Angular displacement is usually express in n0peq4 mx1st0f05e wtunits of

  Angular velocity is ex 4fz5 a4iwie*xl q gn(/ pr/;buh38rimpressed in units of

  Angular acceleration is 2qxem( 3ocwt u :jx.w-expressed in units of

  A boy and a girl are x43ry, e2vce6g8 qjdvriding on a merry-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 angular dv26c,vgd48 r qx3yej eisplacement?

  A boy and a girl are ridivp+nc95p6w:di w cp1o *e4yqvng on a merry-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 t + 6o19y4q*cdpicwvvn :5ew pphe greater angular speed?

  A boy and a girl are riding on a mer-cxuu/bvp 81 )t*pzb rsje3j+ ry-go-round which is turning at a constant rate. The rp tb1-/)83bvcjz ej su+u*x pboy is near 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-go0szs(nszi-/ b,- .frexoxz (r*wxun ,-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer xznrrx f e -,-nbxz /zsosi*(s wu,(.0to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-gom(q jizy();( h-uasho-round which is turning at a constant rate. The boy is near the outer edge, while the girl y( iaqjm h((h; )zuo-sis closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of tho0nfow0sp 04 gb iob,+m+z a:be following is an accurate statementao0sb,+ipo4fwb+ b zn:go0m 0?

  Rolling without slipping depends on5(z,ul;x igs2ozn;co ,kg(wlzxxn f h.xj,51

  Two equal forces are applied to a door. The first force is applied at el-ia9 5tclh2v; s/vj the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exe/; j ll a5-evthcs92ivrts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is appm0ij+x7fz im 7j8b7h*3jbssf lied perpendicular to the door; the second force is applied at 30e tos 77x 8sj 0+f7*mfj zmihjib3b the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to t4)6x syva sdtj, *nji0he door. The first force is twice as large as the second force. The rtvad 6 yj n)s0*is4xj,atio 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 in rotat:c 6znpk pw6nl(mm9 q(ionm( lnm: c p69pkzwn6q(?

  Consider two uniform solid spheres wh uoh.9eja;.(.1 ghaxdd2ap x.n z5rrvere both have the same diameter, but one has twice the mass ofda.(ojxgdz5.aevxr ahp .9 h;.r1n2 u the other. The ratio of the larger moment 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 ofu 12+698xn+ar*kh ky2b wupx v*rnty b the other. The ratio of the larger sphere's moment of inertia to *xrpk6avy 8w*y xb2nk run 1+t9+u2b hthat of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twi6as veam05fpz+r61 d xce the diameter of th0 +rzfmad5e 6avsp16 xe other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If ;6wmin q+ tgs*i0 mzp-c xo*+gthese are increased to 2M and 3R, wn+*w6zmtg 0*g q +pimo;- scixhat happens to the sphere's moment of inertia about a central axis?

  If a constant net torque isv,ed 0mw i ,8wnu :feqhb3k:0e applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis oicyh(wawq vwnv 84 73o82n07tpyy5vsl6 m;iis given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, on1,v mm1zdg4zge wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy ofzm1v z1 ggm,4d 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 sx4kyr-i8; hb9piuxv: +o cl(o- c ;yyalipping down an inclined plane starting from rest. The linear velocitv;oo8u cxr9 i+ 4xy-y-:apikyc (h; lby of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R r hvmblag iq*v;f7f88 -olls without slipping down an inclined plane starting from rest. The angular velocity of the spheravvfl88qigfm-*7 ;b he at the bottom of the incline depends on

  "The total angular momentum of a system of part97aq *g.egic3aj4k ax icles changes when a net external fora.g*g37aia9ex jkq c 4ce acts on the system." This statement is

  In what circumstances can the angular velocity)ewlf4 d5cjz;( fmyb: of system of particles change without any change in the system's angular momentuz ; jd4mb5:yc) fewl(fm?

  The Earth orbits the Sun in an elliptical orbit. Ignore anp: -rjz ;l2qaxy friction which may be present. What happens over time to the Earth's angular momentum about the2l;pz-rjq a:x Sun?

  The Earth moves about the Sun in an ellipt:xt j jw 3.at3g8gs(pvical orbit. As the Earth moves close to the Sun j8wx g:3vjsatp g(.t3, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs,sdi asz 59k5a a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum 5zks9sa,d5iaabout the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his gf2ikkxa07v(b,v w0cx snva9(b m y;4outstretched arms close to his body. 7ka90skc0bg wxnva (m,f2;i(y bx4v v What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a piro uz+c/rlb rinv9( 57khc q1g-muette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertic rhbmn /1z(rk95q -uli7g +vca about the axis of rotation?

State the law of conservation of ang .-ksgdx1 y;rgular momentum.

  What arc length does the Earth travel in a three ;*7d+rq0nl 6 qbhxxf wmonth period in its nearly circular orbit about the Sun with a rafn q7dx6;lhw0*r+qxb dius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the tiyvjr syn . c4/y-,uapkev3+x0uc.so 4 p of the second hand sweep throug.js+c0e4.uuo cxn4 akyyr ,/ vy-sv 3ph in 3 minutes and 45 seconds?

  How many rad/s is 25 revolu(b ws0h2sh aax2e0u,qtions per minute equivalent to?

  A bicycle wheel rotates uniformly thr9kiy/vr qsc . 67xzg7bough 2.0 revolutions in 4.0 s. What is the frequen.vq6 /yck9g 7irb7xzscy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40n0utsdlx; r c+jv)q6hxjn 5ne1ob ko 2)6u6 ;q kHz. The5j qnot e6)q)bxn1hc n6v+xldsuu2j ko6 0;;r period of its rotation is

  A phonograph record rotates at 45 rpm. Thrhyplb o+fo)hq5:t 0 ,bough what angle does it turn in 0.20 sh:b lbqoht 5+o0p), yf?

  A wheel of diameter 26 cm turns at 15 ;hgs(nz )3c.lgq9 s/tkhna:m00 rpm. How far will a point on the outer rim move in 2.1 s .ts(ng3)gm z;khh/c l:n9qas?

  A bicycle wheel rotatesc. zf;l -i.jdr uniformly through 2.0 revolutions in 4.0 s. What is the average angulazdi-; jf ..clrr speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sp v f vjfcb+ggmii:c7t;h1;5 1. What is the linear speed of a point 0.10 m frjc1 ffvi;b;:h v1mt5gcgpi 7+ om the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cablekp +dp6 5b697jv tk zqk(kafm, which moves the car is driven by a pulley with diameter 3.0 m. Assuming mjq9 6d7b+zp kkta6kkpf5(,v 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 og ++bokq o:o2zf 2.0 rad/s. What is the linear speed o 2+kboq +gzo:of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m iac2l 7y sfvme/ ;sf0c:n length. If the motor rotates at the rate oscf72 ;ve/m yf c:s0alf 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 of 22z6d-d(kvqe( l0rjm7 wft* lj.0 rad/s. What is the centripetal ac6*0(tdejdz klw2j m (qr7 fl-vceleration of a point on the wheel's rim?

  What is the centripetal accel; s 0wbe,nvv 9,jhb2fr2gl j6xeration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the biks ,w ,92 bhnj2;eb xjv6rlg0vfe is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space sbqan:kyid9knq /;0n1 tation (r = 1000 m) rotate t1id a0q bnk; 9q/ynkn:o produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m /)18pr0egzru ,xiizxbmj,+ hlw +;eqwith a speed of 20 m/s. The maximum centripetal force (provided by sthz;mwg,+l u) rqeib8 ijpr+/exz1x, 0atic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat cird3k xllij vlx9 m;0b;6j*f::yisj0( -pnmpdhcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provi:j;by:3*l0jdl sjx6 0 vdl9xk mf; -ipnim hp(ded 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.f(stgg t.ylb:ie-m*a +dmw/5750-m string, is whirled around in a smooth level table. If the maximum ten5bty + *l:(s-e amw/.fdigtmg sion that the string 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 and rad 6 53w e;le ztmpwo5x8c3i(tpfius 9.0 cm rolls without slipping 10 m down a lane at; 6xwclp8p t m(ezf353i5tweo 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 wi0 sk xbrsxt9 8*zoz13ith a constant 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 acceleration ono x9nuke t80t0yr6,di f;o0of $4.5 rad/s^2$. 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 0.9x)v*vcaamel ;a (k5qh ,qu1roy 0p .v300-m radius automobile tire rotate after starting from rest and accelerating at a constant angulac* v aaq,lam5)k.xer h1y(v;v 0qpou9r acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an +4o3m vwv()q6as;r fo.9thydzv ,swr 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 consty wp8bhh (0ymnw;76o nant angular acceleratio08bhh;wo6y7n nm wpy (n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rw f1ot ::fo5exest and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions.x15tw:oeo :ff What is the average angular acceleration of the wheel?

  A wheel of diameter of 6-eoq3o5z0q,oo. zpvi8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates io.q05pq-ezzov, oo3in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to reo v6z;-z re*hest over a distance of 11ve*h;6 zzr -eo5 m. What is the angular acceleration?

  A wheel of diameter of 68.0 jzkj2d+ m( gojm4;-jk cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel tz jj(m;kdjo+-mj4 g2ko come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatiga,n1 z cm82ns+sdu9z onal speed of 3600 rev/min. nn zacssum 1+,z89d g2When 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 wheel requi;u 5p++z 3a zsfcviql7re tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the s;a+upf z7 i+vlq 5c3zmagnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 c )y+f9sqyacqk+lq+1 gm long wrench is used, what is the magnitude of the force required when thfqqqsa+yg9 cky ) 1++le force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i0n :(k8 46xvftnxuuh lnertia $3.00 \; kgm^{2}$ 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, ssgnq8z+*h stb0 02a lmass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about sbnh0st* 8 ga0lq2s+ zthe origin?

  A solid cylinder of mass 10 kg is pivote,cq)3 (ld+he4ehw fscw)xq7nd about a frictionless axis thought the center O. A rope wrapqdeq )(4wxeh,+lw h c)37cfnsped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frict -nvmo7k 3rz7wionless axis thought the center O. A rope wrapped around thw77k3nr -omzve outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 tow1)a e7 vd1hat 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 acceleration as it is released? (The moment of inertia of a rod about one end is ML7doea1th )w1v 2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and 5t *k6k 5vd:gvaw rk ,.w:eukrmass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially5d wvwurkgkt:, v6 ak5e:k.*r 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 uuo wak:q/ l81rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular uul a wq:ok1/8acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless difd 2ufwp *(+zqsk pulley of mass 7.07 kg and radius 66.0 cm. z+pw f u2(*qfd What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. Ifm-ue8b y4ht3gni v edm m0pq914z9 w:c 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 inertia o.2 t1gayc ,qquf $5.00 \; kgm^{2}$ 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 re7c v ii.m6d+s ia;f0wost and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of t i;m+o.da7i i0vscf6w he inclined plane?

  A solid sphere of mass 1.0 kg and radjn*6fwcx 8i6kius 0.010 m rolls with a speed of 10 m/s. How high up an inclined k*ic66xwf nj 8plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.tt q8 ktor:1tit3 ),jdfbh18 u20 kg is released from rest and allowed to roll down an inclinbj81tr)idu 8 o kt,ftqt1th:3ed 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 rollsjpan z. l5rx )644szjw without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment owxn.zl5aj r6 4zsp )4jf 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 momentum changes by 8x bxz02v5i(9hk3tm+nmb lt n $20 \; kgm^{2}/s$ 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 inertink3 :*s)nnmp, pes oqtk*x/9wa 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 guxz(r*lz1r 5inertia ol ug5xrr 1(*zzf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?