Angular displacement is usually exprh )w7 s.kwfu3hess in units of

  Angular velocity is l*6dzp ts.(poexpressed in units of

  Angular acceleration is expressed in d 8nx6+nz2sf -e+4k(azprse hunits of

  A boy and a girl are riding on a merry-go-ra. iu 0l7.7xosmv*o6 v mnb53yy1btlhound which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who bm vvion73s abl*.05m yh.16 ly uxt7ohas the greater angular displacement?

  A boy and a girl are riding on a m*sf/ rd5p i +jr)vy+nrerry-go-round which is turning at a constant rate. Thd)rrs/+ir5p*+jn y v fe 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 turniq0j1ls i4ft2j ng at a constant rate. The boy is near the out fl1i4qs tj02jer 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 whi0zqyuj( p 9jvy,hb)p2ch is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the centep(vbhu )zyj jp,0y9 2qr. Who has the greater centripetal acceleration?

  A boy and a girl are ro3lust h5)(: zbhkms*h0czqxr1h90j iding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is cb1(ujxks0mh9ohh: z r3ql 50s* zct )hloser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accugx4 t9d2umuix-y* k7krate stitx72y9uku *4km- xgd atement?

  Rolling without slipping depj v0cb: 7epn1*e: kufxends on

  Two equal forces are applied to a door. The first force is applie9x6a7)+7q t tvsg skupd at the midpoint of the u 9pv7+a)6 7txsqkgt sdoor; 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 to a door at the doorknob. The first force is ga-q*b7u3 r3xv0ptoy y*mh 2e applied perpendicular to the door; the second force is applied at 30e to the plane of the door. * eq at723v3royuxpmbyg 0*-h Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first fo+(:n yz/yklgkh.9 vju)tu2 dmrce is twice as2dm vy.)hku9 +t jzky/lun:g( large 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 resist5tzd(hu+o6ek y:j dj5 ance to changes in rotation?ddkjh( z5o+:ey j u5t6

  Consider two uniform solid spheres where both have the same diameter, but ob88 pa +1dvuxs- y-g(la4vixc ne has twice the mass of the other. The ratio of the large(a8ivv 1-+glp yd84ab-xcusxr moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the ra(h5l oi htn*60aqh9 gadius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere ahlnaq5 i oh6t (h9*0gis

  Consider two uniform solid spheres where one has twice the mass flqeno/ .eh pajl;08kd(j2k*and twice the diameter of the other. Th*ao jdh8n.l;/2 fpe elq (0kjke ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. )mdsd9o i6pt6s4aq8 m If these are increased to 2M and 3R, what happens to the sphere's moment of896 i)6dpstsamo 4dqm inertia about a central axis?

  If a constant net to0tss(di*aja;61 -maok m ha2trque is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axi 6hzb-ezn b4j,s is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to itbjh4zne-bz, 6 s translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheeld.b)/wo/pzf chdq ., mdc6( au 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 energy of the bike? Assumop6 zc f am.,d./(dqhcudb)w /e the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down an in-v 75i m4i/ ns:3upv/hdboly iclined plane starting from rest. The linear velocity of the sphere at the /ibv4ihvd-:3m p5oyl un7s/i bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls with 9jzhduey /n,u;r2qs, +g ufy*out slipping down an inclined plane starting from rest u2gd;+huqsej uz*y,fn,y/9 r. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum1o hl;5kto5ncsv4/4 aki r5zb of a system of particles changes when a net external force acts on the 5r c5n /z4 1ok;5tklhoasvi b4system." This statement is

  In what circumstances can the angular velocity of system of particles change wirs or)5(7hl ,jmu *ytnthout any change in the system's angular moment(*)r tlh5my ,nou7rs jum?

  The Earth orbits the Sun in an elliptical orbit+ n7zw4w 4lvqf5 x2 zzmjor2/t. Ignore any friction which may be present. What happens over tim4ow72zr w 2fxt+5qjv4/zmzn l e to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun ibo)ou,v3ye(. i wh4 ze/f+pkmn an elliptical orbit. As the Earth moves close to the Sun, then which of the +4f.omehyv(uoe /i,w p z)3bkfollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fx7n2v brppmwt ((af. -ast spin) by pulling in his outstretched arms close to his body. What happens tvt. r mxnp7 b2fpwa-((o his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretccv 4pme(n f+vm778dy ;5ysa xfhed arms close tympxce+8vdaf4 f7 (s5v nm;y7o his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fahes ki 9qhd0+ v,q0 s+p9-xsnqst spin) by pulling in his outstretched arms close to his body. What happens to his momk+ndp90h0, q+qesx 9q-ss vhient of inertia about the axis of rotation?

State the law of conservation of angularme2c/l,yvp1o zkruj:a+b* .e momentum.

  What arc length does the Earth travel in a three month perkc0h xyl; dsl0w;cyg 64.nwy; iod in its nearly circular orbit about the Sun with a radiuygs yc;4nlldwy 00; k6cx ;w.hs of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distecv + a ofqd +(+6u.jmkm+7bocance does the tip ofqj f.muo7d+k obc+vm+(6ae c+ the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minuxfztfnc2(1v48 y4 qy nte equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s w ef1q7 /diz8qx(dfz/6cbzu;. What is the frequency of the whezxbw /q/if78ze q(d1f6 zd;ucel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencs )-.tdut z/nc/hge:ky of 0.40 kHz. The period of its rotati zuhnt k)cg-d: es//.ton is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.2 mc ur,mls o)2(qdbqg,( z2w2w0 swclg (mwm)b, qorudq22s(z 2, ?

  A wheel of diameter 26 cm turns at 15fpgr /nv4+xb1gn zg3q18 xa1 k00 rpm. How far will a point on the outer rim mo4g8ag 1xvk1 xpnn/rzf3+bq g1 ve in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 rxe uvl n6p3*i15:lnho 7rtzy2evolutions in 4.0 s. What is the average angula3tnuy v l1:nixp lzore2 65*7hr speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.n z7+oo/-xrk uh..auy 0 s. What is the linear speed ofro/.zk-nxauo 7uh y .+ a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance ofl8to w s+6 58ipf67akripb6 tc 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no lr6w+8 8is7tpita5pc6 fkb6 oslippage, 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 with6kx5h0ic nwj* a constant angular speed of 2.0 rad/s. What is thh5 iwx6*kn jc0e linear speed of a point on the wheel's rim?

  The cutting cord on a1vbwgsm8fm,) ;c2,tjm ev:u8m. w xji gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of thei1sw e vcju,v;t w). g,mmb mx8:m8fj2 end of the cord?

  A wheel of radius 1.0 m is rotating with a ydi)h*w)xfj(6ce(qa5qc:rf 0fe1 slconstant angular speed of 2.0 rad/s. What is the centripetal acceleration xfsfq 0jl)):yhe(a cdq *wf 651r (eicof a point on the wheel's rim?

  What is the centripetalpo8; xljd,a.ksy, 6c w acceleration of a point on the perimeter of a bicycle wheel of diametew.o,,d py l8sx c;jak6r 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rhswsv o0xp (v0dqr0 ;6otating space station (r = 1000 m) rotate to pq0ws;pd 0vh0 6s r(voxroduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular g,u454p-t8g ky ,eczqr z i/skcurve of radius 50 m with a speed of 20 m/s. The maximum centri ,c,ugzs85 -ek r/ztpqiyk4g4 petal 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 s1jcrllg2i 3*);a,pfeu l- lmp(edu1 io)l/lspeed of 20 m/s. The maximum centripetal force (il)/eleuj2salopl r *-l 31;d,u)f cm 1glip(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, is whirled around n( hj7;dm1q khin a smooth level table. If the maximum tension that the string can withstand is 2kd7hjq nh1m( ;50 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 sy.ap;zs)11 tw/r7 :dia ycelv lipping 10 m down a rla: 1sd)/pyacv1t yw.zi7;e 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 acceleratioz2 7z4mh6sqo zn 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 angety ys8 p8l49xular 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 g f5j-n7gvhw(d si8u1tire rotate after starting from rest and accelerating at a constant anghdijf guwv s- 817(5ngular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angul5 id 3+ /hwv:hch6hoqcar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelera 3ujxw s 9sra-2vhgljr6r.bp+qsx/+q b da/42tes with a constant angular acceleration op4hu qxx3qr2+ajads l/swv s.+2 g6j/rr b b9-f $-5.0 \; rad/s^2$. 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 tq +hfxov6s((e m; xjs*urning through 2.0 revolutions. What is the average anx( 6qv+ef*h(jxso m s;gular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s *mnujra + /fb+to rest over a distance of 115 m. What is the ja+*nf mub/r+ total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cbbs/scw4ex- 9m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleratx9bc4- ewsbs/ion?

  A wheel of diameter of 68.0 ;*dp/ (7wf2j18dhs qx t tfpblm0 cwk9cm slows down uniformly from 8.40 m/s to rest over a distance of 11j0wxd t2/flw p *p1(kqb7 tf9mc;d hs85 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotako8 6b:uo5 dr9x)sawdtional speed of 3600 rev/min. When switched off, it rotx)d9dbk5o8: aus wr 6oates 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 reqoigdo m3be+mq(q*wla3j66+ c uire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required w om(6wcqbl* 3md +giqa+6 eo3jhen the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of t d5z jg oh+h908)rx eov9x:;utdoa0f 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force :0+;9)ah9thr8 xd fg 5z vdtj xeouoo0required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment /r x4qo-hldcxe :3u/ vslxj*/b 9+adzof inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mfqzawc m.lfqa31z) f1x1 g:;modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m fm.) az3 q;a1f:wlfcqxzg1 m1is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is p04 +yrk*llgax * cqk6ge- k6wlivoted 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 wrapgg*4 6kelaklq6r lw-cxy0 k+*ped 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 thoughtfueu6p7rb kxvso.+ 4hmp5wc y51p 87 q 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 = 0.50pkosmu7xc 8fvyp1p5b4wq 6 7.hr5u e+ 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. The e; *nv db8s9jcrod 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 released? (The moment of inertia of a rod d s* ;9b8jcvenabout one end is ML2/3.)

  Consider a bicycle wheel to w8nhz( 4r6ddtbe a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a for64wt( hr d8nzdce 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 aroxgw,*e:*eczk0vv li :und a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratv0 liwekex*: cgzv,: *ion of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless m gurt+.ag .cd.h84a b4.s yazdisk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?+rgybd .sh8ata.z ..cag u44m

  A rotating flywheel can be used to store energy. If i2p (ovj fd so1lur9o/(t 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 inertiaiiyzh9d2vif5rb21q oxhu1 ( 9 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 r 694sbbo :j/zi7 w2lfxow)t p-j2xtlrest and rolls without slipping down a 1.0-m high inclined plane. What is the sp9o-:7jx6wiolb ztrsp 4wl/j b) 22xtfeed 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 a speed of 10 rf,( 3cy lror/m/s. How high up an inclined plane can it climb before coming to/y3cl o(rrr,f rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowxmu gg,oeb-b ,)3)gkdm 3roq)ed to roll down an inclined plane. How fast is it moving after dropping a vertical distance o mbg)rx3o)bm3 q ,,egu k)gd-of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm c) ae3h8b3.as ubt;xcb3 iya eof9h.:rolls without slipping down a 35e incl3cayh .fs:;aibxh 3be.uo3c 9 8ebt)aine that 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 momentum chpeifn- nm,tj6m x/7 ;langes 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 inert+ g6+g telzt-0f,o8*wqdvfo pia 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 mom( 3viavf4l*;a q po. qorf9nm5ent of inertia o9(3ail5*q.ovof4 ;m rvapnf qf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?