Angular displacement is usually expresg b-s y ,qsv4jo)33yrys in units of

  Angular velocity is expressed in units(kbyah n*yw++zu7bbq-f6ab- 5gu wb28ws sf7 of

  Angular acceleration is expres7zbbjq)/k aj+y wo; y:sed in units of

  A boy and a girl are riding on a merry-go-round which is tv( tlkwne:,x*urning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has t* e:tnvk,x (wlhe greater angular displacement?

  A boy and a girl are riding on a mer0n 0obbs+dz3k ry-go-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 greater angu db3kbz ns+0o0lar speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constan 19) gj5nvn19d .en k6mcdr70vioh-0wwedglnt rate. The boy is near the outer edge, and the gigg.1w 1) 9e59c jdnn nokmevw06 vndl7dh-ri0rl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-0o nic xmb,/2vround 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 greatexibv0 on2,mc/r centripetal acceleration?

  A boy and a girl are riding a merry-go-round whmp*ya,s +j/y20.g vkb 6eggh oich is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. h2s+*jav,g obypk0g6eygm ./ Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an acc)g lf b*xas l0+w5.* eojftn;kurate statement+ blkf0ls;xao j)wn5*tg.f * e?

  Rolling without slippinei l.5:bjyjsiye:-9 hg depends on

  Two equal forces are appliewz.kmf7 66 hnmd to a door. The first force is applied at the midpoint of the door; the second force is applied at the km6nz7wmf6 h .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. hjd93dwf fsj t3i, q6/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 the greater tor33hd,6jt9ijsq/wffd que?

  Two forces are applied to a doorknob, perpendicular to the door. T)hud(wfv c,g- ,;ukif891u-mhjypjihe first force is twice as large as the second force. The ratio of the torque of 9i1jph-wih,vg -u j,m;(cdfu)uf y8kthe first to the torque of the second is

  What is the quantity used to measure an object'rq5 (etb7 8-znuld6jbgda, 3 ps resistance to changes in rotation?3ulp 5(8bjb r6z7gtn,-q aded

  Consider two uniform solid spheres where both have th6q)mr( cgi)l / jxqk.ye same diameter, but one has jx )q(g crqm/ly i.6)ktwice 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 spheres have tr5rbf/u ;x *uahe same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is /f*buarxu ;5r

  Consider two uniform solid spheres whe srtn0ew3,3q :wsxxqlf *ok8 )re one has twice the mass and twice the diameter of the other. The ratio of the larger momesnwx t:x8 3*3loe k) sqrqw0f,nt of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are (ucfaxkm7wruay c 6(7 u a3;v1increased to 2M and 3R, what happens to the sphere's moment of inertia abo1(r;f mca3aya6 7 7(wxkcuu vuut a central axis?

  If a constant net torque is applied tiwx1lx*d1xcv vl3* *jo an object, that object will

  The moment of inertia of a solid cylinder:fpq64 yt-d yw about its axis is given by 0.5 MR2. If tq4-:fpyy6t w dhis cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whi * ;rhv;i ux/+o1tdhxech 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? Assum +*hd1vhiurx;et ;/oxe the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping lntta 0*9 (cccdown an inclined plane starting from rest. The linea9 c(a*0ttclcnr velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippingv og odj2u7j1; down an inclined p2 joo ;7vdujg1lane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum oflh7 r-6- d k.+dcrixt zq86dfu a system of particles changes when a net external force acts on the system." This .cx6lz d+-h iqrdrdk 7-t6fu8statement is

  In what circumstances can the angular velocity of syvvs 8lg 2fmo:2stem of particles change without any change:v8f2s lgvo m2 in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. ;a v g7-ch;5xsnqixl1 Ignore any friction which may be present. What happe;ahsgv1-nc i 75;lqxxns over time to the Earth's angular momentum about the Sun?

  The Earth moves about the S83mp w0.rtuki6vesnl1 y l6w:un in an elliptical orbit. As the Earth moves close to the Sun, then which of the foltw6em. rlkwils 8v 6 u3yn0:p1lowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstret :5-4j+at*lktns e fh+z bjs;uched arms close to his body. What happens tj:e+ft ;su-tl*kb h5a+ jsz4 no his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pus/drh.n0xjpv r-dakp , 4hruomt98*xgw; x 3 4lling in his outstretched arms close to his body. What happens to his rotational kinetic energy m- jtvr4d9 4. d xx3wkhg /np0p rou;a8rhxs*,about the axis of rotation?

  An ice skater performs a pirouh7 )fyr/ /xutfette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotatio f)/fruxt7/yhn?

State the law of conservation of angular momc9tea0ht,6q ebp-2 i ventum.

  What arc length does the Earth travel in a three month period in its nearly t549 s1n3 go z vwt5 -ylb,kb9mac5ilvcirculmlk,b n1ytwtos54a9 9icl5 -z5v v3bgar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 mj 7b5y+ e,mikk. What distance does the tip of the second hkkij5 +y eb7m,and sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute z-vr9 47u1d ddkm5g frequivalent to?

  A bicycle wheel rotates unifo8f8p: nt6c jrhrmly through 2.0 revolutions in 4.0 s. What is the freq hj 8cn:f68rptuency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits uklchezv -c45;:. 8;rvztyj wpulses at a frequency of 0.40 kHz. The period of its rotation isj l.z:evcyrk ;54 8 hwtcv-uz;

  A phonograph record rotates a; xezc26 g/ro+)ckyj1w wbxl +t 45 rpm. Through what angle does it turn in 0.20 s?2xj+w+)ky6w z1/re o gccxbl;

  A wheel of diameter 26 cm turns at 1d.3m; sjvnox jv-y+ ,v500 rpm. How far will a point on the outer r,xv3o; y+mjsjn- vd v.im move in 2.1 s?

  A bicycle wheel rotates uniformly throw 3 ysozmi 3-5ee.v/sdh ifc*jl-c l+:ugh 2.0 revolutions in 4.0 s. What is the average angular speed of dc+j ysohe3:/si.*ec-3imw - lvl5zfthe wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutio)*s l1oprlnq q ;lk j(;)x2pr:)gxitins in 4.0 s. What is the linear speek*2 prr( ;) sqgq :jpl1l)t;ioxxiln)d of a 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.pr/ (9li wfw,1 4sbjva The cable which moves the car is driven by a pulley with diameter 3.0 m. Aprvls/i9w,41(jw fb 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 m is rotating with a constant angular speed ofx,0xpffnl/, d jce 4ao x*l0(i 2.0 rad/s. What is the linear speed of a point on the wheel's0 no,expi4j xalcdf*/0l(fx, rim?

  The cutting cord on a gas-powered weedi z2/zgl*rkc2 cutter is 0.16 m in length. If the motor rotatk2czgr/il *2 zes at the 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 rota o/agd0 ,06fn)rtlpl zting with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of n/lldf00p 6to)gzr,aa point on the wheel's rim?

  What is the centripetal acceleration of 2aud cd/e6kx-h3; l m4lfgblc-h0( jwa point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m 0duw (6d;hcajhklex-b gl3m/4fc2l- /s?

  How many revolutions pebvgi.: +z c1ktr minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an z+1bk. gitv :cartificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat citr0rtt 1p6 m0c.n0 q2 s0wvkwarcular curve of radius 50 m with a speed of 20 m/s. The maximum centp 0k.1r mr0w0a2vtts cw0n qt6ripetal 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 fhg-fnnn14jp.83 +wzu7pzkm ,s -kvp jlat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (pj,1znh8--+ p7ukfnpv3mz g k4s pj wn.rovided 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-uvw- yyrjg -4.7hn. y7:y fsqom string, is 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 if the wfy rns -.:g-7u y7 jq.4yhyovstring is not to break?

  A bowling ball of mass 7t80m 2tikaxsbdw:9d z6l)m *p .5 kg and radius 9.0 cm rolls without slipping 10 m down a l)9 sl: p txmkb*wz atm2id86d0ane 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 acc*+p b.enao 6eieleration 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 ofu )d4-dpn -zsz $4.5 rad/s^2$. 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 after startingjwju0 ga4sh2f)w;v zlhc. d6* from rest and accelerating at a constant angular accelerationsw0u)j *az j;. 6f4vgwh2lchd of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerati6 -l -otdms lc-yfc2r;on 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 constanccbi ktf;g45u2y8) ept angular acceleration o fbt5 eg42 8;)pcucyikf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s9a9f y.ztyd zko 88u*w9c2ivn while turning through 2.0 9yaz898 .n9ouzkvcft*iw y d2revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to84 k 2 .lyyed4v1hnuqmjnpz 6+ rest over a distance of 115 m. What is the total number of revolutions the w nqd1p v446ly kmj.yn2zhu8e+heel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 pj w26- hv,3i7j3s fy*gryd twm/s to rest over a distance of v*yjjyi3swrp -wtd, fgh627 3 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/+zn1pnj)ipzk,ew n 3/ s)ij:is to rest over a distance of 115 m. How long does it take for the wheel to come to e)wz+ pi)ki3,:1snji npzn j /the stop?

  A centrifuge in a medicab-vv jz,u94slh lf ri33qd4c+l laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constanr 4 l,-l3hvzusqv d3jf4+bi9ct 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 rewo0 eiwoxuv3, /q*3xzquire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the for,wex xov *3 o/z0q3wuice is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. Ifia.*5i,i1 /hfgn2q q 9 wjbbpf a 30 cm long wrench is used, what is qpjf .9/,iqgf 1i2i*ab5nwb hthe magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ,;az4v3g iltginertia $3.00 \; kgm^{2}$ 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 origin,kj*ts( r73al:uthnm - mass 2m is at x = a, and, mass 3m is at x = 2a. :tksrmnjulh7- t *( 3aWhat is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoug 1/4bqtb,zdx7 *omrmt ht the center O. A rope wra zr*qx71tt / bobm4d,mpped 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is0 *o 8sx -7 o0c0zbaxecsr6bkg.e n7oh 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 osxcs6ez - 080nrgabox7 .kbhe 7o *c0the 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 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*oi,3 a0i uypd*cnw oz y5z;h2 one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular accelea, 5;*i2unz *ph03 iwyoc zyodration 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 ofg*-b*pb(68t pg bzku m radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is appliek(bu*tg - m8bb*zpgp6 d 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 o8b noo).. ,ig9jdduts;lice .f mass 7.s .ni. d.,e; go9ldobtj )u8ic07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of ma*b x2n1bb79 dap vm:2ncts ,fy-k pgk+ss 7.07 kg and radius 66.0 cm. What is the accelea1 tdn c g,f9s27 2vkbympbkp-b n+x*:ration of the mass?

  A rotating flywheel can be used to store energy. If it is required. z o2f;9fd2 ck3klc*gjubw n, 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 inertia ofdv j)fvt7;+o(g bog r; $5.00 \; kgm^{2}$ 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 fr +:hkn/vg8y. y w;i+zfxpo. meom rest and rolls without slipping down a 1.0-m high inclined plane. What is the fnxo+:+. yhv;ykem/zi.w 8p gspeed 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 m/s.fti)/m+ 9d 0tpwz- vat How high up an inclined plane can it climb before coming topa) z9t0 twd-it +/vfm rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from re82cj0 gfi4eg tst and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of e2f 8iggctj04 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down3xslk( ;3fjq go /xk 9edll3b. a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of/sg;3lkb(j x 3q lefok.d3x l9 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 chang1k0r c cle(z+ges 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 u;u8ram r8.p0qreus+ :3qmst5w3g epo2d8thmoment 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 wi-lg5m6 7)f rk s;qannkth arms extended has a moment of inertia )lk6r n f ;7qsk5mgan-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?