Angular displacement is usually express in nclr, ,h,tc0d units of

  Angular velocity is expressed is:z g8wmf b1:xn units of

  Angular acceleration is uy nrmk+2;av26ak-m 5 mtpo/qexpressed in units of

  A boy and a girl are riding on a merry-go-round which is turl ridw6s,i n )2:1 plq x;gq6s25ow:xb al2nidning at a constant rate. :x6w1x;gd 6l5s,2bndiq2ia ln :o2iqprsl)w The boy is near the outer edge, and the 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 turni(:xc-lp +ual2bin(d o ng at a constant rate.n o(+b2p:li-cxda(lu The 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 turning at a co6u:lqb k-6jex s 06*zb4zdt33ngm a lwnstant rate. The boy is nel-dnzkb3eq azs6b4xu6lt * 3j06 :mgwar 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 coszo1 w 5 :yko8wpw/b5cnstant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?wwz k:wooy b5ps1/c5 8

  A boy and a girl are ridin(+9 wissct rb*byj;v/gauiopn :u/(; g a merry-go-round which is turning at a constant rate. The boy is neac jn/:o yarvw ug tu(bs+ii/; 9bp(s*;r the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatifl)6 m,ahky 7h ga8fh6ng. Which of the following is an accurate statemenyhk6mh lah6) faf7, 8gt?

  Rolling without slipping6x )su(kac 3h2mvxdw 3 depends on

  Two equal forces are applied to a do75xtn k+ i;jsb ms25ugor. The first force is applied at the midpoint of the door; txgj m+ns5 kiu25s 7;bthe 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 do.3y 38 *u3wy b ldyz+s6yhzspeorknob. The first force is applied perpendicular to the door; the second force is appliedb6y3*lp.u+z33zy dhye 8 sysw at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorkwgqo:f x +p(s(nob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the seconxpq s+:(of wg(d is

  What is the quantity used to measure an object's resistance to .l a/y+faodk*mi80th changes in rotation?.0ya/ it+olkahf *d8m

  Consider two uniform solid spheres where both */k29ud xhgwh have the same diameter, but one has twice the mass of the other. The ratio of the larger mome wdk 9g*uhhx/2nt of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of th ys8m0vomc7 u*e other. The ratio of the larger sphere's moment of inertia to that of the*8 7ucomsy0 vm smaller sphere is

  Consider two uniform solidj* .m 6oylj/upwhcx: + spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment +lc pjx / huw:*mj6o.yof inertia is

  A uniform solid sphere has mass M and radi1* *wqw nwomdgwyhyx5k:im4n)q3d-( us R. If these are increased to 2M and 3R, what happens to the sphere's moment ofgx dn qwyd3nm-iw(w* m4 q :k5*1)woyh inertia about a central axis?

  If a constant net torque is applied.3scetuh5f6u ro k-,y3tg r3k to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given b,mph+xb- y3i.eo incn)nwk .-y 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotatioopx,.b- yk)ei+ 3-nnmwchin .nal kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass ofhc4no 4w rr*v8 10 kg and a radius of 30 cm.r84 ch*ro wv4n What is the ratio of the rotational 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 an 6wq-)m,kqr/evkr;1y ay5 xgld radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline ym wk vqgeka,q/5r)r x;y-1 6ldepends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an i-yt 2qolz*s7o nclined plane starting from rest. The angular velocity ofl*27t qo-z syo the sphere at the bottom of the incline depends on

  "The total angular momentum h13jo qn)y3h6of 7qanof a system of particles changes when a net external force acts on the s6ho af3yqqj n3)o7 nh1ystem." This statement is

  In what circumstances can the angular velocity of system of particles chang .hfz fnnh..,ye without any change in the system's yf..nnf h,zh.angular momentum?

  The Earth orbits the Sun in an elliptical orbit. q0tnl+ qt b6d*Ignore any friction which may be present. What happens over time to the Earth's angulatt*6b 0q+dqn lr momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the j9 g,w 5n09cx/otz lbaEarth moves close to the Sun, then ,na/5 w9glc0 tobx9 zjwhich of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast xx4v4x)pxjzyhn8rj v; o3.q/ spin) by pulling in his outstretched arms clos/v. 3zv ph8r4xxnx j;4oyqxj)e to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hins-sm8+blp0*lq;jy ns outstretched arms close to his body.pymlsnlsjq8*n -+; b0 What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pull4/z 1ohuv mp8uing in his outstretched arms close t4vou1 mu hz8/po his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of ani(l g uy37n,qu94p gjagular momentum.

  What arc length does the Evdkfaq z4g/dvl x,ue- (,gv1* arth travel in a three month period in its nearly circular orbit ,vvqfl4*zg e 1,k/vd -xdu(a gabout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. Whq*i k8ju o4xp9at distance does the tip of the second hand sweep through in 3 minuteskio *q9xu8j 4p and 45 seconds?

  How many rad/s is 25 revolutiu99b e90t jrw :9 jjfxl ndfrk:-(vy5lons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 rc3val+foz 1tui 6 *ft7evolutions in 4.0 s. What is the frequency of the whi vta6z fc1tu+ 7fol3*eel's rotation?

  A pulsar (a rotating neutroo 2k8z 6z1g+sxb*qou ln star) emits pulses at a frequency of 0.40 kHz. The 1*z s lgb6ox2o+u kq8zperiod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angyyqfweza x3e2wd4 d 3ys0;k*8le does it turn in 0.20 sdwa y*fz8yqx2y;3k4w0s3 ee d ?

  A wheel of diameter 26 cm nb u01md 3;hd sfuu(d6turns at 1500 rpm. How far will a point on the outer rim move in 2.1 s?hf1b(0; su3du mndd6 u

  A bicycle wheel rotates uniformly through 2.0 revoq)*nd ((tac pup3/jpb lutions in 4.0 s. What is the average ang(cpb n/3ujtpqap(*)d ular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions inih-(;p/q g6 jkuy qh)8eap9qb 4.0 s. What is the lip(hk-hq/a6) g 9yi jq ;quep8bnear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resortdooj90 w.2q ok6yhkqe aag)- ) carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fas.qaawy kok 2oqj)dg6 0)h- oe9t 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 angular spay1 )afk* ek-need of 2.0 rad/s. What is the linear speed of a poi afae1 k*ny)k-nt on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in l9n61wd ucrf :blo9l 3kength. If the motor rotates at the rate of 20 rev/s, what is the apprlo 3wb9r1 dufkc: 9nl6oximate linear speed of the end of the cord?

  A wheel of radius 1.bf+(nz.klp ,w 5boamei ma,08 0 m is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the ,w 5.0(l+pa afkobnezm 8mi,bwheel's rim?

  What is the centripetal acceleration of a point on the pebyo u 5f4na;l7 cfc10hrimeter of a bicycle wheel of diameter 70.0 cm when n0cf5;4ohfcybu 7a l1the bike is moving 8.00 m/s?

  How many revolutions per minute (rpmt fam/gnr0;jq) g7cgqn0 vr; )) must a circular, rotating space station (r = 1000 m) rotate to produce an artifgcrg/ r0)ma jn0tnq q fg;7v;)icial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circul2pyyyfvep *n k5 6*d+ri1l pnc.1zdj0ar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force yez260v*f.51pplrnkydi1p +y*jc d n (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 cirtx3y4*5.jonz/v fe8f oto5frcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static ft*e n5vo4 3 rfofzt/5.o yjx8friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attacwq,*j om:lvt+ l11usw hed to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string ca*vwj lw ,ul+q11s:to mn 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 and radius 9.0 cm rolls without slipping 10 m dow38r1rahvqy *yn a lane at 4.3 m/s.* ahy81yrqv3r
(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 o 0z4efq 3;qakur; u :w 4a7yp9skjt9hyf $4.5 rad/s^2$. 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 accelso tt;ic2wn.5dj df,: eration 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. z xc75wl(rl jxmw91:e4pon q2300-m radius automobile tire rotate after starting from rest and accelerating at a constant angmq nl2 xrjxpw(w c1o57ezl49 :ular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acl/c-m 9) lt6jnwssg;g celeration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating am5pryda1culb aw5p -: ebt1.9t 20 rad/s decelerates with a constant angular acceleration of rb5mdua :p.cpt e-511ayblw 9$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 v4+ szzxhgj+1c5nv r-rad/s while turning through 2.0 revolutio1-g snxv5+crhvz+ 4jz ns. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from k2lq6m 0t ne.4d0xsev8.40 m/s to rest over a distance of 115 m. What ix.em sq4n6t v0el0k 2ds the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s t t5pl3 ;nirp2eo rest over a distance of 115 m. What is the atri 53p;lnp 2engular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly f usukj zqc93r8 :y 6*fxo;)rwyrom 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the strjcwk 68r:yf;3s yuoq9zx)u * op?

  A centrifuge in a medical laboratory rotak 3t*2j j xx2xuh*jg91m6j zjqtes at a rotational speed of 3600 rev/min. When switched off6jxxtj12gu2 khzm *j9* j jqx3, it rotates 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 require tightening to a torque of 90 Nm. If a 30 ceai( 0ls8,d b6,5roj4q0bwtzuw pz/sm long wrench is used, what is the magnitjdalt65rws eqp0sz(,ow 4z, ib 0b8u /ude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of ek. i8wc.; yme90 Nm. If a 30 cm long wrench is used, what is the magnitude of the fo. 8i mw.;ekcyerce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerthk**yxrs,ndom2q hdyin; * 45ia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeljhne1+ 10ieh . e qf)uhnt*s8jed as follows: mass m is at the origin, mass 2m is 0j h1f8isnee)h+u.tje *qh n1 at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionles-r7zh l vt328zc6sp pxs axis thought the center O. A rope wrapped around3czpv-6r xhst 2z8 p7l 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 massljsa./(ur d8zku-vp+-caj * d 10 kg is pivoted 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 8u c- a.kjsjdar+/up(dl-z* vdoes 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 iseay) a94 ; vas/go 7l55abff .nf9qj 7osiyxg; initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular af .of5 ;7svg o9;9gsji5y7qlae)af bx a 4/naycceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm andlxy::g mxn 79 v an4ji5d)p em* y.cts,oe;q:i mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied i:a gspxv jd9.4xn*q:m)ie : n5t,yl7;yeom ctangentially 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 ark:i:. 1hn0sa)lwj 9wl hxtg,kound a frictionless disk pulley of mass 7.07 kg and radiu01t 9hkl):wkglxai snw .: jh,s 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionles9 ag0nzeb9- q0nb3yjrs disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accele9 nq3nzgb0 ry9eaj- b0ration of the mass?

  A rotating flywheel can be used to store enexww k(wh5 hphjfhgf.5z+3lmw)e. + g4rgy. 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 ofiy *5;nbsfq0s1w2gmzh zv142q (hh qr inertia 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 rolifd0x/ua1m 0: .epw eals without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclinaa/i.0 epu0:xf 1mew ded plane?

  A solid sphere of mass 1.0 kg and radius 6vcs1r.q vd/io/z- npav/g9c 0.010 m rolls with a speed of 10 m/s. How high up an inpd qr.z -/agv n/isv/19cov6 cclined plane 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 andylz 6s f5,mftxw*ms/troz :/3 allowed to roll down afz5o3m6ty*:lfws t// z ms,rxn inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and rade;e/ p 2epn b6,sc;wzxius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inep/wnc,ebz 2p ex;;s 6ertia 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 moment du5nx zh.3l4scsn lqk6n3 f99um 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 inerti2gievk *cth(:pj 9 oc-a 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 inrkis0cn mqb*hr-/ 5n)delj* (ertia oseil )rc5j/(*rd *nm h0q-nb kf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?