Angular displacement is usuallz1 .y6v4y bedqjf,.9fe6uy oby express in units of

  Angular velocity is exp7gs -hfnlewf 2 v op+c1,mj0uo;qe53u ressed in units of

  Angular acceleration is expressedv/j eog5lf*2 i in units of

  A boy and a girl are riding on a merry-go-round eh3-wshk.8ysn7 f/ ko i)s0k y*3efsswhich is turning at a constant rate. The boy is near the outer edge,)os .sns7k*w/-e3kshhi08sfe 3k fy y and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning nxddiy 2a(ug f4od s ;cyj;)/7at a constant ra n7;df2xi;)g4d y(aucjo /ysdte. The boy is near the outer edge, and the girl 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 constpopguv/*ao 7;ant rate. The boy is near the outer edge, ; gvao/7ppuo*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 whic(+ obyt 0+icbfh is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the c0ic f y+o+bb(tenter. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a concf(2)bfzau 9i1v pdr :ciwh ,9pj*2 zxstant rate. The boy is near the outer edge, while the girl is closer to the cen9 jc b9i zx a1vfcdzp,fhp()r:u2w*i2 ter. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whic86 p:v25nn g lybwb/vxh of the following is an accurate statement?6bv n xlv2yw/ngb8:5 p

  Rolling without slipping depuro 4ey2ym,7gtc5pm5 n9 f:fzends on

  Two equal forces are applied to a dooyy ifi0ruuo83 )z bs-5 zdw.v7r. The first force is applied at the midpoint of the door; the second force is appsd3.i8 bz7 r-iyfyu0)wzv o5ulied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force ivj:1m8ju o zp3s applied perpendicular to the door; the second force is applied at 30e to the plane of thpmu o8 3zj1j:ve door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular t):py6gf rp9uf z* zniccrw06)l8rsg3o the door. The first force is twice as large as the second force. The cp 9)lz 0cy68 :prnw*3 riguzffs)6gr ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure ae. 8 (hrz)lx9:bv qf1z3fr egpn object's resistance to changes in rotation? p:bgf hqlre.9x83ezzf ( 1rv)

  Consider two uniform solid d:wl l,guy(927ds jcm spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertiuy: l7s9dm g wd(c2,jla to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but oneyvm-b4f1p0 uz has twice the radius of the other. The ratimz-yp bfv 0u41o of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass ak;1;prkn clegrvq4 6o2kn:z;s u:; ui r)d e/nnd twice the diameter of the other. The ratio of the larger moment o 1nngvks ;e ur ;rrl;ke:i/np:64oqzudk;2)cf inertia to that of the smaller moment of inertia is

  A uniform solid sphere v0wzepk* ie;p +o:jb.b+ax 7ihas mass M and radius R. If these are increased to 2M anp*i;b+:0+wex7jpbk .vzea io d 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that g+0 beosdu,jy1a:)u ) r pyqv)object will

  The moment of inertia of a solid c m2 j1k*/bmnndylinder about its axis is given by 0.5 MR2. If t *bd mjk1nn2m/his 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 which hae+pwx479kx*xqnlg7q5ko+hp*6ah 0nwy( u lls a mass of 10 kg and a radius of 30 cm. What is the ratio of th4l7n*a e *l+6 pxk5 0xqnp +k go(wq9ux7whlhye rotational kinetic energy 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 jc1ovlczmw(q; 9t3c / 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 depends wqccm; j v l9o/1(3ztcon

  Suppose a solid sphere of mass M and radius R rolls without slippingcv*is0-/: m i h xchn*fj0od4m down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the inclinemcx4-:m*0ch i0 *ihfsv jd/on depends on

  "The total angular momentum of a system of particles changes when a net exter+c3 z ; nqfpfggoyr)/y;.+sygnal foq p +f yggfy3oyg );r+z;/.sncrce acts on the system." This statement is

  In what circumstances meya0qpzu3 4g55 o,udcan the angular velocity of system of particles change without any change ipgu5oeuam3 4q05 dy z,n the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore hxl* hq*;t6byany friction which may be present. What happens over time to thex*6y qhb ht*;l Earth's angular momentum about the Sun?

  The Earth moves about the Sunb.h x3 ie yep.gu 9:jz6s5ux/wor./nd in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best deex 9s oywx3p/e:huju.z/ngi 6..bd 5rscribes the orbiting speed of the Earth about the Sun?

  An ice skater performsbai v7grm sens-( 76,v a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happene 7sis n(,6vrmv7 g-bas to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fac:6kw+ tt8dt krc( l8vst spin) by pulling in his outstretched arms close to his body. What :wd+tk8r cl v8 ctt6(khappens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spm+we,a 3 ms,zfin) by pulling in his outstretched arms close to his body. What happens to his moment of i s3f,wm,e az+mnertia about the axis of rotation?

State the law of conservatqwteu 9lubt ((; :3c zdjeo2b5ion of angular momentum.

  What arc length does the Earth tm0zh/vn ;to+gv1s)sxa6 uu0 y ravel in a three month period in its nearly circular orbit about the Sun with a radius o1/) ho+ ng06av ;svtz uymx0suf $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.ecoybp+pa *r9 74i b2tk4nn.r30 m. What distance does the tip of the second hand sweep through in 3 minutes aniar44y 7rebn onbkp 2c.t*9 p+d 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent tnb16mznn:q 88d . yc7wj,ftd lo?

  A bicycle wheel rotates uniformly through 2.0 revolutions i 58 ij 2r5)lbd)sde. bosug*rln 4.0 s. What is the frequency ofbr.)b rsei us82*5g ) do5ljdl the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulseshm edmf 2 q,;r49t kdwxige48. at a frequency of 0.40 kHz. The period of its rotation is im; xm2e498gtr k,qhwd. d4ef

  A phonograph record rotates ati:5ko7va,d3ifh.g zg :sc l p9 45 rpm. Through what angle does it turn in 0.20 ihik3s l:9.cfv,a 75: zgodpgs?

  A wheel of diameter 26 cm turxgpe klgngakc 9lyt8o)97og8 :zk / ++ns at 1500 rpm. How far will a point on the outer riog9 :lzgpk yknckg /9aoglt)7x88e++m move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What isnba*e3(x l1eauyl )x; the av lne3) yu(lx;ab e*1xaerage angular speed of the wheel?

  A bicycle wheel rotates un38or gf:qf v6s0px* 5;42ubpxfzba sziformly through 2.0 revolutions in 4.0 s. What is thesgpbof8xvb2q54; :z zsfx ap*6 0 urf3 linear speed 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 wt mg ydtv55s5:hich moves the car is driven btt5m 5yvs gd5:y a pulley with diameter 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 speed of 2 oo)a. ; xhwjgp9*,j.wd0dzx,jkl /yf .0 rad/s. What is the linear speed of a point on the wheel's rim gwoyj,x9wjfpd;kz,a) 0 j/.o .d*hlx?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length.js2)ty eqdmyp a/o7)to 57f t2 If the motor rotates at the rate of 202oo)75tspaeq/t yd2 mjy) ft7 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 angulaa :yf:shxkt lgxuypw4u :z)31wd /(a 7r speed of 2.0 rad/s. What is the centripetal acceleration of a poz a4 7wxhylg/ft): xkd3(uuw:a1:s p yint on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bx62 svy/8wn j/m5dh/je7sg;- haridgicycle wheel of diameter 70.0 cm when the b/eg dhr/m7sdj5v6h/8wj i-;n2 ys axgike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spn5+ syw18qjjface station (r = 1000 m) rotate to pws +qj5jy1f8n roduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a spec 9b-9i4rpwj v. xtho*ed of 20 m/s. The maximum centripetal force (prov9h.i xowtrv*4-j c9b pided 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/ aaa5pgf(rc,9tzmsrli b;7sfl5 - q ./s. The maximumt m a,gb9-aia7 rqr5;/s (ff5.p lzlcs centripetal 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, :8. ol n(d*fd,btaxrv is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, th8 o.n(flr,xbd:a dt *ven 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 m3ped km2w2 dw, down a lane atk m2e,3wp2 dwd 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 wsl6ylv(0s de.ith a 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 with a constant angular accv olx 9rx:w+y.g5ckn .eleration 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 .r 2moada mp)f jx+nxb+)* i0ex0b+ix 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular accbxifia r2j+oe)0)+m0pax* m+.dx bn x eleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceler b 3morlk97qos;6b ap/ation of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating aq u89.j rud2mlt 20 rad/s decelerates with a constant angular accelerad 2.rmj qlu9u8tion 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 while tu+xjg*te2l t v2rning thr jvt+e*2xgt2l ough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly fromkkbcsdw s2;z +ck2(zo ;xw4,g 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to 4,bz+k2kd;wgwc 2s s(x coz; krest?

  A wheel of diameter of 68.0 cm slows downa9a4ty/ik 6id uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acce iy/ik 6dt9aa4leration?

  A wheel of diameter of 68.0 cip/hlo6b60vkcnc ib:p ifsbv115d 3 8m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the w/vk 6l1vipbbi:1p3do6cc0bi n 5f h s8heel to come to the stop?

  A centrifuge in a medical laboratory ro npb:af+ 9v0dxtates at a rotational speed of 3600 rev/min. When switched off, it rotaf+: 9pbd 0vnxates 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.ww1wzmju:2, :k v+lwm5 xm ca to a torque of 90 Nm. If a 30 cm long wrench5m+w,k.xww v:uwz:12m jlm c a is used, 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 Nm. If a8qq-yxdx (xvy.w g5 p5uy4fk; 30 cm long wrench is used, what is the magnitu5uy (vwk. 84q-;xx 5 qygpfyxdde of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti )t2(e0z0lxgiedg2 tma $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled. s8.e*x8os fvxvk+r9 yvd 8+i9 jwvlu as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the 98rju9d8s o..+w xsl y+x*vvv 8ivfkemoment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought run(a)f p (9odthe 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 angular acceldup9foa) r((neration of the cylinder?

  A solid cylinder of tjztl /yb9n. (mass 10 kg is pivoted about a frictionless axis 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 ropyn 9. tzbl/t(je 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. Te*0sp v,w n,gfhe rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is rele0fnv gpsw*, ,eased? (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. Necpy g xelz. fp. 6mk5ad00n4(/j 6toxt2i tre-glect 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 i6y2e/c .-pf40g56(0x n rkot tzpxledmjt.a wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionl. x7waid n(ow,j6i s*mess disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular xii6w7da*(omjn.sw,acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a friction4lckx gq t p9kgo4mea9 -5.l8zless disk pulley of mass 7.07 kg and radius 66 gk9zxk-94q8l.c 5 lam4p gtoe.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to store 02ek4t 8r2bhu)4v *iliiwr oj$1.00 \times 10^{6} \; J$ 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 inertia cs6r0ipvf* /t 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 *k 7xt ,:rnvgtb4gxn1 from rest and rolls without slipping down a 1.0-m high inclined plan xg, 1tkn7:nr v*4gxtbe. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1ba++o73xn o igt/( 3wsvuvoo 2.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined +av/v3n3 o x wu(gt+2o7s ioobplane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.2v7.pz dscr0 k rcz9rod 9kzv1he6-+ .t0 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance ofzt +vs76vhcd90kpz -.z.r1ce d okr9r 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm roll7q7eh:dn pg2gs without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is givnd2p 7 eghg:7qen 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 changes)rx1fg:u/es s a2gsa 7 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 eu y;2sofjri f0(z;:q/:y0 dyu 3fjnymoment 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 exten7qq;pbeaph) (ded has a moment of inerti(;pb ) h7qqpeaa 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?