Angular displacement iox 1a2sunv 89( qkvu*bs usually express in units of

  Angular velocity is expressed in uni0u roa6jx;-i,w aiytexmnsr3 x7q ,8 4a /nk+zts of

  Angular acceleration is expressed in unit -7y.2k vmbb ep*iruv0s of

  A boy and a girl are riding on a merry-go-round which is turning at a constant -t( 37)oyb6 xnxf xnnprate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacemox f7xtb-)x nn p3ny(6ent?

  A boy and a girl are riding on a merry-go-round which is vj/q 6qyw9ny/turning at a constant rate. The boy is near the 6qwqj vn/y /9youter 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 vdy cq6z (4z)nconstant rate. The boyy zz4(c vdn6q) 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 atqy87y qcboi,sb7e r .oc:p7*i a constant rate. The byy7es7*ir: 7iq ,cpo q8 bco.boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round whsdebiqfs;t +d 0zj.j.0f8t 9 pich is turning at a constant rate. The bsiesf .p 0tjz0b+fdj8t .;q9 doy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an ac2mrtr6 zd;p9i curate statement t92;d6riz prm?

  Rolling without slipping depefai15q ri r,ucl*zi46m9sg3 uigo7a :nds on

  Two equal forces are applied to a door. :u9epamphdo+ kvwj4+:ljz 8n( y p*l; The 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 force ex:jml4pyw*dvozpna(ku+ + p;l9 8eh:jerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first4kety uqm2jd 0,c 3.iuzb0d 7p force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts u4jm 02.bi3tuq7dkd c0ep zy,the greater torque?

  Two forces are applied to a doorknob, perpendicular t:5s l:*mbdc dto the door. The first force is twice as large as the second force.m dtd:sb*5lc: The ratio of the torque of the first to the torque of the second is

  What is the quantity u4aoa g9 dm*s)jsed to measure an object's resistance to changes in rotation?o*4ja gd ams)9

  Consider two uniform solid sphefdh nr,8h ,)okres where both have the same diameter, but one has r ok, n,hfh)8dtwice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid sph ;ucpo0/tw3fo (n pxa3eres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of tw3pcf(nux o3t/po;0 a he smaller sphere is

  Consider two uniform solid spheres where one has twice the0;n6q afv dzrdpu8v86 mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller momenzq v6;f6p0n r8dadu v8t of inertia is

  A uniform solid sphere has mass M and radius R. If these ar 9fid2lpt46ep e increased to 2M anp2f9pe 46litd d 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torqu9r uynlyf84j 1fey+*re is applied to an object, that object will

  The moment of inertia of a solid k8ws xc+9cv s7chq4 v.cylinder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of z s+n2j 43 yz5qnr0o2hg+ xm2hqs l.wnmass 150 kg, 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 energy of the bike? Assume gn0.+q+sm42qnl z yhn o22xswhr53jz the wheels are uniform disks.

  Suppose a solid sphere of masv2f-p19l npup s M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere a91p2-u lpfnv pt the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius -jd)ffrw*x j0 R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the inclinejfw*jr- x d0f) depends on

  "The total angular momentum of a system of particles changes when a netaorz9wmnimzd:f l hs;,er( o0-xc :1 + external fodl;r:mr+ ox(m z0,hcsze:-ia f won91rce acts on the system." This statement is

  In what circumstances can the angular velocity of system 2:usek8,vvt iof particles change without any change iek i8,:vs v2utn the system's angular momentum?

  The Earth orbits the Sun m18s7*9ndfj z 0uim 8v vrf)i2 iaq7zein an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum abo17ffs0vaizdzrnj7iv9u8m2 em)8 iq* ut the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves closc c+ n d(l,r( cit f5surf*+-xbhx0hh)e to the Sun, then which of the following best describes the orbiting speed of the Earth about ( n csxx)(hb c+f dluht0r*h5-+r,cfithe Sun?

  An ice skater performs a pirouette (a fast spinw,)ph;j 9znsy:,tqv3 b aji ;a) by pulling in his outstretched arms close to his zainys)9w,j ;h3 :b ,;q pajtvbody. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his ke6 xoiqsgr my6-6,:boutstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotatio ie6 6r-kb6ygsxmo ,:qn?

  An ice skater performs a pirouette (a fast spin) bjh(k v.xc, p3z7m xm(nrqw,l *y pulling in his outstretched arms close to his body. What happens to his moment of inertia about(w xvj mphx.l3kq(n,7 m z,cr* the axis of rotation?

State the law of conservation of angular moment 4a4phx-hn2(*s wj :uhscr2vjum.

  What arc length does the Earth travel in a three month d,kh 319fmtcw period in its nearly circular orbit about the d wf3c19h,kmtSun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock zf8.ox.3:o i npsvgi 3has a length of 0.30 m. What distance does the tip of the second hand sweep througno.8ix.: o 3 3pzifsgvh in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minutu8wda 6.bn:bue equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What td3d52o.)fqp f d pwh5is the frequency of f5dt2)dq.hp3pwf 5do the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency o ;)cqobw i(c*.r m3puqf 0.40 kHz. The period of m o)ib(.;wc 3*prqc quits rotation is

  A phonograph record rotates at 45 rpm. Through what angle does ip+me 38y(6uq y v h4vr;ybari8 ik:f/ct turn in 0.20 s/ y8q ;f ie3:kybu(8ay rp+himv4rc 6v?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a pointxnv 08c.s ,fei on the outer rim move in 2.. ,x 08sficenv1 s?

  A bicycle wheel rotates uniformly through 2.0 rl *vnk- +lrak*7 mn+jjevolutions in 4.0 s. What is the average angular spvanjr+k-lj nmk l**+ 7eed of the wheel?

  A bicycle wheel rotates uniformly througs- uu;*5;dp z1 tbrk;t4hwpoeh 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of *otz;u;;ph bk1dtr- pe 4swu5the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whig..cj5*i k tj(qoy g kc/5zbzp4 i0c,ech moves the car is driven by 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 g4 5ciozzey50bcjkkjtiq, g /*cp ..(12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular spe+b sknm6s) b23 jqne1d62mmpred of 2.0 rad/s. What is the linear speed of a point on the wheel's rim )bdkqrs 21empb sj2n3m66nm+?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If bb/5rzsd l xo2cyq ,us01(rz(the motor rotates at the rate o1cbz(0 u5rx r,o (2zlyss qdb/f 20 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 angular speed/:pb d6/hpls3kd.b9 5-op;n t:yjdbaas0tey of 2.0 rad/s. What is the centr3.k :ap/bl0 s tp9yos t -5ad :dydbjbn;p6he/ipetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a v pv/vkj5z0(u point on the perimeter of a bicycle wheel of diameter 70.0 cm when v pkz05vvj/u( the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space staw7n 6ace45 msrv v0h2(rnp +lm;1 ygyvgyd/: ztion (r = 1000 m) rotate to produce an a1:42/l n5yd6pyhm7 eyv 0maz;vgc ngwrr (s+vrtificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 qsd9,v fpp gfe+e5o 7,04lylmm/s. The maximum cen9g yl s4lvfefp,m5e0p7 d+qo,tripetal 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 fw:s71jgqk1.t d6,dj-rka i o m/s. The maximum centripetal force (provided by static friction.f1ds:o,ajkrw tdk1 ig q7 6-j) 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 05i-)b0 rste8r buni9vjzz1m 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 mass have if0sm9itb051z rern j 8uzi-bv) the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rollauj w0twrh ;/g87y- vvs without slipping 10 m down a lane at 4.3 ujva-ywt0;8 hvgw/7r 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 constys**smhz1 4cn1 xw dc mb/(5eqant 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 constantk)/n4mtkbsb m i;a1u( 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 does a 0.300-m radius automobile tire rotate a* p(t3 nfdbx(u 5sb+safter starting from rest and accelerating at a con pxbtd bs+u53(fna( *sstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerag1x;p /2rgit)zgh ( vy.yy(fg tion 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 angula dtv.;, hdba7yr accelerationdy,b t;dh7 .va of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angularry+6ap7hqy k(a hxe 46 speed of 6.0 rad/s while turning through 2.0 revolutiok4a phq(6 e7xyhr+6ayns. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8+l ftyw*:zhf7 .40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to resff lh*+ :wyz7tt?

  A wheel of diameter of 68.,8hx lz1hv5u a0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. x5v h 81lzuh,a What is the angular acceleration?

  A wheel of diameter of 68.0 cm sl 3j0 d.sm xob7y3ieod8ows down uniformly from 8.40 m/s to rest over a distance of 115 m. Homoebyi3xjs0 od 3.d 87w long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 revw5ge (qb; fukg.csk6: eh-z517uzpl a/min. When switched off, it rotates 50.0 times at a constant angular acceleration bef5ebs fcuh5k7lq-(pg aw1ukzz.g :6;eore 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 tort1pt zvtq n076que of 90 Nm. If a 30 cm long wrenttqv6p10 n7t zch 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 a 30 cm lo*nv: cjio(f3qf7zk5 sng wrench is used, what is the magnitude of the force required when the kcfo35q* 7ivnzj:(sf force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o,8nt9c8qn ps pjz,eu gvp/t2.f 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 modeled as followue8 meh8x*, st34 aryhs: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of iner3* 8hux8sm here, 4tyatia about the origin?

  A solid cylinder of mass 10 kg is pivoted about 6sii wfqh1)0ka frictionless axis thought the center O. A rope wrapped around the outh6fwi )0si 1kqer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought cpma kj)/37 7-5l;bsoif nnappt1eb) the center O. ali);pp m1f -a be7n) c3jtk pn/so5b7 A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 rod is initially held in the hor zmmzo);ez; 27 xy:hbjr, ntb; pu*d*yizontal 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 on2z):p;teobh by x;,zmyzm ; * ndjru7*e end is ML2/3.)

  Consider a bicycle wheel toz0jp+ -:s 5k frn6c f8/ftrwwx be a ring of radius 30 cm and mass 1.5 kg. Neglect 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 lrw/tfc-xkjnz58 p :6f w0+sfrinear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mn)xftmrb84e )bv8 fy4ass 7.07 kg and radius 66.0 cm. What is the angular acceleration of f))48v8tbe4 yrmfx nb the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mass a/5(t;b4f o)2 pdamscjaa,tl 7.07 ktlbaaa2ac)/f 4st5o( ; ,pmj dg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel canw 65cvmm) ;oxa be used 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 inerff3cigs v:hl(7g ,uj9 tia 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 rolls wi6 qkls2llf,m,eg782:oqnv.z ijk2nmthout slipping dokm78e:,gk jl2f q2q,snl z i6om2v .nlwn a 1.0-m high 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 kg and radius 0.010 m rolls with a speed +g7brc bdq8z;x8 0a7,z ynty yof 10 m/s. How high up an inclined plane can it climb before coming to rqrycnb7+a7xyyd0t , 88b ;zgzest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released i+9nz.x6rijop ux--b from rest and allowed to roll down an incl.9 -i+jpz-bxiu o6xn rined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cmr 5s:.* rvkj9framk1k rolls without slipping down a 35e incline that is 7.0 *51rja. 9r sfkmk:r vkm 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 momebkslc g4tn. (eiy+2t 4ntum 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 moment of inertia o88hz:p ql uev4f $5.0 \; kgm^{2}$ 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 xy3t,bow+ ng 3uw1t c,a moment of inertia 1c+3,n g, y uxo3twtbwof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?