Angular displacement is usually tls9llo( 9fekhqc :;6express in units of

  Angular velocity is expressed in units otn-luma //:bnf

  Angular acceleration is expressed 61vio hq8w:da in units of

  A boy and a girl are riding on a merry-go-rou w1/n/s a6on l i6m6ui-1qzhqyubgi13nd 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 angus qa/ib ywh-z6n6 no3u1i1u iq6gl1m/lar displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant yud:w(-kit95 hzw ,fr rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular9f: (dk-rt, hu5wwizy speed?

  A boy and a girl are riding on a merry-go-round )tee iq5843/1pcoxfrj x nw*m which is turning at a constant rate. The boy is near the outer edgeowx*4/ 3cpi 8n1qxmjere5) ft, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-g dp pw*07oh)mp j5k;oso-round which is turning at a constant rate. The boy is near the outer edge, while the girl im jpo)p7o;0*kw s5hpds closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round whi65 sw3q 7)c7ajjixeo .-q mflmch is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the i a 3j)o-l5j 7xf7q6seqm. cmwgreater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accuratezhnaky -m6qqykn 7l 859drr8( statemen6 h ndl58kzr(-8y 7 yk9mrqqant?

  Rolling without slipping9 6fkwdi+ 2 :a5o(uxce dbq8fs depends on

  Two equal forces are applied to a door. Thch0kgj5s) wd: e 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 forhdwk0gjsc ):5 ce exerts the greater torque?

  Two equal forces are applied to a door at t+ /q)q;p nw8gdc jzjwch1zb,9 he doorknob. The first force is applied p+cg) 9jph8,bzw1w;dc/ zqj nqerpendicular 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 door.6u*c 15ddmtff The first force is twice as laf 5fut dm6d*c1rge 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 resistance to6l nf-nnn3 p10nu/ /ied tymp) changes in rotatim n/ue3tfi1 nnpn 6p)/d- 0lynon?

  Consider two uniform solid spheres whead.skrgo1g:slgt5 o:hj i8 12re both have the same diameter, but one has twice the mass of the other. kdro so:21: 5j.gsiha gl18t g The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, ifjygc 46 7m k(4;g+gg/49 jbbjvbicabut one has twice the radius of the other. The ratio of the larger sphere's moment of inertia tockj/yifg4m;( 6 i9bjgjb4 4gvc7ga b+ that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the masm1 km- m3r0/u7tsp 4zu xhot-ns and twice the diameter of the other. The ratio of the larger moment oho4 t1n/-u x7tps0k-m3z umm rf inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increnl5.0/x bjuv u1gpt o3ased to 2M and 3R, what happens o1lxvtp.u3/ gn 5bu0jto the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to aevjuiea hxg47;3cc2 ei 2*t .an object, that object will

  The moment of inertia of a s 68g atc-bvbd2olid cylinder about its axis is given by 0.5 MR2. If this cylinde dbv8 gt6c2ba-r 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 ha e3bgvrau zp27ks5 ao:(ke ,0 j+sgw,gs a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotatsa2,v ka:gk owu, 7pg+0s3rjz g(b ee5ional 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 and r2:3w 1cz 8ea q zq,p78xqfbeczadius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom p8zz 2:1 a8xce3 qqeqf wz,cb7of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping tr,z7ve(o+,hc w2p:- krhgwg down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends rco :+tvwp gw ez-gh2(,7 hr,kon

  "The total angular momentum of a system of particdah2z ;lja(*h.h,biq les changes when a net external force acts on the syqa2h;(a*z bdlhji h, .stem." This statement is

  In what circumstances can ttn3:a:s-w 7h lek*dym he angular velocity of system of particles change without any change in the system'*3nal: :mw y t-dkeh7ss angular momentum?

  The Earth orbits the Sun in an elliptical orbit. vnszn *g4z:scgf2//v yyp/ 7zex rs/7Ignore any friction which may be present. What happens over time to the Earth's angular momentum about/vscsy*zgyxz r7 n 7g2//p4 ns/ efzv: the Sun?

  The Earth moves about the Sun in an ellipsklh/ 7so9,;ue7s duhtical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting spee7 ls, shd9us ku/ohe7;d of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulldh75lx ser7h- ls:99n 4kyffn ay 4pm4ing in his outstretched arms close to r 75af9ky7:de 4nx4 ps- lly fsnmh9h4his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched 0 bkh)e2ppongyx7f s ;,.+m-os3 lehuarms clou sb ),7pnxkhomgyh+0eo.- ls e;pf32se to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast m)g bp+ exmkr3tg*;o) spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about th)+b3*o;xtmrk mg)pg e e axis of rotation?

State the law of consllie 0qfg3rg nj2)n4 : 30oiydervation of angular momentum.

  What arc length does the Earth travel in a three month period in its nearlsp;n f9wt8 o)vy circular orbit about the Sun with a radiu;w) 8svnt9ofp s of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length ofg . 88pt-1jb6er8g *iegru poz 0.30 m. What distance does the tip of the second hand sweep through in 3 miug18g8otj zprr-8 6gbi.ep*e nutes and 45 seconds?

  How many rad/s is 25 0m9xelavvoe;x /- y+6kzsrh; revolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whaw d5lbk/,hpgrv/ s0-eb8er1a t is the frequency of thrp/ rshb,l-b8de0 ka/eg1 v5we wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHnwh+ goq v.2a)z. The period ono+ag ).v2hqwf its rotation is

  A phonograph record rotad+czm + 4-h,:l kxit.ra.ix cc(9uznktes at 45 rpm. Through what angle does it turn in 0.20 s?mkhutixn4 (i +,xck+drz c.-al9z: c.

  A wheel of diameter 26 cm turns at 1500 rpm. How b 5gb--pfvj 9qfar will a point on the outer r bbf-jp5vq 9-gim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whab+hjenzx+ws6jp oe;++ c7 zo4t is the average angular speed o 7zejo+;eh+ox6bs 4j+ +pwn zcf the wheel?

  A bicycle wheel rotates uniformly through 2.0 revo my j; *z)mi7yu;3mreiuwd4z 1lutions in 4.0 s. What is the linear speed of a poin 7)zme i3ruumm4jy *;i dwyz1;t 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 k +q2alnsz 2a,*ag fe:jm. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pu aljzsfega2 +q*, 2na:lley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatiq xadj :00lee*5n)nxn* 5ptzyng with a constant angular speed of 2.0 rad/s. What is the linear speed of anjt0n5zq n0x *5l*)yd:paeex point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter isw5 vhee qqgqi 3f d2jic4799u, 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the hd5u,9ejq7iqef2gqc 4i 9 v3wapproximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant , 1/s :l(wqgblo6 mv u1 jbay)weq/ci.angular speed of 2.0 rad/s. What is the centripetal acceleration of a pob(qwbuigo.ysq:j1/le/ 16,) l a vcwmint on the wheel's rim?

  What is the centripetal acceleration of a point on the periwy29qnbmb *x-meter of a bicycle wheel of diameter 70.0 cm when the bike is mov*qy nw29b b-mxing 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotatl yly+ 5xl5 fz+ko(uf;7ut de/ing space station (r = 1000 m) rotate to produce an artificial gravif x;yl5klyuf+5oldze+7 /tu (ty of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve +fvvda.d;8 cpof radius 50 m with a speed of 20 m/s. The maximum centrip;dpva.fcv + 8detal 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 ofo;vhzuug5 h( ; 20 m/s. The maximum centripetag;;zuo( hhv5 ul force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attax 7a1vyeybm69ched 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 250 N, then what maximum linear speed can the masa 9v7mbe1yy6 xs have if the string is not to break?

  A bowling ball of mass 7.5 kg and (zlx7ny-o z2df. w-krxw:;onvber1/ radius 9.0 cm rolls without slipping 10 m down a l2ebxr/nz : 7.-fyvdrxko- ;oz(wwn1 lane 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 off*d7uw9 -7zjdb qw/ hv $4.5 rad/s^2$. 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 )j5ekss-,vqmwxu9v o0 fq /hl kco847acceleration 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 rotatey 8qr9jux*dzf7r/ (nq after starting from rest and accelera*(zy rj9u8qfd qn 7r/xting at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an j3/hx5ep4gux/5w uupangular 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 tn a)j2nf f* q4 sl3hy8);ttxsconstant angular accelera4 ls;tyf))n*t3jn 8xst2 faqhtion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angularf +;llq9ej8ql speed of 6.0 rad/s while turning through 2.0 revf ;lqelq9+l8jolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down vf3:v y17lzrkuniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in comi v173zyvrfk: lng to rest?

  A wheel of diameter of 68.p :ni /j/+ioas0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Whaj/ in+/psa:o it is the angular acceleration?

  A wheel of diameter of 68.0 cm slows downp *v:plixp3mh:gwh+ 5n9 0ujb uniformly from 8.40 m/s to rest over a distance of 115 m. How long does itu l*nh3iv jxpwp0+5hp9: mgb : take for the wheel to come to the stop?

  A centrifuge in a mez3x. yk :xkuq/aq*. ufdical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration: y*kqua.q/z 3 x.fxku 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 tighteoxhj m zfnk,a1ag.tj ;;c a99vp8 z68ening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpfa9ja;k p ajten6hc8,.z9o ;x81 zvgmendicular to the wrench?

  The bolts on a car wheel require tightening to a ;/;kyqu:kiqfx.w bqslw211 ntorque of 90 Nm. If a 30 cm long wrench is usq . ;q wnb:yk1x;uwikf1l/q2sed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of .rbxwsp/z. 1uvo3 ti4inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as fohipk5qr/*a 9 m4p l+ufllows: 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 the origm9q*/ l af hkui+prp54in?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis q+mez )b)onmlr j x-m,vm075gthought 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. (See Fig. 8-1.) What is the angular accelerat )r0 l jzgem-ox5n7mb)+mmqv,ion of the cylinder?

  A solid cylinder of mass 10 kg is pivofw+qgepw,;+ m8 a8lbid9rc8dam1g d4 3z7 cgoted 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 rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does thlg 8g4ed8d +719 rco+8;aa3 ,gbfzwmwcdmp qie 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 is initially held in th(;)din9 j)w piuf jqq3+s*ug ge 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 enqd +)qnf 3psuu;ijg*j9( gw)id is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. vd qia rj2;dd54nfv 7l4/.gkrNeglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.7lg4dr4vn i.fv/qd ;25rakj d0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on ab 0:nmy2,cwcm rope wrapped around a frictionless disk pulley of mass 7.07 kg and:0cmnwy c2, mb 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 pulley ogx;9 j,/ i7ngq at9kcgf mass 7.igkgj nx,7q;a 9tc/g9 07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used 4 /cq* r+k0o oegn9j/k+biipbjq.) fx to store energy. If it 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 inertia ek1p(ti7/lw,xs :2w tn;fjlt 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 ne wpk- j :b,gd0-e2yro:lzw4kv3g2q 0.010 m starts from rest and rolls without slipping down a 1.0-m hbzy:ww qve -d2,0g3p g k2l-r: 4kjoenigh 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*bk v:a6b o ;lxs:hnt/d3tgz 4 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined pla xsat;n *bohzlbkv/t:34 g :d6ne can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and uy+-a x235.wvvg 4rdtk *ivm lallowed to roll down an inclined plane. How fast is it movinkvwl+ur-mi v atv5.4 dxgy 2*3g after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping downu gpsa en* /e i.4c(*)+v uccsvi40mmk a 35e incline that i ) /g*s 4upc+cnmeaem0vvuik*c(s4. is 7.0 m long. 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 momeng4 * 5gkovlhrdb.dz-m(8g(w ttum 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 momi0cnvx yk/3ywb)u9 3 v0je5ooent 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 inerz(y,cy :8 h fhhcb:th6tia6h cyhcz tb8: hy(:f,h 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?