Angular displacement is usually express in unit1u 1cj5f4y xte(7zrp0b hti4oz 7zkk. s of

  Angular velocity is edh+,/v2ql+qn ,yyz z xxpressed in units of

  Angular acceleration is expya g:99e3doqf8ls n1+diktwkq;u 3lfwt -c2, ressed in units of

  A boy and a girl are ridingq e+u( y5amh(b on a merry-go-round which is turning at a constant rate. The boy is near the outer edge,e( bam(q5yh u+ and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ridi 1g4 8rrzxkn +vd;)ts.dkg5j zng on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closegvdz z.xkg+8td;1)nr sjr k45r to the center. Who has the greater angular speed?

  A boy and a girl are riding on (mfc a.hr ,5mca merry-go-round which is turning at a constant rate. The boy is near thhcfa(cm., rm5e outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merqkk+qp-.pl 4 lry-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+-qpp kq.kl4l has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round why( bir,* g3vt9kqro1eich is turning at a constant ratee br tgq,r9 v1*oyi3(k. The boy 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. Wyfhftj*if3 /. hich of the following is an accurate statement? t fyjfhf3/*.i

  Rolling without slipping depends on/o+tlojs0a em(wn7nryd8 +)r

  Two equal forces area)*(/ ixppl mi0i dfe6 applied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied pep0f i / mx*dli(ei)ap6rpendicular to the door. Which force exerts the greater torque?

  Two equal forces are hj x.e;rd;t an4tc5r(qa b*de0 0) zrhapplied to a door at the doorknob. The first force is applied perha;;qd cx5(e *d 0t nb z4t.j)rahre0rpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Theevmp 8:y1 jm b)p0)fuu first force is twice as large as the second force. The ratio of t8bfyeuu)pm )j: m 1pv0he torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in rotathr5)nmleb7q 3iql )35 en7hbrmon?

  Consider two uniform solid spheres where both haveo2 nx)/- zik7:zubsc oyi5:a a the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller momozi/7su2abkzx)i: ac- 5y : noent of inertia is

  Two uniform solid spheres have the same mass, but one has twice the rzd*oq8op s k.,x3s+rz adius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphersx8r+*oqpsz od, 3kz. e is

  Consider two uniform solid spheres where one s /og-x9+n2ij+b r nhq.jqr( khas twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of(xni++.gjk jhbrs-o r2qq9/n inertia is

  A uniform solid sphere hyw yhj fg2:0g6d7m g aqy;4c54 zg.gosas mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment qj gcdgymy 2gygazf0o6.:;44w g7 5sh of inertia about a central axis?

  If a constant net torque is applied to an object, that objec,lw:i5+i bef )xjs21j2ov r jpt will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. z:uo2dwa,(0o(g *js ,f cewwxIf this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic ener:zaw* ef(,c(dg 20xwujo s,owgy is

  Consider a motorcycle of mass 150 kg, one wheel of whivv5e fm/s1sc2ch has a mass of 10 kg and a radius c1sms/v5e fv2 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 the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping *;e bgm6.pte km8 int5down an inclined plane starting from rest. The linear velocitytgm; k5n6e e .mitb8*p of the sphere at the bottom of the incline depends on

  Suppose a solid sphere oki3zy+n:6f ss f mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline dependsi+z fy3:6 snks on

  "The total angular momentum of a system 7r2mugnw0 5 zafe i3z5of particles changes when a net external force actsf m5niwe50 zguz7 a3r2 on the system." This statement is

  In what circumstances can ;m89u2eqbc eqthe angular velocity of system of particles change without any cha29mu c8qeb q;enge in the system's angular momentum?

  The Earth orbits the Sun in an elliptick((:xs, 8,.hbognpi w7gqmgk al orbit. Ignore any friction which may be present. What happens over time to the Earth's angul oqgxghp8in (,s:b7wk,kmg( . ar momentum about the Sun?

  The Earth moves about the Sun in an elliptical or j.d esa(j,p+xz v1z4kbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth akvjx .aez+(1ds,pjz 4bout the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in .dn cf1h5/mi ud;nyf /his outstretched arms close to his body. What happens to his angular momen f ui/dy5/nc1d .;hfmntum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin 9(weml1 arxmp;,aolsn*l h:3) by pulling in his outstretched arms close to his body. What happens to his rotatil *l awm1;a9(olpe r:xsh,nm3 onal kinetic energy about the axis of rotation?

  An ice skater performs a-dufrl js n/)lzn jmo;5i96x- pirouette (a fast spin) by pulling in his outstretched arms close to his u;f) z jnrxl/sjn 596il -m-odbody. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum2j( w2rn ezf.d8oiuz3+sx)p-yon xy * .

  What arc length does the Eartw-w)1o(eum gx h travel in a three month period in its nearly circular orbit aboutw1u-e(wx) mgo the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock bmq5d14bvw/ ah4 c4llhas a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 seconb 5l4/cvdmw4 bq a1hl4ds?

  How many rad/s is 25 r*sgb-q0dvpzhn6y* /yevolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4hnd,twf+clg ) u3l45 n .wql5z.0 s. What is the freque.fn wllw+h t,d3gqn54uz)c 5 lncy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a q0r anfg,cfb7 ty0 z/s-+q8yi frequency of 0.40 kHz. The period of its ybq ,n +agcri/ sf8zq00 t7-yfrotation is

  A phonograph record r*z wtqzz,jo 1-kk-jo +otates at 45 rpm. Through what angle does it turn in 0.20 s?kj- -zw*+zo 1zo,tkj q

  A wheel of diameter 26 cm turns at 1500 rpm. How farir +o bmz7z2-. r6gxtv will a point on the outer riz .r2+v6moibrx g -7tzm move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sbv-vy e (dbo o tauct05les 30v3y;g:6. What is the average angular speed of the whee-3v30gbo yos;de0e y6tvltc5 a ub:v( l?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is t.hf*46 vu6ykle *ul shhe linear speedfhu6*lylku4h*. s ve6 of a point 0.10 m from the center of the wheel?

  A cable car at a ski resortylw-w v)stp 958;tlxm 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 fast must the pulley rotat58w );9llxvmt y -stpwe for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular spee 8jj g)o1shfdkyk* 5hzv x02o3d of 2.0 rad/s. What is the linear speed o 0ozvhfo8ygs3jkxhd ) k51j2*f a point on the wheel's rim?

  The cutting cord on ah4 2rlaa1i :bi gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear si 2:iaab14hlr peed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speedb q uiby:r259d of 2.0 rad/s. What is the centripetal acceleration of a point on qb2uy5i:9b rdthe wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle w5 * nowt4uqe og7na66vheel of diameter 70.0 cm when the biken* e6u54oga 7 wonv6tq is moving 8.00 m/s?

  How many revolutions per minute (rpje w8 g pnvx/4+m: l(. p6dnw)ldzrs.vm) must a circular, rotating space station (r = 1000 m) ro/nxw:.4ml+jpv). nsg w8d d6ezl (rvptate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular cu (tefo,k((i mn (tcv3frve of radius 50 m with a speed of 20 m/s. The maximum centf(( m k,v( fne3tti(ocripetal 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 on52 *,,(rnbdtts nohradius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictirn52n n*dt,o( stoh,bon) 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,lo zw vs 5-00y565z tnulvjcg, is whirled around in a smooth level table. If the maximum tension that the string can withstand is550cvngl,uzt5 ywo0 6zl -jvs 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 rmyl7x3byj. x c7bppfl:j*9+ oadius 9.0 cm rolls without slipping 10 m down a lan l by +9bc.7fjjxyx:p*p3lo7 me 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 constxfp4(qkhmwda8gm -l; q ,/t 1dant 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 constant angular acceler0iyw+ak 4 xy2u0.r oa2cjh9 nqation 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 aft/cssbqoc xym 7e5hqvmk-;v; s.t)e (6er starting from rest and v hk.c;c)-xy56;te mq qv /emsobs(7s accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acc9dpng3r4cnus c- .8y beleration 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 accelerwaj+ a qyn8d7clmrf6c(xh56 h , mom;*ation of 57*,odhy wc6 ma a+xnml 6m;rqchf8(j$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6 g3;e rzu z bmfacl)55b8h,qm).0 rad/s while turning through 2.0 revolution, za;5q5gmeh)r bbzf83)lmu cs. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows do .w7cgvti-e-r wn uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates i-vi-w.er gt 7cn coming to rest?

  A wheel of diameter of 68.0 c*tm9rg-c itr(sn /p a8m slows down uniformly from 8.40 m/s to rest over a distapc/ai m(8s*9 trrg-nt nce of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down u 1h09us r,y (tool,pbaniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to co (oab91,hslprut, o0y me to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 ren/a vnjhw39rp y7l.f 3v/min. When switched off, it rotates 50.0 times at a constannr.p/3yh janwv 3 lf79t 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 y s)sm:ld4dlcg/ *p+oto a torque of 90 Nm. If a 30 cm long wrench is used, what is thyd4mcp dso:s+ gll /)*e magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a tor ,f:g;hn7zx nl 1omc3rque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force appliex1gr,3f7;zo hcn:nlm d at $53^{\circ}$ to the wrench?

  A wheel with moment of ine5 cnb hr b :q-c6(d3bqhtrg-/ln **ypmrtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mo rb);ilo3( yg;wsu2 ocdeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is thg)iuo3 y(c lsw2;br ;oe moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axi5bs, j:zxk cy26 4m/fp jfn1ods 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. (See Fig. 8-1.) 5czxfpokjmdj: 1byn 6s2/ f4, What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the f3zj3qrwaid n/5-f r-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 does the cylinder rotate through in the first 5.0 ran3 i5jrq -w/ff 3z-dseconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is igg6mi:g,+ nxd nitially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acce6g gd,g m+xni:leration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a rdlap z;2q st ;( eplci-:xg2.iing of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle a2dal;gp;ise ixp-.lqt :2c(z nd 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 ft /;n er q)sf8o nurht/3+.iaa frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whr n sr.;feouqta3/ )/t+if nh8at is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionley/m g;(benh.f:cz 6 l+leuhi 4ss disk pulley of mass 7.07 kg . :h yfebg6nlh+; zl4e(cumi/and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store ene4 )z dhh-0lc3 uo,xdxa 0xwy8ergy. 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 in vc kgb jk(3c9j.s 9b(p,g4fvxertia 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 1l ua6l+ ywl:+w- blq.k.0 kg and radius 0.010 m starts from rest and rolls without 6 ylal+ w.blulk+q- :wslipping down 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 mass4p25c s:b0 upqjgz d(l 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to rezul(q: cjp dp4520s gbst?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest andxyyjq9br4, j * allowed to roll down an 9 ,bqyryxj*4jinclined 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 withpkl5a-g mi+ i 1opcnfw::j /;qout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is /5 mpg :cjnpl wk:-;1+f oaqiigiven 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 i6f0a-q9q,x r1jr7rj9 sgs f uchanges 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 of ((ki4+nxk ;zvy l9ped $5.0 \; kgm^{2}$ 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 -hieg busl(xqp*1fbmp qy4(25 t7ml(a moment of inertia ofq7hb-* g5fl(((b42 1upepiql tm sxym
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?