniform solid spheres have the samxfwg1;7j s5 hmpgz) 7ne mass, but one has twice the radius of the other. The ratio of the larger sphere's momemw)fgxh n ; js57p17gznt of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one hasli:n3wa:y5 h6 zr hw+o twice the mass and twice the diameter of the other. The ratiwhl65+r hy wzn:3:ioa o of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radiug)su4f n24nj / xpmnef+kb1;as R. If these are increased to 2M and 3R, what happens to the sphere's momen kb+p saj4/4ff;2ng)1mnxunet of inertia about a central axis?

  If a constant net torque is applied to an object, that object will v 0znxfhpv.dr:ir;(;

  The moment of inertia of a solid cylinder about its axis i hvp3q+p l)zhhtw/k(2ci6:ao/rbl y1s given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy i2h+ cr /vi3y1:pa lzklh( /wopqh6t)bs

  Consider a motorcycle of mass 150 kg, one wheel of which has .uyi+96h mchk/,lfwz x y buh,m,oi1:a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic eneck61z.fi/y+o:9 ylm,bhh ,um x uhiw,rgy 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 rolls wit; x+ elqz c7vj,yxz-k8hout slipping down an inclined plane startingvlj ,z-z 8;7xe+ckyxq 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 slik2.t. wb; m4)oooz gs2: hhkiwpping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom s hmkoot b wikzg;2:w4).o h.2of the incline depends on

  "The total angular momentum of a sydq-.w* cyah) 8tjb4igstem of particles changes when a net external force acts on the system." This stateme8qicb4g )j*h. wty -adnt is

  In what circumstances csrzy 9tt.wrm n ,wo6c: 1gt *5*bpbp+uan the angular velocity of system of particles change without any change in thesnto6cr+ 1 *w p .wby*9 zm5:pug,brtt system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore 8 w.gnjxhnf ((any friction which may be present. What happens over time to the jfnh wgx(n. 8(Earth's angular momentum about the Sun?

  The Earth moves abou76 sahh0q h9agt the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes 0gsh aq69a hh7the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spino x7;i4ny7w bdu.vpe+(/ z62v ybsxvp ) by pulling in his outstretched arms close to his bodydx6yeip +nv7.7 v uvbox; pybw(z4/2s . What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullingtan 8hcr w9fcztzzr; 6d y/ 9(h898qnd in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotatio98(nnd d rczwcryhq98t8zzah96f;/tn?

  An ice skater performs a pirouette (a fast spin) by pulling f lz zc.gpo5z3p9z.z9 *kdo,n in his outstretched arms close to .zdppfo l. z9kz5g ,93*zozcnhis body. What happens to his moment of inertia about the axis of rotation?

State the law of conserv,ze rj5 mni/ r:0zy4qfation of angular momentum.

  What arc length does the Earth travel in a three month period in6yrspu-*g76jxj, v0r vn2hyd its nearly circular orbit a 20prhjsxn 6-g7,v* yyujr vd6bout 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 distance do6:,srp.druj2 is,8xhxn rfj; bf5 n3i es the tip of the second hand sweep thxn 5b,8:2isphsfu6, 3idj .fxnr rrj ;rough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equdkfa;h0/v b m5 n*iyyu0t4sc* ivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whm1war znen3 d .55zh*bat is the frequency of the wheel's rotatmn3r5dz. nb* 5zae1w hion?

  A pulsar (a rotating neutron star) emits pulses at a frequency oi /4 69z+jk ptuihzh(-ez 2dlmf 0.40 kHz. The period of its rotation itzl idm+ 4peu j2zzhi(6h-9k/s

  A phonograph record rotates at 45 rpm. Through what angle does it ad .k0mbxl*2vvvu1ht ,h1b u, turn in 0.20 s?bkultvb.,vx0um1v2 a d * hh,1

  A wheel of diameter 26 cm tuz+lp-f q/ys*e8nyemtd6,a , vrns at 1500 rpm. How far will a point on the outer rim move in 2.1 sy v,+d/ qzat,-86f l*yseempn?

  A bicycle wheel rotatesd.z3/je5 j/) ulvv ddctmw:g, uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed o).um/3cjd/dv,z vg j:e5d wl tf the wheel?

  A bicycle wheel rotates uniformly throughgxwe6kum to+41:h. cj 2.0 revolutions in 4.0 s. What is the linear speed :6mgt1ukj hoe4w .x+c of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whicuqgr9 o6gqlz);9 4 ,-)mzwq 9 yvrqgcch moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must )9ygmq wrqz),rcgc gu4;69l-qzv o9qthe pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a cy2lc9 ad6( drsonstant angular speed of 2.0 rad/s. What is the lin yadr9c(ld s62ear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0qo pp .cinzuf-p 99t 9bmy)(r:vmv t,0.16 m in length. If the motor rotates at the rate oftoqn.) pv- pt9ib ,0pmv9y r9 muzf(c: 20 rev/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 angul ztwrf -;xn46uh +yajd9032v8hyf vst/z;cyaar speed of 2.0 rad/s. What is the centripetal acceleration of a points 6cz;uyyxt wa3f/df h+-vra; jz2vnh9t y408 on the wheel's rim?

  What is the centripetal accelerati;v*g33e8kw ozvqmp3ne kc; ;yon of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 3w;ekm;v ge*cky 38qz3n; p ov8.00 m/s?

  How many revolutions per mijh9uqm5p90hqi a- a*fnute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produ9q ham9p-fiaj *h0u 5qce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radipfun-ol80g z*:by*cqhv( oh7us 50 m with a speed of 20 m/s. The maximum centripetal fvn -z*ubyoo 0*qfl8(h 7gph:corce (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 radius 50 m with a speed of d3p; p:f4 upcl20 m/s. The maximum centripe pcupfpl:3; d4tal 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 : uu9 ui+ejv+lmp+e kj5d 0g,qof a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withst+vu0quluk 9mgdjje+,5 :p+ie and 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 x7z81p jvrrq,77y zjg4:i3b9vwnoc 8 ,oteya radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s.7yoj n,z ,jqx t:793rpavc v8eo4iwr1b7z g y8
(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 accm, xntoel h8;zm6za.8eleration 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 wyf 8vt3:ibcnhz 11b0 pith 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 0.300-m radius automobile tire rotate after starting fro*crdn ys;e ap hpeddbk/*w/l g,:x9+: 7xp:oim rest and accelerating at a constant angular acceleratin/dh*ix:/k ;:p7x e,e*p r+9clybsw d d: opgaon of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest o u x1bj1j-ntf)4ut3 s-nu5fl, 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 constant angulaau/k by; 7-nawr acceleration oa ua7wk-/byn;f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest .h ( (qxoe75womgpn*band reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleratiob x75gepo( h.onmwq* (n of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 mk jg/n)c9sbova1/up z9peo 4 nje.3k3/s to rest over a distance of 115 m. Whukn19gb/4z p. jkvo c)9oaj 3sen/ep3 at is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovdpsr s(xhqiscy(1ptq/2w : + +er a distance of 115 m. What is the angular accele+ (p /:xs1dqsyhw2iqt+r pcs(ration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/tgn.bvdkz:wp 44-.yhi)5 cx as to rest over a distance of 115 m. How long does it take for tv:..w gnpyz)hx4i- a kd45bc the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationarf:0h ch);gw5 xiyqqk sw21z x afn(w /5gfm/-l speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration bef;n q/ xg:hyf 5swaz0f k-(hw /fmc)rxi5wg2q1ore 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 wheeb6.g x(+.pum gd6qu zrl require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, md up6x+guqrg6.z.b(what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 N:vmo x+b y)-+pv6w/sbo2 kx ;tetws ,rm. If a 30 cm long wrench is used, ; e+w6b+t)2swtv x orvoysxbpm :,/- kwhat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti 0njsa i30kslc, zhd.*a $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as foxzikftl9v q 4qu/w/)h. hv 9kv ;ytbs:a0 b59wllows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about thew zlk/x ts9t9ibh vkw q; b5u)hay049fv:./ qv origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought t.run8 sin7xo2he 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 another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the an8s .oruxi7nn 2gular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis tlnfp +d l7jy83 /3/hgpsthu.- qxt7hzhought 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 another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the cylinder rota s nl3 p8xh/yg-t/t q3d+f.7j7zulhph te 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 qnaxw gf0gw+ 4i+6t5oheld 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 of a rod about one end is ML2/3ngtfgq xo60a w+iw4+5 .)

  Consider a bicycle whpr7zwq )pe+n 4eel to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sr+p)znepw7 q 4procket. 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 wrapped around a fric yzeqvi(2: c*l4mra vki/g/ f6 ky3,cytionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of thev:i y,6(iyq34*mgc2 /l/kcke azrfyv pulley?

  A 1.53-kg mass hangs oj lb6jxfzt, pc ,5*1von a rope wrapped around a frictionless disk pulley of mass 7. lfc5*,,jxv6bz1j pt o07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it1jq/six zpn3 )wr rfta51p 4h* 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 inex p7b(njj*nx;rtia 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.c ,5j: w5sq ;rhoqqfc 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 inclined planers;jfco 5 ,qqqh. c:w5?

  A solid sphere of mass 1.0 kg and radwt:pzj9cr( dy.tk.) hius 0.010 m rolls with a speed of 10 m/s. How high up a(w. : )rptktjdh.z9cy n inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releas;b2pf g0cn8iwo ta0 r3nr,x+jed from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3ca;,02jb3 0gwirf8nrp xn+ot .0 m?

A solid sphere of mass 1c4 ,vzwiwl l:*s55x lw.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it stal *x,5 vlw5wscziw4:lrted 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 momen(8t cc q9f*,jvsh 0eyntum 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)qiqu2wu+p75virgs+;ug lo2 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 of inekh1j5-y21j-a lad ggfrtij- 2 1-ggfky hd1al5aja 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?