Angular displacement is usually2ee;- )sx,x y vqn5f9 iysat::jg; tku express in units of

  Angular velocity is expresse.z.lzet98d b gp*ngw p j-:yg7d in units of

  Angular acceleration is expressed in units ;;ypmh b rfx5w8ib7v.of

  A boy and a girl are riding on a merry-go-round which is turning az 1)kaxt5idwnei+i x+1 +uyt +t a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angulara+1 x5y)zeu1+k w +iitdi+xtn displacement?

  A boy and a girl are riding on a merry-go-round oz -w/a/mfp l:which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has thew:-lfp azo//m greater angular speed?

  A boy and a girl are riding on a merry-gj.2g ih g0hy2zo-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center0yh zj gg2.h2i. Who has the greater linear speed?

  A boy and a girl are ridtp7j5lolav: ri6ilagrp) *s.lp +9 3 ying a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceplt95+ rsya6p:ja.lg vii*)lp7l r 3oleration?

  A boy and a girl are riding a merry-go-round which is turning at a consta(i 83bm0uwaji5qzr q p;gc 3)cnt rate. The boy is near the outer edge, while the girl is closer to the center. Who has the g8 )03wgz5jmiu cqab r(;3icpqreater tangential acceleration?

  Consider a rigid body that is rotatinbc .z-**yd k2nm yuq9tg. Which of the following is an accurate statb yzn *y-uqd*2 .km9tcement?

  Rolling without slipping dep uk wa:r:6ub9cends on

  Two equal forces are applienad8g49 f zxv4d 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 perpendicularg8a 94zndvfx4 to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door au ge(krp2).zl t the doorknob. The first force is applied perpendiculg2 z ke(.p)urlar 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 1 vgc shgn 9ixc;b,*9pdoor. The first force is twice as large as the second force. The ratio of t hsnc9*bg ,i1x ;vcgp9he torque of the first to the torque of the second is

  What is the quantity used tov4b8 uqbkv0wi 2h1 t+p measure an object's resistance to changes in rotation?2b0hiwk p41uvv+8qt b

  Consider two uniform solid spheres where botad9i ti;i x/g9h have the same diameter, but one has twice the mass of the other. The ratio of the larger mi9/dag i9it ;xoment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the); p)ll9d+u/mfid baf radius of the other. The ratio of the larger sphere's moment of inertia to that of the smalle;dm)ib lfd+ fu/9) plar sphere is

  Consider two uniform solid spheres where on fqu3+c 8g0pine has twice the mass and twice the diameter of the other. The ratio of the larger mo38cf 0+ngupq iment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M andmah3;d 6tl4er) ki ht9 radius R. If these are increased to 2M and 3R, what happens to the sphe6era h4;dt)kit m93h lre's moment of inertia about a central axis?

  If a constant net torque is appli8;e0t o585 k47 iwzj e der:bkyzrw9yd5w,bd ded to an object, that object will

  The moment of inertia of a solid cylinder abae 2petkg-+g5out its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energgek2 eg5p+-t ay to its translational kinetic energy is

  Consider a motorcycle of mass 150 kgj b8s2zq5op /r, 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 en qro/2jb 5zps8ergy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M an5jvb wuw59 ;mnd radius R rolls without slipping down an inclined plane starting from rest. The linear vjmu9;55 vnb wwelocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and v;p t *q4mcyi69lt0 dmradius R rolls without slipping down an inclined plane star*v4m0 6;yqt9timcpld ting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes wo+ d a+2/h as-gs;pjg abuxj;-*/zivx hen a net external force acts on the systev+j*-i; j z/ +-/ sg; uxbaohs2pagdxam." This statement is

  In what circumstances can the angular velocity of system ofgbvqj+i;p flx:zh2 8(dszz ;) particles change withovs;b2 z;x(fgqj dz8:i + )phzlut any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whj8 1 khj4lll5c/c g+h/mlicm ;ich may be present. What happens over time to the Earth's angular momentum aboumj4/8l+5kgmji;cll /c 1h lhct the Sun?

  The Earth moves about the Sun in an elliptical orbit. wxv,j:70ci0jdyygp- As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun:jp-7,j i vyx dyw00cg?

  An ice skater performs a pirouetturs oa /,h)yy5e (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis y,s oahury/ 5)of rotation?

  An ice skater performs a pirouette (a fu*7l +k 5zivt dsg54qwast spin) by pulling in his outstretched arms cl4utl5 zv+ 5q7kdig ws*ose to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pironr*/u*f 0m,7crjg tf fuette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment tcu**gjm0f, f f7rnr/of inertia about the axis of rotation?

State the law of conservation (i+.b/;yp pqu ;b,xdc/f ykn lof angular momentum.

  What arc length does the Earth travel in a three month period in its near y a 5zug;elcd;ro4a.ap:0c .cly circular orbit about the Sun witho l c5ydu zac;pr0c.e4;a:.ag a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does thxrt55fx 3cl2ne tip of the second tf2 5xlr35xn chand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalenc* xb)sqcw3 :ia2i)r gt to?

  A bicycle wheel rotates uniformly 32 hlu,0.px n(ldot)qe81zwqg7 ay,u.yh yy j through 2.0 revolutions in 4.0 s. What is the frequenz(x 21).l 7ulyh0 yydqn py,ewoug83j at,.h qcy of the wheel's rotation?

  A pulsar (a rotating neutron dgvs-6 ic* s1/hdqqk4 star) emits pulses at a frequency of 0.40 kHz. The period of its -i/1ds vq kdh4q6sgc*rotation is

  A phonograph record rotates at 45 rpm. Throucdq ;2s3 5 twpdl/u:k;k 2xidzgh what angle does it turn in 0.20 s2:q;3/sp k2c kdz dixt5d ulw;?

  A wheel of diameter 26 cm turnsk kvgq00* lmx9 at 1500 rpm. How far will a point on the outer rim move il9kg0k*v m q0xn 2.1 s?

  A bicycle wheel rotates uniformly thro4aa8e xg:0lmqugh 2.0 revolutions in 4.0 s. What is the average angulaqx04:l aag8 mer speed of the wheel?

  A bicycle wheel rotates uniforml,z5u/tz cdduf 2/9k(us mhf 1vy through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from /u1 ztu c2u k (9mhvdsd,fz/f5the center of the wheel?

  A cable car at a ski resort carries skiers a;9x4snv:7jtgm ky2le ilsp// distance of 6.8 km. The cable which moves the car is driven by a pulley with diam7j ; yktmli/n4e/ vs9lg:sp2xeter 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 angular spe duc -z e7xw/ftgg zb41w/z3yy0dqs:q xke:3.ed of 2.0 rad/s. What is the linear speed of a point on the wheel'b1:yt wq 0w/3ufzkqcxz 7xg/d4d y3es.gez-:s rim?

  The cutting cord on a g3x)sdevc-4 korg8m -has-powered weed cutter is 0.16 m in length. If the motor rotates at the rmd hes-xg )ko43cv8r-ate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating w46j2gggs* n opj qdo).n/93vpvkl p *aith a constant angular speed of 2.0 rad/s. What is the centripetal acceleravaq 42lnn6kpo3*g*vdppjj/gos 9 )g.tion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on thx uq6gw6 q.hq1e perimeter of a bicycle wheel of diameter 70.0 cm wh6qw 1q.uq 6gxhen the bike is moving 8.00 m/s?

  How many revolutions .crrs zdclt 8tshb1 qit .)-8+yy(s8sper minute (rpm) must a circular, rotating space station (r tbs8lts.)h cryst( cs8+r1dzi 8qy-.= 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating aw:ib + 3dipytwso1 u33z j.jg/ flat circular curve of radius 50 m with a speed of 20 m/s. The m1w:3 pioji 3jgy +tbz3/d.s wuaximum 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 radius 50 m with a speed of 20 m/s,2nf3 n, )uuh ppi/vhb. The maximum centripetal force (provided by static friction)bpnh/2n,u3pv ih ,)fu 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 around 6 u4e706b zgi-ef,ovyrvf ub r0*r0xsin a smooth level table. If the maximum tension thasub0efb07r0*ri- 4 fu,vx oz6ev6ygr t 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 1o 4xk r .qj vzd(o.9hzvj0s4cslipping 10 m down a lane ato4czd(.z j 0v qs.v j4or91khx 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 ata/+bz7ik-o s km +xtbuk57s 1+xaeo( cceleration 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 q3 g52*cy+ z-si rzdeswith 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 does3e1w s , jckqbnlqk0;; a 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceleration of ,cnsl;1; j 0qbkwe3q k$2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleht36tjo tds,,1 9ht0 q 7kx7 vwbu 5gkja)1ekzration 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 angular acqww,1b nq k rpb7y20w)celeration o,7) w2bwq 10qrpkb nwyf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an ank/xhfjp.9j 6uzm -ntna4 :g ,usz ,il9htxl0:gular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleratmxgz jnu-9l/j:k ti 0n6.fhupa,,hx9ts: 4zl ion of the wheel?

  A wheel of diameter of 68.0 cm slxl/gb64v qiq3ows down uniformly from 8.40 m/s to rest over a distance of 115 m. q34 6lix /vgbqWhat is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of zgbmu 0 w;*l9z68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleratiwzz g9b*0 ul;mon?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ov8x*bcax)1shr .7f lxxer a distance of 115 m. How long does it take for thelh. r1* xx)xc8xabs 7f wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationaww) 0jq6l vlb/l speed of 3600 rev/min. When switched jv6ql0 /l)bww 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 tightening to a torque7pk5c4f.y oka 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 t 5c7kya4.pko fhe wrench?

  The bolts on a car wheel require tight :qxn(k 77aynmening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force :ankn7mxq(7y required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiuih n.,l9y)eq:d0-7 i nw zlfta $3.00 \; kgm^{2}$ 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, mass 2m,z7xp 4ksv7sy +p*ft1o0xc uq is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about ths+ o x xp 7us7*y4zkqt01v,fpce origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless ax6vjr fjxp;qd ;v;,uh, is thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.j j 6,prxvqvud;;; h,f0 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 angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless a1*:axfjs- o zau8 e ot*l y*+td:ahoe6xis thought 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 rotate through in the first 5.0 secon6 8y otx*hao+ aa*stoe*l: fju1-d:zeds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially hel r dcf)/zldj8ig :*; xp;tnk;dmyxd0 -d in the horizontal position, and then released -iyd* )x lrxtmzd;:/ npd;gj0c8d;fk 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 n2-xs 62 jw t5: nwn0f.auuivmand mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 2av. n:t0fuj xi62wmw n- s25un0 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 frictivba*u+vy 4m v516ehu6yz4 fixonless disk pulley of mass 7.07 kg and radius 66.0 cm. What is tu6vx5h4 mefyau4z b6 *viyv+1he angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless -d 62z8ua+lvgkr p9wz disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mass2a6kzdgu9 lp rw-zv8+?

  A rotating flywheel can be used to store energy. If it is reqzq(mnj90u4 ln uired 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 inertie:xtpjinip t 4m26:0 1z4oqbcin/ lt*a 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 1wob m*z)h5l 7rso0b0;qs l1 ff.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 om* b zloor01fwbq7 fsl)05;hs f the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of )sv09a9 tfmag(qk4/j*h d rm u10 m/s. How high up an inclined plane can it climb before coming to rest*a)tdrsku0 vhmfg/9 4m9qa (j ?

  A hoop of radius 0.5d3wq3 .jkl1khlm0n 3w0 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fas 13 mwl3kl qndh0kw3.jt is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and ra23 uzvdk 9waqp, -p2ubdius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started frombup9ud a2q -pvz,2k3 w 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 ch ey6 vi.*yoj 8nzmhd6/anges 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 mom/li2: dwjdr* tent 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 9-7tz ycusuy 9vnohy8 .vvz64 inertia ty674szh 9 yvuvc9-8n yuozv. 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?