Angular displacement is usually ex bx+efz)/8qez press in units of

  Angular velocity is expressed in un.0zukr9 ahrc9its of

  Angular acceleration is expressed in uu;+kt( t4 eakrnits of

  A boy and a girl are riding on a merry-go-round which is turning at a constant q-6t/ f bkty8trate. The boy is near the outer edge, and the girl is closer ttkt y/6f-qt b8o the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is o4 led,w)f 50ves+gibturning at a constant rate. The boy is near the outer edge, and the girl is closer to the centgfe d ,5l we)4i+obsv0er. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning u z 6wh1d4(l n*,oz7seuc.vr 2ajybw 8at a constant rate. The b 2lv7n(d4,buez8s.c *wa61u o hryzwjoy is near the outer edge, 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 which is turning at a constant ratrqdx.xx62s. 5n .o g uy6uxdr9e. The boy is near the outer edge, while the gir ..5rx6 xs qo2.dguynx69urxdl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding 5)ossy amp2e.n3h v)md5hd-2dik8tu a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is c.d pdoku)2 et-83vmhh5m) 5sd a2is nyloser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of t;1k hkakb -h lun)nqvd0)0x4che following is an accurate stateme0 h)kdx01ka;hkqb-nn )c u v4lnt?

  Rolling without slipping depends o(v: .xhci/;ao zgf+ xtn

  Two equal forces are applied to a door. The first force is applied at the mxsy) jay8gl(be 98*ntidpoint of the door; the second force is applied at the doorknob. Both forcbxy(a8tlje g 9*n8sy)es are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a um.ok x/z8er8 door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. /k mxo z8u.8reWhich force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door.ur3- /-levnuxm z5s:d The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the s-ev s5z l/ u-udr3n:xmecond is

  What is the quantity used to measure an object's resistance to changes in r9:t 7 +wpgftp)qim vttop598a otati:tt9tpv7 + i9po5at8 mpq)gwfon?

  Consider two uniform solid spheres where both have the same diame2 l*u tg:jc;9 vpe5ziater, but one has twice the mass of the other. The ratio of the larger momentj;2 ugve :l*9ictp5a z of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the samd im j-b,s9sq(e mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller s di(9mjq,b s-sphere is

  Consider two uniform solid spheres where one has twice the masm)na)ao s.*pps and twice the diame)n aas)p o*pm.ter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radx :1w1ex tk4/glhlfr6ius R. If these are increased to 2M and 3R, whatw: k6rghx/ft41lxl1e happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an objys4lr -;p1rz b mc*t.xect, that object will

  The moment of inertia of a solid cylinder )tnfkv.)tosc2a3 u(+moy xhe .ow94t about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotatio(.wek ) 2th3 mao4v txo9fsocyt)u.n+nal kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wxbw3oah f5: ;5rbhohkt) 9m y/heel 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 35woth/rbx hbhm;a koyf :95) 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 without+)su, q;pk r tqd qgwirb+0:6i slipping down an inclined plane starting from rest. The linear velocity of thrq k+:d;t wi+up06 bg,is)qr qe sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radiusiyu0azo u6. s, R rolls without slipping down an inclined plane starting from rest. The s.oa0,y uu6izangular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a sysejf 66wza d(z: 5(ars(j we6hqtem of particles changes when a net external force acts on the system." This statawe f(q ar6jedsj(zh: w(56z6ement is

  In what circumstances can the angular velocity of system of particles change witg: gr ,m3j58lu-whyjmhout any change in thrmw gjglm-, 85uy3:jh e system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whiq1 m+)o2k8db vaj g8hich may be present h oi8)gbj1q2 kdm+8va. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the /cfoo 7l.sqhclh2/ 4l ymfp+,Sun in an elliptical orbit. As the Earth moves close to the Sun, thenfq/./2l+c 4h osl7p yflm,ohc which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fasbuix/9v ,.n 53ds zf0azy :(j :ycgnikt spin) by pulling in his outstretched arms close to his body. What happens to his angular moyin39 ub 0f.( 5a gzk:ijdn/z xc:,syvmentum about the axis of rotation?

  An ice skater performs a pirouette (a fast sp-rz w b7p7(f:cb v:xwjin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the cw 7: bx(w:zjb7vpf-raxis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his ou;.jc4 ay mcm0eqy:i* btstretched arms close to his body. What happens to his moment of ineq :c; m eimca0yy*j4b.rtia about the axis of rotation?

State the law of conservation of angular motc;me*;sw3 gjql 09qf m d-mg4mentum.

  What arc length does the Eky-+6s 5yu gaoarth travel in a three month period in its nearly circular orbit about the Sun wy ak+s5gyo6u- ith a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock hayo4k m31zid9d2 h)wvws a length of 0.30 m. What distance does the tip ofw vw9i413ody zh) 2dmk the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute eqj:t)mlv;:j q kw3( djnuivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wtnji6g0w*eu.o ( hltw5 (f5w jhat is the frequen5wi w (e l5.htujt *(gfo6nw0jcy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a freq 9nfu*jr7-wb+g(y gauuency of 0.40 kHz. The period of its rotati y7 -ufngu*ab (w9g+jron is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.i5e7 - kmby+gq20 s? mybgq7+ iek-5

  A wheel of diameter 26 cm turns at 150b 5gl vtveg4 wt;l.t2*0 rpm. How far will a point on the outer rim move in 2 tb54 ew*2tll gtvv;.g.1 s?

  A bicycle wheel rotates uniformly thoq/ s4 otsx(fyh q.b(4/icl,xrough 2.0 revolutions in 4.0 s. What is the average angulayqhosl(.,qc/x(o tfxib /4s 4 r speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whrijyc4af7.c0 gby y/fx9so q.+d )z 0qat is the linear speed of a point 0.10 m from the c9jc+.fz0 0yfa7r xs oqiygq.4 yc)d b/enter of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The c9jia92 thtwmg1euw() able which moves the car is driven by a pulley with diameter 3.0 m. Assumi(tegm1t uah)ji2 9w9wng 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 anyaoadl, i9k q9d wm(-4gular speed of 2.0 rad/s. What d i4-l9 dowma,(aq 9kyis the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-poweredvdn+o+ hp;hoe bnp 72( weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approxi+ o7pnnopb d;vh+ e2h(mate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant ++3j*i,zbnpeecssn71u67n 8 smg z/ k vqtc9 tangular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the whee,n ictgbet6 7nnsueq3s9s1cv+p z8*+ z7 /jkml's rim?

  What is the centripetal accew xowsx7 evym+537 w qqiqx;4d. 8xq)eleration of a point on the perimeter of a bicycle whe+mwww;dqx84x e x5qy)i7o q7e.3x qvsel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (r24zkht7o+xeind,s n7 e:o (d r = 1000 m) ro7(4rx+ne2 z ,niooh d7e: skdttate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circulal8bacdh a1 4n( +fr8qsr curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) 8r+c1a(hdf4labs8 q nis $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat cir)toxdu f 0m5d*pq: nmv(z.d :bcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by statim z (u*ddxm)t5.:qofdpvbn0 :c friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the eg dz;*;oja (p.wzql)7 ggbs;pz -w+fy cyi/ t9nd of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand plg;*w9;q7yp + s .coi)-gzzgtj fawy(b/d ; zis 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 lvvq7 a+/9jm uradius 9.0 cm rolls without slipping 10 m down +mjuvva/ 9lq7a 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 acchy+s;5w+ bkwn eleration 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 accelerati l9 )t-ecj:gv+ny)wu q8mxfd* on 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 s6 h-hued.r/iqtarting frohr.he/-qd ui6 m rest and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest y(g8z(barvl *, 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 un+elfg g + +jn09lrzn4.dg*j w5c )9e5zm jtd20 rad/s decelerates with a constant angular accelerat.)t*gd z +ngl4 j+e mgz5j9 n9e0fwunljd5+cr ion 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 whc -au:p(ot;ioin: l7uile turning through 2.0 revolutions. What is the average angular acceleration of the wheel?o-:u a(:;uplno7i tc i

  A wheel of diameter of 68.0 cm slows spqtc bc;m04di j::.vdown uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming. i;cqm:b jps4tv0 c:d to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40ws4c t0m c6wkj/9bz14 i slwz0 m/s to rest over a distance of 115 m. What is thecmw6l bi04wzw01/4j9tcs ksz angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/g(qt5 g0q;s *u,a ovejs to rest over asq uvg;*(q og05e,tja distance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational spenp /z f efi2t+vu97h.hed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accele ef2hvf nu.pz9h+ /it7ration 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 t1nffysez45i77 (gwh xightening to a torque of 90 Nm. If a 30 cm long wrench is used,wi x771(zsn e5hfgfy4 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 torqueeo 2un /4lyd+x-ixcr) of 90 Nm. If a 30 cm long wrench is used, what is4/ r xdlyx)u+onc 2ei- the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti vfkl2 7(g*q. y en-y*igualte*ju5, xa $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follo3.c wdhjy, c-ows: 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 3d-,oj c yhw.cthe origin?

  A solid cylinder of mass 10 kg is pivotedam tpas( e)00 4vy8zmt 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 righttat ) v0ypam4z80s(e m. 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 axis o:: vb /ev hwap;c.ffkc1( y9cthought 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 seconds, if it starts from rest?;hk owcva9f.c v(1:bf :pecy /

  A 4.00-m long rod is hinged at one end. The rod is initially held i8wmmc0 5.eqj u lg92e(r t-bdkn 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 inerti(c5m-kbt w m9d 8.qege2 j0rlua 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. 5c:p,rq vs p)kwmv4 u7Neglect 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 dovrp: c mw54vkp,)u7qses the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless m g *s.rfjro4:4b- psh.1rwytdisk pulley of mass h:41t rj p.f4 b.soy w-rms*rg7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aro8 vj g4wqitt)tpb80*jund a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratioj88 b0gt* pt4)iwjv tqn of the mass?

  A rotating flywheel can be used to store energy. If it is required tc8 wmwha254dxqs(c ovv+zd; oh,2a, do 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 inexc oie u1rj0(;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 from rest and roigl0kkef) + l, w.a5iulls without slipping down a 1.0-m high inclined plane. What is the spe0) , 5fg.l+uki aelikwed of 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 wef 52.ze,y v*t vw*tza speed of 10 m/s. How high up an inclined plane can it climb before coming to ,e.v v z5zwttf2**yewrest?

  A hoop of radius 0.50 m and a mass of 0.wg niic*dd )(020 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving d 0)i dwc*ni(gafter dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radizyuc( aq(c c(bw6ul-.hx( l* bus 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assu.cc-zyw6hl(l((c aux uqb( b*me 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 vn0.7ljgdnqkl/8 sn y69l 8 gdchanges 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 of inertia oj,q8ovt 3dd2k ,luw)hf $5.0 \; kgm^{2}$ 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 atd6z2- z7 5nf fwdrputib;+k)z 5.00 rad/s with arms extended has a moment of inertia5w dz kf)ifr2dt-6+uz7z pb;n 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?