Angular displacement is usually express io/tziyceagn+2+ oz+8u x+1cin units of

  Angular velocity is expresse:p22p +clya y a8l:kpsd in units of

  Angular acceleration is expressed in units o6 xptygs7;.0 (:e zje; zlkuodf

  A boy and a girl are riding on a merry-go-round which is turning at a cu o/.dm.v 4zh gh:n kv2r+hnn4onstant rate. The boy is near the outer edge, and t24khvnv .nhdr.nu4o g/:z+ hm he 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 at a constant plbn9aox4n7 hb6:: f/yh,/gq bei,qvrate. The boy is near the outer edge, and the girl is closer to / yxblf /hb9ih vpb a,e7oqg6n,:4q: nthe center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round sj((zrc (k/74m zqmqgwhich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has thekqm z j/cs 7(rg4m(z(q greater linear speed?

  A boy and a girl are riding a merry-go7gm6: sdaa*qf ymp4(x-round which is turning at a constant rate. The boy i :4*fm76pqmays ( xdags near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridw/qr 3fmss-,2p bd;8zcwhb- c ing a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?wb,wz; - 3mrpdc bs8-/2cqsh f

  Consider a rigid body that is rotating. Which of the clgas; j97*tufollowing is an accurate statema;uslt cg97j*ent?

  Rolling without slipping depends oezrv * 7ff0a l77s)uamn

  Two equal forces are applied to a door. The first force is applied at thecbr5l 30c.ucv midpoint of the door; the second force is applied at the doorknob. Both forces are applieurc c5 lvbc.30d perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied toil lxfmwi-(** a 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. Which force exerts thil*-x l*(mwfi e greater torque?

  Two forces are applied to a doorknob,(n0fmwe27af0 xvf+ckc; wwl f.3 a(uo perpendicular to the door. The first force is tw(. mfxoc2f3uw;7flw0e nc fa (kw+0avice as 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 resistance to changes :tc0p- y,)hi paq9;ulnh;;ow( ueupzin rotati:z;0u ;p uyh-hiwq);p u tnoae9,l c(pon?

  Consider two uniform solid spheres where both have the same diameter, buaiw:h:ma j-n)t one has twice the mass of the other. The ratio h: w)mai-j a:nof the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid sphoo b6b91 qvl:reres 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 b:b91qo vo6rl the smaller sphere is

  Consider two uniform solid spheres where one has )a8fe rd-n; )ec 1ikfetwice the mass and twice the diameter of the other. The ratio of tha;e)r 1f e8-)fn ekcide larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius Rfs mgsi;4kg6y .pj*2m( kls+i. If these are increased to 2M and 3R, what happeng4(;sk.y2fg+ms mi *s6kpj ils to the sphere's moment of inertia about a central axis?

  If a constant net torque ir 75el,tt0aj gajt)o tl:eeh3 op :-s4s applied to an object, that object will

  The moment of inertia of a soli xji3zy l-(jtq1( 9mdew t)kg-d cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational-t)- tm31kxj9((izelyj g qdw kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg/ybh6p wd ozow.j:lw0c+h)1 ctzf(,t and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the .b0do,1oc+ z6t:(jlw htpc) ywh/wzf total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and rad :oo mnmql)4kfl2bz fs *a s(ss1a.-l+ius R rolls without slipping down an inclined plane stal)nl:s4s a b(mf2+ qo-zo*sksl.m f1arting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls witv /rw;qs(agn akf 3-e-hout slipping down an inclined plane starti3w;v(n-aa fqge-/k s rng from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particl2 k(+,mnh vssdp7+b;mx qkxc4es changes when a net external fnkp msdmcx+4;,(k +2qxbv sh7orce acts on the system." This statement is

  In what circumstances can the angular veloh*z-)i+pz k orcity of system of particles change without any change in the system's angulapz*rzhi- +k)or momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction m,-tsp+ zhku 8fk*i ww* hbf/5which may be present. What happens over time to the Earth's angular muwk+ 5k*s ft- wi 8h*fzp,/bmhomentum about the Sun?

  The Earth moves about the Sun in . pn;f-g nhiy*an elliptical orbit. As the Earth moves close to the Sun, then which of the follow h;g.fny -i*pning best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast;hf6f -j mkleo)ms;d; spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about6k;)j dmflfe -ohs;; m the axis of rotation?

  An ice skater perforc5lvu.0p y 6pth a*w)ams a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic hpvpa.u)*a6 tc 0ylw5 energy about the axis of rotation?

  An ice skater perfor y+,;bulm2 r,his bf*hms a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia aboutbylmhs u* ,hi,;br+2f the axis of rotation?

State the law of consxpp8k ,zpbag 4 68gos/ow d5u3ervation of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly ck1 0v9)ne f1gj9jvto*zl3jz wircular orbitnojg*90jzv 1)1 lf9 v kej3ztw about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has +sr)13fw+yh;re jgte a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and f1rey hs3 t+jr+)e;wg 45 seconds?

  How many rad/s is 25 revolut fyiww x16tut 21l0n+e)hn2ssions per minute equivalent to?

  A bicycle wheel rotates unifh t.vgag*f- zfn.; +pyormly through 2.0 revolutions in 4.0 s. What is the frequency of the wheela;hg pv+fn *z-gt..yf 's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencu+x pqqdy10.yincvq3 e c,(l/y of 0.40 kHz. The period of ityy0q.ni l(cedv 3q/cp +x, 1uqs rotation is

  A phonograph record rotates at 45 rpm. zm sji78rqfzkg(t 3icv6i ,7( Through what angle does it turn in 0.20 qf7r (sz, i8i(g6 vm7ji cktz3s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point;7 tlkii0 :u abh1x,oz on the outer rim move in 2.1 st:0l ,1i7a z o;bkxhiu?

  A bicycle wheel rotates uniformg)g/z8sr p,wv(8j*aan z l .zmly through 2.0 revolutions in 4.0 s. What is the average angular speed of the wha(pg wg /sz8jn rvz.m8az,)* leel?

  A bicycle wheel rotates toqc*urdfb-a(z +1 vk 418vxcuniformly through 2.0 revolutions in 4.0 s. What is the c(xtkzrbd1 uf+1 oa 4cv 8*qv-linear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distankj f0vnx k m481o2/yhzce of 6.8 km. The cable which moves the car is drive21fzv0 x8nmok kjh4y/n 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 12 minutes?

  A wheel of radius 1.0,v:xxuxmaq7.v n 1-ops/b,zo 8g d )hr m is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a poqrv,7uzx o8 m o .advx/s:)bx-h1p n,gint on the wheel's rim?

  The cutting cord on a gas-powered sxpsg1+:kg m4iy *h+ a+ thhx:weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approxima+is+xm*1typ+ a g x4khh :g:hste linear speed of the end of the cord?

  A wheel of radius 1.0 m is uv7i (7f26e3 jshfiw qrotating with a constant angular speed of 2.0 rad/s. What is the centripetal accelerat3hfvjw fqis (ie677 2uion of a point on the wheel's rim?

  What is the centripetal acceleration of a point onki/hb00lb f i.v24ms/z, xymtbbr k(f j x(a*3 the perimeter of a bicycle wheel of t4xv0jbz/ .0* ((xsy2b m,fkm /rb3lafh kibidiameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space romh8sye 14kin9 /9zt station (r = 1000 m) rotate to produce an artife 9y/1r tm9n8o4ik szhicial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 2f8 f5*:qe8ref,4b*f xi z 1das6jj dfv0 m/s. The maximum centripetal force (provided by static fr6frfes id8fbf*x4 , :d5v1*f8a e jzqjiction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat l,v2q/gf7e.7 yfkj bkcircular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal for.je2 fl y,k/v7kq f7gbce (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 am fy l5.1*afv;*ez lmz eeha 0spw-39dround in a smooth level table. If the maximum tension that the strinwl3;a. 90ayhepmesef-mz 1 fz*vd*5 l g can withstand is 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 anda. y svsuk/6o4x+j*hu radius 9.0 cm rolls without slipping 10 m down a lask4a j h/s6ux+v*. oyune 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 accelerati : -plsl5mzv;e28ip f(i d0luion 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 acceleration +9hs jx:c o4yzof $4.5 rad/s^2$. 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.f5 m::)48;ebfhbji vdk hpe2iee.2kb: txt0a300-m radius automobile tire rotate after starting from rest and accelerating at a constant ang 48)vbtx ei aihh;20t .e5jfm:2b::ebfekdkpular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, andz1xtkvji8q l;mgy;7 0 has an angular 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 constant angular acce-ue* 9/n vo/nuq9*/hu lcgui zlera9e9o//*uc q/ z-n hlug n*uiuvtion 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 6kb5 t:ftmf1he:v(9 dov hqgo4/ci9dwhile turning through 2.0 revolutions. What is the average a(dh9ofvt:1v:5it9 qmf4bo k gehc d/ 6ngular acceleration of the wheel?

  A wheel of diameter of 68.0 cm s :q)ng.)c4g: r -wbhjr cck2zwlows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the tkw:gb4h r2j)g w nc-c c.:)qrzotal number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter ob;q4eus, 77 ua uq5kxogy-x3hf 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Whao x, ua5ub;hu7q34gqxs yke- 7t is the angular acceleration?

  A wheel of diameter ofj*+tt16)*wcdoe s*j8v k xf esyqu . h,*g1lus 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it takeyxotsj6ekgjtu d s8cu s1*,*hl+**f1 q) ev .w for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatir.ic1v s ianws (7 cu/r;2vlg8onal speed of 3600 rev/min. When switched off, it rotates 50.0 t/(rwcg i1ri7nluc2 vss;a. v8imes 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 to a torquetoggp ihzvt8 5 (12r3d of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the z 2g(h r1 ogitd83p5vtwrench?

  The bolts on a car wheel require tightening to a torque 11rz/ hm/ iaxw*gkz(ab :kdi2of 90 Nm. If a 30 cm lonb:(/2 mia k1 r g/dk*1xwazihzg wrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o c0p (1qcxx csopo4*u8jq;y6 fx2eo )if 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 follows: mass m is at the origine imb0ocm6 ch: q (+b(,jyf1qn, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about thec610(qqb ,h +obe:jynf mimc( origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless s)fq:y0 iwi+lf etof;d-+lh5 ,/hvdhynb:-paxis thought the center O. A rope wrapped arou ;t5ylf,h-+lb)nyosf+ :id hveq:pd/0 -ifwhnd 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 acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivote e+ gcidn+rw2n 1 r7at/90)zcgqx v.bud 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 rxuv/ir2cc bg7 91w)qaz + e.gdt+nn0rope 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. The rod is initially held in the horir2 khumu,l7f +dv,uozg l26k2zontal 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 276+h 22v,ldu f,zukormgklu end is ML2/3.)

  Consider a bicycle wheel to be a ring of radi3i4g2izb z h)k yg-)qjus 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 linear speed does the wheel achieve, assuming it rolls without sl -ybg)zhg)z k4jiqi32 ipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionleofk i:20a2 bmrss disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceloark2fb0 2mi: eration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fric+ 6nxf4:5afjl:k avr cw51fhyywz;ke d:u:z8 tionless disk pulley of mass 7.07 kg and radius 66.0 cmkyxa5wz h 6 +f:5nvf:azy j;: df18l4 uwkr:ec. What is the acceleration of the mass?

  A rotating flywheel can be used to store energ);0 8mnfdy )xa9slqo gy. 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 inertim9/reo lh e );gj;-ggra 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 startsk,yc4-.c a4(ejjur :jr mnn )f from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere wraj.c: ymf)enk4ujc(,nr-j4 hen it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a s vl41vdfv ,2ylpeed of 10 m/s. How high up an inclined plane can it climb befor vf, l2v1y4vdle coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20)bm0.hsl+l 0cnd 1zeb kg is released from rest and allowed to roll down an inclined 1)s+nlmczl0 .hdbb 0e 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 cm rolls without slipping dow z1mfi lp5a47kn a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere ip ak5lfi17 m4zs 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 cxvy u+s,v9eb5 q0lh; rdgp07;kuw1j qhanges 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 momp/ t-qxxy-5vbusi4+ ient 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 extag;fn26hk,1 pt-m q bmended has a moment of inertia mpfa2;m bh nq6g1 -,ktof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?