Angular displacement is usually express in units ofvj(j0q9/5 ny-ghq5 j8i *e dxmk8iln r

  Angular velocity is 159g fu z 9jz(sthz 1st: 37sjhrgbgs5n ks+)zexpressed in units of

  Angular acceleration is expressed in unil(i y qahl ::gjg;b-u.ts of

  A boy and a girl are riding on a merry-gs(0y(l )jxw) v)mkl ls- pyle:o-round which is turning at a constant rate. lp)ylm(k0-e xj w( l) sy:lv)s 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 is5+j z.gmyypc3ls 1w*f turning at a constant rate. The boy is near the outer edge, and the girl is closer yfpl.wm+js3zc * g15yto the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-r:ziks (ri2m:,n*hkh t5mufw . uuk s.;ound which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Wh mkti;:u u2zs5u(:n.rhs* wmkf.,khi o has the greater linear speed?

  A boy and a girl are ridin6n+;lauf9iqqja + nna(hw77 gmr3 jm,g a merry-go-round which is turning at a constant rate. The boy isa l7a(nn9 fjq+hn6 i+a m,3;qjwmr7gu near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl arez6 s f;,6ajmnc riding a merry-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 h6s c,6nfja;mzas the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following v-i47j aaoh.3b7e gdz is an accurate stata47deg -o7ha3 vjzb .iement?

  Rolling without slippivnanfy:-b758h 7 wg gvng depends on

  Two equal forces are applied to a door. The first fssk+ q.,/ vpj-m qd0,6sdeyeb orce is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the doodspe. sd y/ sb,jv6q0- +k,emqr. Which force exerts the greater torque?

  Two equal forces are applied to a doordg+ mbldwv-n3 xb9-t 6 at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which w b v-l mbgd9-3dntx+6force exerts the greater torque?

  Two forces are applied gt)8+k vgpfv*ltp e .;to a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ra+p8f;k gl* .tpvvegt)tio of the torque of the first to the torque of the second is

  What is the quantity used to meac)(t bcwlq ,y0ag.zdc3w)j ,fsure an object's resistance to changes in rotation0l wwa)fc3 c( t,dgyc )bj,zq.?

  Consider two uniform solid spheres where both have the same diameter, but onez* je6zd n far/oqn8aq+n ; :,nl-bxx0 has twice the mass of the other. The ratio of the largen8ndq qnxno* lf,;e0+a j-zbr :/z6xa r 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 r: k8.zbz3w rgp3i)b vf4xcjuem ;)x6radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere i.zw :fzum8 grb3px)r3ie 4ck);vb6xj s

  Consider two uniform solid spheres where one has twiw koq+z o59y3bgt g:j.ce the mass and twice the diameter of the other. The ratio of the larger momentky. g35wb qj:9z+og ot of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M.hpo s wei;,l. and 3R, what happens to the sphere's moment of inertia about si.,hlwp;e. oa central axis?

  If a constant net torque is applied to an object, that obje0d4gsocj n0 u.ct will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR+ijixff 8phis75 g7 4r2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energysxfir8+hiji 5 f7p4g7 is

  Consider a motorcycle of mass 150 kg, one wheel of yj o ygysi6o),qb- +9twhich has a mass of 10 kg and a radius of 30 cm s9oy qb)to y-,yjig6+. 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 rc2r w om n47-vzz2aq:wp0plp9olls without slipping down an inclined plane starting from rest. The linear velocity of the 2w m4lq:azwv pozp- 0p9n72rcsphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an gfswc aw ff;r ,0+57kkinclined plane starting from rest. The angular velociwkkf5;a s0+ r ffgc,w7ty of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whenfes:+ jv,70 tclz6py l .t-ppq a net external force acts on the sy f-vyt+tlpl67c , p:z 0eq.jspstem." This statement is

  In what circumstances can the angular velocity of systcz2 5vx8t byi0em of particles change without2vxtiz05cb8 y any change in the system's angular momentum?

  The Earth orbits the Sun .j ubgc4xz0udhvo:)tz. n:t 3 in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular mom:xg.cnt .h uu:4t z)3 zovd0jbentum about the Sun?

  The Earth moves about the Sun zlp)6jjb mh v5ey7-i8ks6q9t in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbitin8 6py- qe 7h9mjjkvlizts b)65g speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast so:w(s5r46p)he0fj li .ejl dapin) by pulling in his outstretched arms close to his body. What happens to he0( r6jhwosa e pij.l:l 5)f4dis angular momentum about the axis of rotation?

  An ice skater performs a pirouetted3m ows6+4ac f (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic ene63a+swmod c4f rgy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by9nkxnmx2c4ot; c i:4zl 8i3o v pulling in his outstretched arms close 8xcni vl4i cokot49n2;3 zx:m to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservationsh f;1y 47dsms of angular momentum.

  What arc length does the Earth travel in a three mo+yber8i dx oqz3)) z/knth period in its nearly circular orbit ak+/ rbq8)oei yx)d3zzbout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the1 tcxoaq0yj7e-n- 6 fqdx4sp + tip of the second hand sweep through in 3 minutes and 45 seco1 7- qn0 stdq-ajpxf4x+6eo ycnds?

  How many rad/s is 25 revhjb+41iqlgq 1q2 wzj() 1g woqolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ixzgnq6 1wtpdzx* , 1w9s the frequency of the wn1z6 q,w 9zp* txx1dgwheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency z9jb*mr/ y ,x0so7bh 8/cq djjof 0.40 kHz. The period of its rotatiob zdo xj9yh/jb*7/s8,mcjq 0r n is

  A phonograph record rotates at 45 rpm. Through what uabkpsvyh bar.98-8 v,( 0qcoangle does it turn in 0.20 s? qs,9 v8vb(.orkbc- pau0y8 ah

  A wheel of diameter 26 cm turns at 1500 rpm. How far will ,unnlzyr b5s4 +io26j h4x s2;z.oq;;zwtbtq a point on the outer rim move in 2.1 6n4j 2bt wyzsuxq t;2ziq4zo.; r ;solnb5,+h s?

  A bicycle wheel rotates uniformly through 2.0*uzqr3ss 2, ftc ci(v94cyhf3m6lct* revolutions in 4.0 s. What is the average angular ft2vl3 r*c6mscy 4,39cs iuz( f*tqchspeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0,tf fdmj1s/j9833pa/f roi8xoo y np0 s. What is the linear sf xo p1f 3/dot 3,80 manr/i8js9ypofjpeed of a point 0.10 m from the center of the wheel?

  A cable car at a ski re *jp.etujhvg4y/* h n)sort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assumi4)t*p*h/e y jnguhjv. ng 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 p8ye6y-hz fy, o,h3bzm is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's ri 8oh,-fz z6yye,bph3ym?

  The cutting cord on a ga-/ 7 0 pdy z1mcn4tnrx9frfto;s-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximfz19 cdnm04t royf ;rtp 7/-nxate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating 6 p)zrl: juw0y8-ajfqwith a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's rujja 08rpy: z-)6qw flim?

  What is the centripetal ad mb.;c2x3n x4mum 76 /s b2sdlw*srpnw3ohi,cceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is movingr2d ms.b7d ihpww4sn6 xsb3c* mu,o3lm/2nx ; 8.00 m/s?

  How many revolutions per minuteuxk989b p( h-+wqepzc (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce au+b(eqc-98k zhxw pp9n artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular cuf ;czuper nbyue 5145,rve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (p p 5fyeue4,u 5;rnczb1rovided 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 cuxsg- ds0z(8; rub- .w*cjxkeyrve of radius 50 m with a speed of 20 m/s. The maximum centr.sczebgy*;8k rxu0-xs j- d(wipetal 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 z fzzgskt 8yageun:mb-r7o8x.vt786.a9tj8 -m string, is whirled around in a smooth level table. If the maximum tension that the string can wmg zzsr8jv8z ba6:-uety x .8 f7ok.t9at78 gnithstand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5fp85h7vh ko8eqk m+f j27u, vw kg and radius 9.0 cm rolls without slipping 10 m down a lanhh 7e,fvkk8u2j7qfm5 + vwo 8pe 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 acx) azx6bxf(5 bhns 0m5celeration 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 withvw6yvq z.xhqu8e(m7+ obw(0 g n(9krn a constant 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 automobv7p( v-9 f,gvzwm 0mtuile tire rotate after starting from rest and accelerating at a constant 7(g wpt0u zmvv,mvf9- angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an h5zf; o+dbn3x7.cjpnangular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 q9;h y +)g0auy,hmd17 mnb nckrad/s decelerates with a constant angular acceleratio)m nubhgq7n 0 9c;yhk1yma,d+ n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest ajj dtx zhan3,85jl3w- nd reaches an angular speed of 6.0 rad/s while turning through 2.0 jjx-,jdzha t33nl w 58revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/skh9rj0 9) f0t 3-ufpxqx0jrd m to rest over a distance of 115 m. What is the total number of revolutu3 9k)jtmx-rpr df0qx0h90 j fions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uhe qsqg 4,y fqk,e.5h*niformly from 8.40 m/s to rest over a distance of 115 m. What is the angular a, 54* gqhsykehef,qq .cceleration?

  A wheel of diameter of 68.0 1dm 8;u qw:qwiftrhpe2:f /9g5bne ,xcm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. hei1qd:w82/m 5q wp9ue;tf,bgfx: nr How long does it take for the wheel to come to the stop?

  A centrifuge in a medical9,3 /ffztol5o-tig ipxq* b)z laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before cominzflob-9xiio5*tzt f)3,/qgp g 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 wheesqytt)sc;jx5c i pog f:4+5x)l require tightening to a torque of 90 Nm. If a 30 cm long wrench is us +y)xt4fqs5xotc) pc; gjs5: ied, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torquey 5*e0lo+ktkde2ye9d 7 tjta, of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the e k2oddty,y0 e7 at*ek+lt95jforce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine tkt3rxz8/h(ftp9ia 3q 8 wwk3rtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as yo.(g jntv4:+kj5ta c follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is t o.+ac5 ky(4:g jjtvtnhe moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought t apv gthi,49c3he 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 v4at9ig3 ,hcpsection 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 is pivoted about a frictionless axis thoujtb)n) ee:tz gngqkht65f+jql; 1iav+*gn.7 ght the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0)nj+eq 6g )+ tn1; ijenfq7 hz*k g5.galtv:bt 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in the h g3jl,79rfn 1judr;ze orizontal position, and then released as the free end is allowed to fall. What is the n79dergu;rzlf jj 13 ,angular acceleration 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 of radius 30 cm and mass 1.5 kg. Neglectdm*nc(kwh* k*awi+ 9e 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 (a w9chiknwm+k**de* 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 pulle f5tj: an:bxoy0e1r0gy of mass 7.07 kg and radius 66.0 cm. What is the angular ax o:00egfj:b 51ytn racceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fricti* t cq(sjkwn*yu /*2fw/*qowconless disk pulley of mass 7.07 kg and radius 66.0qcwoc tw*//w*k y(j *qsf 2un* cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to store 0xd 2sb7xh wu($1.00 \times 10^{6} \; J$ 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 iner0.4mdu m85mhvhmfvuw-utbk 8d)l , m+tia 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 m79gsp)glx4 k lixmy6q (lj1x- starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is t1x j( lg9kyp6 )sqx gl4ix-7mlhe speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radiusbx, 3w bv*dx 0 9d,.nt3d*kf:yzdadvg 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to rest?0x xddnf b,:,d.3 k9* *wagtyddv bvz3

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowennkhf2o; ,ca* d to roll down an inclined plane. How fast is it moving after dropping a vertical distance o 2 nf;okhna*c,f 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cdek b-57 ,v cvtv78 xz0meqd5mm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphervm8m7vd e5v0xd b zct,-e7qk 5e 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/m,gu fhdx ;;d egge67um 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;2w)37 /. twajxlwnwxkn ch ;d 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 .*)aaaea8 vwk arms extended has a moment of inerti*a)8v.awea a ka 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?