Angular displacement eir;26 -ij.ku c rt- nnkk0+dris usually express in units of

  Angular velocity is expressed in units o 8,)id nlt;ul *fgrg+bf

  Angular acceleration is expresse,n7(taiw;, pk(bqh3qek i, x gd in units of

  A boy and a girl are riding on a merry-govb;uhj03zrf.lo 1 g 3i-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the grefrojzb0ul .v1g; i3 h3ater angular displacement?

  A boy and a girl are riding on a merry-go-round which isok6j)u8k:pllmq: w.hi5 0ocpkq8(lf turning at a constant rate. The :q0ikco8m( qf86uplk.:)lohk p j5lw 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-roundtombpz k6*1r* which is turning at a constant rate. The boy is near the outer edge, bmzr*1o * tpk6and 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 turn3kpr8j l0 bfth07l788kztdoqing at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Wpr87d3qo kfjlz lt080k 7 8tbhho has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a cj tpt9r .6 8, ipwe2d9aziex6honstant rate. The boy is near the o9d., xe 6rwti6i8z 9t hppje2auter edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body tha90n/u 4rg v9x uukgm wled:)v2t is rotating. Which of the following is an accurate statemenue 2u 9ru v:v4)wdxk/g l9gn0mt?

  Rolling without slipping dependh zt-s / i+rx0ppdnq7td4h,l9s on

  Two equal forces are applied to a door. The - zg(,wmu mk cm(f-7fafirst 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. Whi- mmuz((fkf gmw,a 7-cch force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is2 ymvgi 0a/bc. applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force /a.0yvib g2cmexerts the greater torque?

  Two forces are applied to a doorknob,c*bi-po*vpory( w 8 7z perpendicular to the door. The first force is twice as large as th-ib(z8 v*cwryo*p7po e second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity ; r4vh-hh eg9pused to measure an object's resistance to changes in rotationh r9 g4h-;vehp?

  Consider two uniform solid spheres where both have the samnoq). s n:s0zme diameter, but one has twice the mass o):0 qmsnzon .sf the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spo1enxd1 +f ml0x fn6(jheres have the same mass, but one has twice the radius of the other.( d+06j11nnxe xlf mfo The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one haddcasb-69ql//r k 4f70ffovps twice the mass and twice the diameter of thd/l kdfs r-faq9fbc 04v/p7o6e other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass .rof wm; rgu+-1qz0c gM and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia abou.ogr+c;f1zw-u mg 0rq t a central axis?

  If a constant net torque is applied to an object, th vihtb.s.y5w8 at object will

  The moment of inertia of a solid cyc2e/c k-nry62+rnr79s a vece linder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic er7nr29vn e- 2aecye+k/6 srccnergy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheeir h.2 , mdn)w3fr8 t26e3;sra iszciul of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinei sh3r3)r uiane sc2r mfd8.zi 2,w;6ttic 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 and gr54j-ml35jz :j8o cvko4jea radius R rolls without slipping down an incliz5va - jo5m :4r48j jjlk3gceoned plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass Mco2 a2ms3uc4 vt:r1e4 ce gy5elq5n .r and radius R rolls without slipping down an inclined plane starting from res4e :elaru 2gcs ct1rn3545 qec.omy2 vt. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a h+kx+jhbygwgcmh8ecj4:s*27obe + 6 net external force acts on the system." This stategsc +x7w h hecjh*+e2y4+ k6g:oj8bmbment is

  In what circumstances pe ) ev*)e3awqcan the angular velocity of system of particles change without any change in the system's angular momewqv)e )a*epe 3ntum?

  The Earth orbits the Sun k+71h)qp*fak9y)l il w wpx2qin an elliptical orbit. Ignore any friction which may be ph*qf 7iqylakkw 9p1+x )p w)2lresent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As tj ho;k6e-z ;zwhe Earth moves close to the Sun, then which of the following best describes j o-ezkz6hw ;;the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pull95 zyz31y hnww1 un7ading in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotation7yn3zu5hdw wa1n 1yz9?

  An ice skater performs a piray*j9p i37jzx ouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic pyz j7j*9 3ixaenergy about the axis of rotation?

  An ice skater performs a pirouette (ax)rxxl dogz.8/a8c8 7 tluja9 fast spin) by pulling in his outstretched arms cl xj/gctd)ora.u 7l9xx8z l 8a8ose to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of a 7gz24, aagqjengular momentum.

  What arc length does the Earth travel in.e0r1fyfkm9 5 ujxsj) a three month period in its nearly circulu9 j xsfj1fym5r )ek.0ar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length hrrb2jv2 29tmof 0.30 m. What distance does the tip of the second hand sweep through in 3 minute29hvr t2j mb2rs and 45 seconds?

  How many rad/s is 25 revolu ef8 tr((3o.9sooeoo/ wp/gxltions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2 0;onl lbqtp(p8be6 a2.0 revolutions in 4.0 s. What is the frequency of lot ( apnbb620ql8p;e the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. T/ 8uq3ov)( lmaj i.dvzhe pei3 vvl (u z.dj)am/8oqriod of its rotation is

  A phonograph record rotatxad- yb5bo30yn csu10es at 45 rpm. Through what angle does it turn in 0.20 s?13-ydnuc b bxo ay50s0

  A wheel of diameter 26 cm turns at 1500 rpm. +sqv 5agf:4qy How far will a point on the outer rim mov5g+y:4sq faq ve in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolu.nx d- j(lvug4o9i3(ew *jxt8 x1cuxctions in 4.0 s. What is the average x(go8cx ( 4dulx e*x-n9i3jjw1 u.vctangular speed of the wheel?

  A bicycle wheel rotates3mg6;dkk p- h/m+v/ ibw sf-ze uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a gvmsim; k+be/kz-hd/36w fp-point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km.g9amn-8:j(bm -a +mmfp1itj -;bohs p The cable which 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 a pfi (9+b-msohm-1;8gn -:jjbpmtma to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular spexhm )nn;oheitf fq)8 x+2gz 0:ed of 2.0 rad/s. Whf0 z qtnehn 8fgix; :xo)2h)+mat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 ht( e2w,k ypzx ,gd.c.m in length. If the motor rotates at th.2kzgw. , yde (thcxp,e rate of 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 b;ghq2e opm0qa54b3mzy mz1 ix6 gl+9 of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel'46mzgbxap1qmo b+z y2 iglq;53h90 m es rim?

  What is the centripetal acceleration of a point on the perimcy v92zhf-+0ub b zz6reter of a bicycle wheel of diameter 70.0 cmhz y 0+f 2bbu96-zcvzr when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spac w)bwu/l gfv2 3,uonw/mcl46ce station (r = 1000 m) rotate to produce an artificial gravig)f low4uc2b6ww//c 3 n,uvl mty of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed ofvruf-t , 8f+i4 zatyc81vsw3c 20 m/s. The max 8s-ayft 4i rv+cuv3c8,zw1 ftimum centripetal 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 * 8r ln42nf ggrtb-fx;radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by st84 rnf*b-2rfg ln txg;atic friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachp- ft4d clo ij7wb90n.ybb; z(ed to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what .-by jf 40zw;7 b9c pbndt(iolmaximum 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 rollmbu*of :34z /tgkn*,+ ghp k-ljo ;jnws without slipping 10 m down a lane at 4.3, o;guk zhbgw j*nno-t4 fm k*l/+j:p3 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 accnmwf/iy:z, m/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 angula (p5s7oav q4vdr 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 -tv/xf:u)ddv fter starting from rest and accelerating at a constant angular acceleration o)u/dftvdx :- vf $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has a vga vs+ka6a*a8w.cqa5l5:lpn 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 i-ld8s 0 d5pvaxvv:(ba constant angular acceleration o:(-isvb8x5 vadvp 0 ldf $-5.0 \; rad/s^2$. 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 turnil n2vbf o(q3(jng through 2.0 revolutions. What is the average angula l3(2vj(bnf oqr acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest j8 8 a+4ltpoowover a distance of 115 m. What is the total numo8 p4wlat8j+ober of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows d jnt:z/3ki d.ne rlbla2,/k *pown uniformly from 8.40 m/s to rest over a distance oln. kbi/p3 *2ne, /kr:la jtzdf 115 m. What is the angular acceleration?

  A wheel of diameter of 68.05crts9/l4 t-xj h k-eg cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take f-k4stg r ejhct9/l 5x-or the wheel to come to the stop?

  A centrifuge in a medical laboratoryt8vd;s) cf pkvk:*lq0z6v6 dv rotates at a rotational speed of 3600 rev/miz s:dl8; *6pkt) ck6v0vf qvvdn. When switched off, 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 whelb(i.n)qu,,iwc*dmd p7 x j,t el require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requiidm n*jlbt, c.dqix7upw),(,red when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90mzd k e57ixvo aw/4y6+ Nm. If a 30 cm long wrench is used, what is the ma xoa5y67de/z i+4vwk mgnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia 4lo8h 5m83n w sqt9gpndsx3p2$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows0b6* 0qh wzjtezhsku-g . *sx*: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia0*bhu z 0tg skzewh *q*.x-s6j about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frirnbx.d0 lz5*dctionless 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 forc.dr0bdx* nz5l e 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 thought the z2rucy8r c:mrwn+74bcenter 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 Rmnu:2 rr zc4w yc+b87r2 = 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 hemc0d0+hn;k6 j d,fv-ou o,x ucld 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 abodmx0hu-, fcokuncvd0 jo+;,6 ut one end is ML2/3.)

  Consider a bicycle wheel to be a ring of ra jn+l:,7 ayddbdius 30 cm and mass 1.5 kg. Neglect the mass of the axl,: bda+j 7ldnye 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of masr;mz5 n9c c 6goriyf8)s 7.07 kg and radius 66.0 cm. What is the angular acceler r 9;86c)fyrigoc5znmation of the pulley?

  A 1.53-kg mass hangs on a rope wrapped lq 0/jxn:xr n7x.hu t4around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mass xt :rnq0x7xhju/n.l4?

  A rotating flywheel can be used to store energy. If it is required to storez e4ft2n4wqdki 55mvg.t ro/: $1.00 \times 10^{6} \; J$ 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 inertiai :h.gw 7(u nvs2rka8rg21xhu1f .cyl-4vmfv 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 restc*g qfqw58b6gk 5d1sl /c4y jt and rolls without slipping df8g1g/5cq6w*j4ylc sd5b ktq own 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 s52 9c lkr6n(acvun-fr peed of 10 m/s. How high up an inclined plane can it climb before coming c lcukr 2ra9(nf6 -v5nto rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest s:br s44o(hdaxt2m6 qabwj4 y,(;mk cand allowed to roll down an inclined plane. How fast is it mot6;,j a2 mb q4 4sy s4mhoc:xdar(b(kwving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm ro a)kkzw5 thc3bowe( (*lls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The momen ka 3(bo(ekw 5zct)w*ht 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 moment)w2i.ywpew 9fq6x0l+ ,jhp fyum 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:(ph 7vthhe7 ays 57ji 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 fgsuy 166 w/:ili1kdi 5.00 rad/s with arms extended has a moment of inerti/ik6f6:iidusl1 ywg 1a 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?