Angular displacement gq s(wl275 kcqq )7ozx bk92kiis usually express in units of

  Angular velocity is expresses uyl/ 1(-3yjmf)cng )4 +tmbj 7w.z-svlmvkdd in units of

  Angular acceleration is expr ai3 s(z,8h fk6(u9lmcac6in cessed in units of

  A boy and a girl are riding on a mervp1 gw 7y vg3zcm )5k.rbv,n8ery-go-round which is turning at a constant rate. 7,gwyn.p)8vg bvzvkc351 m re 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 turning at a co jnh0zzbolkd4+-+ 9jwnstant rate. The boy is near the outer edge, and the girlo +4d bz+zk09hnlw jj- 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- h+yefa :2eghnj;oql8 o4y,q a constant rate. The boy is near the outer edge, and the girl is clon fy q4 je;h2g :hy-lq8ao+e,oser 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 constant rater9k4b+h w5ta he c7*xzsv;p s-. The boy is near the outer edgvxhapst -ch +r*e9;57zw bs4ke, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constan p.fhz gpjoa1*+:ev: gt rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential o*z1 faje:pgg +:ph.vacceleration?

  Consider a rigid body that is rotating. blo2 qsrg;f +0 Which of the following is an accurate statemerg;s0bqol2 f +nt?

  Rolling without slipping depb6sil h6j-x r0ends on

  Two equal forces are applied to a door. The first force is applied a p5,,oile q; b.jh.*pbeintm4t the midpoint of the door; the second force is applied at the doorknotj.e b i5nob. pimhe 4,*;q,plb. 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. Thnj6l s2;j c/pff/r /tq h6x6nb4v+ r2dxwadq4 e first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force ex r4/fjs2q fabjcr6xxn 66 ;d+/w/lp2 d4qvhnterts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The fir/r ud .l *is.am1jhy5gst force is twice as large as the seci*h.5/1sda.lygrj m uond force. The ratio of the torque of the first to the torque of the second is

  What is the quantityrrr* v faj n)d;t0b5:8p7o cmg used to measure an object's resistance to changes in rotation?5pr:ravo7*)tcd m bn8 j;fg r0

  Consider two uniform s8tduwt(f:y r56dbv nv q--x- lh7)zrnolid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smalleq-yv5 lrxrtdf(v-nud)7:b w8tn -z6hr moment of inertia is

  Two uniform solid spheres have the samkn n2vi cca))2pp4z4 me mass, but one has twice the radius of the other.n2cvz) nca2ip4)pkm 4 The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the dilqz+f4/hip+3dzba p/ / k z9rgameter of the other. The ratio of the larger moment of inertia to that of the smallergip3b/qp 9 zz+/hrfz4/a+ kl d moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are inu8wvufl/2hzk5 g o - s))plz,tcreased to 2M and 3R, what happens to the sphere's moment of inwf5-)zvl,th2lzsk / 8 upog u)ertia about a central axis?

  If a constant net torque is applied to an object,5llh:y1+1-z rxxqi hb that object will

  The moment of inertia of a sol:*4 ig7esrxl q.:nsdkid cylinder about its axis is 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, one wheel of which has a mass of 10 k5e;oz8 s9 y -j yaqv)u;h+smbug and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total trae; vsusz u8-y5q; maoj+b9)yh nslational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippwcnmlit1c: :k5;9eq 7 8nylujing down an inclined plane starting from rest. The linear velocity of the sphy c ;tnmq:9c1j8wi n5:k7uel lere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls with89fz c w.9g7v,b *iwzk qsps s(sy:py:out slipping down an inclined plsqbzc:kwps zs8p ,*iv yy9 9ws7( :.fgane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whf-;;-x z seycjen a net external -xsfe -;;jcyzforce acts on the system." This statement is

  In what circumstances can the an0vy0 a.6hadfp yudt/qs /r06kgular velocity of system of particles change without any change in the system's angulapdy/uhs f 6rk6.v0dt0/0aqya r momentum?

  The Earth orbits the Sun in l;omw,94mokrnz9udj5 7kx( *n8oi oy an elliptical orbit. Ignore any friction which may be present. 8z(idl xn5,oym o7nmo4r9kw* o9j ;kuWhat happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in il4cayn s fi/3c,qiz j65 m gn:cb+vah,6i1w+an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed ofiz ic,s4njq al1i/66w + y35v:cgachnb +mif, the Earth about the Sun?

  An ice skater performs a9ntz qirfc. 9+7tbw +x pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular mome n+ 7tq ftcirw99b.z+xntum about the axis of rotation?

  An ice skater performs a pirouette (a fast s6 oef0e8b5 loapin) by pulling in his outstretched arms close to his bodeoe a560blo 8fy. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in)3*zwxmwd/ gu his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotatidu3 *)w/wxgm zon?

State the law of conservation of angular momentum.vvj)hb pepoebh9q-+y(n;6pvl1+.q m

  What arc length does the Earth travel in a three monthyx ogi89ido * xct7u)2m1x( ih period in its nearly circular orbit about the Sun with a r cut(xyo h 1im*8dxgo27)xii9adius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does 1) vji y*0f5vqfb 7akgdh3js5 the tip of the second hand sweep through in 3 minutes and 45 secd0*1v5a73 k) h qfjyg5jisvfb onds?

  How many rad/s is 25 revolutions per minute f4k;jf;1eu g: kulia 5equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolut 8.kzve q-:lq9 lyk*rfw1r ajgr;)c3y ions in 4.0 s. What is the frequency ofw3fl*ky.-ze;r j9l1)krq r 8vcqy a :g the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a fref*zi+ms32fs i quency of 0.40 kHz. The period of iimf +isz*2s 3fts rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it tur- rl3 wf* 8rgepe;0yt(thj le,n in 0.20 s fe ,rrp;j (helegw083tty-*l?

  A wheel of diameter 26 cm turns at 1500 rpm. Hout:xv ;hc bq68w far will a point on the outer rivtu ch6q8x b:;m move in 2.1 s?

  A bicycle wheel rotates uniformly th8hwcx 7k9lgq6)7cm1 iwm nf z2rough 2.0 revolutions in 4.0 s. What is the average angular speed of the whek72c78 zf i)1gmn9mxhclw6 wqel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is tplzl( m 64 h*1z6tnonkhe l 4hl* z tz(k6no6m1lpninear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distanmvg5y3jpe g4)y ty 5 pwkn3-w+ce of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippa5 pgk+gwyv p5 4wy myn)e3j3-tge, 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 s u n/5b:md,no1 h.jqleqo:)x7 r0nde opeed of 2.0 rad/s. What is the linear speed of a point on therdxh50o/,m l:o o b edq1)nj .7nqen:u wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in ly08 emx ea67 zush w9/r. a2axd5rtvc3ength. If the motor rotates at the rate of 20 rev/s, what is the appro r26eyw dare 0zu9c8a t /sxvmaxh75.3ximate linear speed of the end of the cord?

  A wheel of radius 1. wm-vrzarway-k;h/ra h q600 *0 m is rotating with a constant angular speed of 2.0 rad/s. What i*q0-mawv/ar0 zwhahyk rr- 6;s the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point ajlcp9u) 7maopev8n:,8an (l on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is ulp(j8: 9 8,a mlpneaa)7cnvomoving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statis fun9o s.)po5) 7waqion (r = 1000 m) rotate to produce an artificial gravitysopqw) u7o.i s an9)5f of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius f9j/l;b6n ntdavr;,m50 m with a speed of 20 m/s. The maximum centrip9jl;f ab;/ md,tvr n6netal 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 radius 50 m witg8lyyx /tophv3 . u9z;h a speed of 20 m/s. The maximum centri gy8 vp/.9xyo zuthl;3petal force (provided 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-m strii qx2x 8;ekib,d0k3s)i+y bjong, 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 mae03)x,xio jd+ks i;y2ibq8 kbss have if the string is not to break?

  A bowling ball of mass 7.5 kbfp4v8 8 wsqnv sb)n10g and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 04 bvsvq)w18sf8nbpn 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 vlsst6zz-4/wci,bj+3fs/4onzrf 8 k 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 confy.un+b /k 2oxl0*rki stant angular 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 auto fjnrg marva;0yf2;*am 4h2l1+s 4ekdmobile tire rotate after starting from rest and accelerating atgffhjr4eny+v42mm0 l sa* a d2ka;;1r a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angl7boih n 7o 8 6wuy1pt80 n:y-brzfo)iular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating acpklli9v3 62n t 20 rad/s decelerates with a constant angular acceleration lp n v92kcli63of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 q -t h- fbcl,wcn29nb-rad/s while turning thr-hb cfw2n-tbn ,l-cq9ough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm sl pxp/v,n8t h)r8fv,w xows 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 in c/w,xpn rf )hvtx8v8p,oming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8skj81 4pbg97n8psjr uyh0 ujeh-+* eu.40 m/s to rest over a distance of 115 m. What is the angular accelerationuu1 4hb9jugrss0p-78p *+yk nheje8j ?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/atu1 f 7 f,zeh 1*sz,kppol4m,s to rest over a distance of 115 m. How long does it take for the wheel to come to the1s7 zp1f4hmo *utza ,ef,klp, stop?

  A centrifuge in a medical laboratory rotates at a rotal9;m4fag r fwc /3szr4tional speed of 3600 rev/min. When switched off, it rotates m944r; flrfzgws /a 3c50.0 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 dukm:*n(1)ccc l qip6to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude pcq*n ( :)umcc6kd il1of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheemruwhoe ,b7)4l require 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 fohwr eb)mou ,47rce applied at $53^{\circ}$ to the wrench?

  A wheel with moment 8 8ybj-m4nh/ erz7 tlhr74nlxof inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mdqz,9cavg -x,d38 s g(t vzru1odeled as follows: mass m is at the origin, mass 2m is at x = a, an x-3gucvv,q(g9a8 , z1t zrsddd, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 1s ;brs+1lvd+2a2 g xkj0 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer rb;g1x j+v rad2s2k l+sadius $R_1$ = 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 frictionless axis e94e0l bt5vcrb m9fb5lhs;(b thought the center O. A rope wrappe9 m brft;vl 05cehb be(sbl594d 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) 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 hel 72snf t *s:ux+ azno755lpzbpd 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 isp5tz5o+7 s u lz2p7abfn*: xnnertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 /, w b,v m-7w8hroh/nsnrja+acm and mass 1.5 kg. Neglect the mass of the axle 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, asbr aw/ar n+homn j,-/hwv ,8s7suming it rolls without slipping?

  A 1.53-kg mass hangs on a ropp/jnnaj blkk960,xkz 6 * efd+e wrapped around a frictionless disk pulley of mass 7.07 kjn6xfpn0b kk/elj *,dkz6+ a9g and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around 6eifgv c.fbjt /2r( ;)fcsbba dt4ye* d.ed:,a frictionless disk pulley of mass 7.07.*jidc:by42 6v / )abr;bcff ft std e.,e(edg kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If iii2 8hczfrn+az: -i8, lzpsk :t 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 .ct*uy,07hrg qyfu. ,eg(rf vof $5.00 \; kgm^{2}$ 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 0.8*m v)xatcwm.xu6kq3 010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed ocamt8 mwq uxv.)3*kx6f 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 witlb s/yk /t0u,kydb,9f )9dw injn rd92h a speed of 10 m/s. How high up an inclined plane can it climb beford ,k9b j9sln09, ny/yti)kr/dbwu f 2de coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allow,gt y6cak5/used to roll down an inclined plane. How fast is it moving after dropping gas6 uy,k5tc /a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping dow5yvsz /1b1n gao2fuqp)35unkkd8c f9 *si l 1sn a 35e incline that is 7.0 m long. Assume it15us 1sza8kvkundigy2ffn/ s 9ob5 l*1 qc p3) started from rest. The moment 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 momentum cs 2/a g ctj/xu+kdo.+l5e 77rkv8 dgbthanges 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 mzn i++zk 5)cmjoment 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 with arms extended has gy8ky6 7v wrsy qj8xxf9u65v8a moment of inertia g6 qu7j5v98 k6yrxy xsw8 fy8vof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?