Angular displacement is usually express in u49z *asiv dij*nits of

  Angular velocity is .oi+ttj * pien8o 0+twexpressed in units of

  Angular acceleration is expressed in t 4);uds p3 eip:6iughunits of

  A boy and a girl are riding on a merry-go-30 dag*xy5my srw6bg,zvt p,1round which is turning at a constant rate. The g0y, b1raz5, xwmg6 pydt3 *vsboy 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 riaj+uv;nxlv y; k9;fbtw/w ) /zding 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 +wa nt) wx/ k;v9bjz/f;u;lvy has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turwj0h08 6ff, dmrm.a6kn kyirqxg .6q7ning at a constant rate. The boy is near theq mr nr.,0k fjd mw06i6.6h7f qkga8xy 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-go- gc9f kkxy+hi3+5y)qxxpx: n yh7+ie (round which is turning at a constant rate. The boy is n g hxni 5 c)+xx(e37+ qi9y:kkyfyp+hxear the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a m:817 ysl3vh pjxbhd *yerry-go-round which is turning at a constant rate. The boy is near the outer edge, 38h d 7hbsy1*l:x pyjvwhile the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which 0qh uagxqetnjy5 9 s-x: y*s/;of the following is an accurate statement?5xn0sj- eah :y/qux;* q9ysgt

  Rolling without slipping depends/4 s gu:oq*cp8 pp2wwo on

  Two equal forces are applied to a door. The first fodv7 .0tjw6u 8uysgm8k rce is applied at the midpoint of the door; the second force is apply0msj8kduv8gt. wu76ied at the 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 doorpa /;g as/g3-bbt led )pn)sm;knob. The first force is applied perpendicular to the door; the second force is applied at b s/;/dg;atg 3 n) mbep-apl)s30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door.v-na hm;ub/a- The first force is twice as lau/ avm-h -;anbrge as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an obmx(5 juqccz,h0 p,*t vject's resistance to changes in rotatioc5c qpx j*h,u(t,mz0vn?

  Consider two uniform solid spheres where both have the same diameter, but one4wug nn pvmimf4 + .zsn.4. rfer(d(3m has twice the mass of the other. The rati.+dvp3uwm(mmze(44 sfr innf4grn.. o 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 g;zil.ym x,j0exew:6twice the radius of the ot,e0egjx;.y: i m wzlx6her. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniformuyi5) ahgyxl3y17y - q solid spheres where one has 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 inertia yx1ga)l iyh5y3u -yq 7is

  A uniform solid sphere has mass M and radius R.l0o bqiv3 1q-2b v6he1p4dj op If these are increased to 2M and 3R, what happens to the sphere'bjh0o p2 1vq6e d1q-4iblop3vs moment of inertia about a central axis?

  If a constant net torque is applied to an object, that objecuc9bh+lff1dlp z2/2k sz, f(f t will

  The moment of inertia of a solid cylinder about its axis is 8mk5;jx m,p; gni gw9sgiven 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, oney0 h3zmbg8(y p wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rota( 0hm 8bzpygy3tional 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 radim)/ (nit pq66wy8wtlr. oyy: uus R rolls without slipping down an inclined plane starting from res nt)w :/oi6my6tl qwrup.(8yyt. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rv7 xje0p6/a qholls without slipping down an inclined plane starting from rest. The angu06evaqhx p7j/ lar velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum orzlof(u y; 03kf a system of particles changes when a net external force acts on the system." Thi o(f3ly ;kurz0s statement is

  In what circumstances can the angular velocity o3td :p p ,x-qgfubx6/q-l k9bnf system of particles change without any c3f:/x9q-k 6q,t lbb p-dupgn xhange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frix43vrusupv 3. t0kvl;ction which may be present. What happens over time to the Earth's angular motuv x4s3v0p kvr; 3.lumentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. 2i dq n+uda.fgka1q h439a9psAs the Earth moves close to the Sun, then which of the following best describes the orqs.qah9na+312 fgk udi9pd4 a biting speed of the Earth about the Sun?

  An ice skater performs a vh d2wvd cl 0ke ,9dt qevnl(u0*pk9,)pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum k uel ),pl hv9kn0vd*e0q2(dd9w ctv,about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his ouqoh6 8:r n gv)ls ejq8q(9j/lbtstretched arms close to his body. What happens to his rotational kineticq6:rll9q jh) 8(jqn/ ogsvbe8 energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulli/::h0h j :yc ay:qtxp x2tic.lng in his outstretched arms close to his body. :xh/ xlca :0yqijp:tth2:cy. What happens to his moment of inertia about the axis of rotation?

State the law of con+qe 9t(ww0zx vj8 h)zo ;;awqqservation of angular momentum.

  What arc length does the Earth travel in a three month per ,. cu9lov3wtbiod in its nearly circu , bw.9ltv3ocular 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 m. Wv 5jcibu3 3k:ihat distance does the tip of the second hand sweep t5:ucv3kbi 3ij hrough in 3 minutes and 45 seconds?

  How many rad/s is 25 revp 6h*9ik q* wulnmc)7vzl69s qolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revo7 d1 n1w y.wb2 ck wv)zrznu3b:bp0qm+lutions in 4.0 s. What is the fre3wrw+ 2b 7wb 1)d0y.nbmz pvn:kq1cuzquency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 08a,5;d)cceo 5nv idh f.40 kHz. The period hai vf8ccdn5 )e 5o;,dof its rotation is

  A phonograph record rotates at 45 rpm. Through what angle doemxg+m5ek0 vlxq-f v )/s it turn in 0.20 e+fq/k-gx0mvvlmx 5 ) s?

  A wheel of diameter 26 cm turns at 1500 rpm. Ho)yzh: rg/e0m 3 a)xomyw far will a point on the outer rim move iny/3omz) h:my erga) 0x 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is tf b5gdx2imirg +-jhi+g;p9-l he average angular speed of+;5f-gi gi2b+p dlrgh- xj 9im the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions for81l+av )vvin 4.0 s. What is the linear speed oo r la+f1vv)8vf a point 0.10 m from the center of the wheel?

  A cable car at a ski resoy*1/. z mrqy8djc2axyrt carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 xy8 2ya1/.rmjc* dzqy m. 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 constanto1i1 +.du/l o:qrcklq angular speed of 2.0 rad/s. What is the linear speed of a point on the wh.+lru : okq d1cq/1lioeel's rim?

  The cutting cord on a gas-power (4 nsrd sgspsf7*u46oed weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what isrsdf6( 7 *snposug4s4 the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant a (nwks;,mr*mo;9e zc omf-wc4 qn k0l;ngular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's;z4o(;;* l w e -9rmsmcon 0mknkwqfc, rim?

  What is the centripetal acceleration of a point on the pj1ovui3ygy f*r77/; lo i izj-erimeter of a bicycle wheel of diameter 70.0 cm when 1vr77;y 3 /jifjg*z uiy li-oothe bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotrf i7p4p7(jmbutt fg1(lo s 55ating space station (r = 1000 m) rotate to produce an t otgp(bf sfj7l45mr51i (p u7artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curven*7byt8 bw l(p,gq, 9vpi elx/ of radius 50 m with a speed of 20 m/s. The maximum centripetal ib8,e7q(w *tlv/g p xyl b,9npforce (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a f ;uvrx,x 7l/pzlat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static upz/xx,vl r;7 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 string, is whirled around in6c8+i o apn3gazvsw g99t;3cu a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed cat+w; cgz9 ovsg93 a3pciu86na n the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and r/* cl- 9ullnejw js*yw(n8ov,adius 9.0 cm rolls without slipping 10 m down a lane at s, j*( nj-o8 lyvl l*9nwc/wue4.3 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 co.fnp* /xs +lypaa6p.cnstant 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 with8h svcuqz*(b h48k vxfmhx mx203 5n9p 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 automobile tire rotate afyq vk r9: 0a 3tnpe6ua q+h.*unver1*nter starting froana vet kr 9*v0:6rqhun*3 1uq+e.npym rest and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at respc,p)*4 oaxttj29d uhfudr*3t, and has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotati v 6wbsltf)mf(*w:oe7ng at 20 rad/s decelerates with a constant angular acceleratis m:bo7w ev6*twf)( lfon of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed nx4-y+yy00ndhgn gsz+ yu3 e 1of 6.0 rad/s while turning through 2.0 revolutions. +ynu3z 1ny0s0yy gxgh+dn4e -What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly frcf :;vqa *qnvagl+ pw;5 pd,h/dr6 xy0om 8.40 m/s to rest over a distance of 115 m. What is t,wq6lcqvr*gapv0; ;/nd: dya h f5+pxhe total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly lov.6g2la2vgov3 b0 e.ry 4oa f8hd6bfrom 8.40 m/s to rest over a distance of 115 m. What is the angular acceleratioo0.2h4.e b6vaog av8v f gdly3rbl26on?

  A wheel of diameter of 68.0 cm slows down uniform9 q60f/qqd x6b2l wgqsly from 8.40 m/s to rest over a distance of 115 mfbg9w d q6x qs0ql/q62. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationdrcxcrf: u k(:a*1z6 nal speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accele1 rc(fxa:6z r*cdu n:kration 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 to6 c:g3m;1ap. bpm fazd a torque of 90 Nm. If a 30 cm longm36:f cz ga1;bdmpp.a wrench is used, 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 torque of 90 N rppos:j1+wc/m. If a 30 cm long wrench is used, what is the magnitude of the forc/r:p wsoj+1cpe required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerthkg2fro (*.q wia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modele +* b3bme22bw .tbulp)ey (qvjd as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What isbbm )2ep*+vl.qb(tu3ywjeb2 the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thr e d2*u5oj)vymmg -4zought the centerrm5u4me*yzg-odj2 )v O. A rope wrapped 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 pivoted9 ,*b l;xeux c ii;kv,mk901 im2qoses about a frictionless axis thought the center O. A rope w;mxx,ibs vkies 9oe2 0q1k cl* m,i;u9rapped 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 held i n lf0o)d /9kb3ombd.cvdcdseg -/ 7)gn the horizontal position, and then r f 7g))ldb 0dmsndk //oeccgo-3.9dvbeleased 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 ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kga. 86:/yqgu0xel hizz . Neglect the mass of the 6/ile80 ayxzgu:zq. haxle 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, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frict( )zq . jq1 p4ddbn)l*yg(fgmoionless disk pulley of mass 7.( dzyg ( j*4dgbp)moqlf )q1.n07 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 maswdj3zj3x. m l8s 7.07 kg and radius 66.0 cm. Wha8 wjxz jm.3l3dt is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requ.* el3ibjit8id2 mfw*ired 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 inerti17e g c-yewr,: d1b/b w(ui*cjy*fhexa 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 m starts fr137 vm:urg tt:8sv(;wm prgckom rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sppv sv gc7ktmt8wurr m1 ;3(:g:here 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 aup/ 6dhbff0je*k .urcd)- +oraxs71 10 m/s. How high up an inclined plane can it climb r s0 fa7r/.dx6)k eco+-fbu1hj audp* before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allsgzv)3wv ( pw;owed to rv );w(wvzps g3oll down an inclined 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 rolldjolrt8uw0p7;if9wv vkb * g(,p . a7is without slipping down a 35e incline that is 7.0 m long. Assume it started from resi wfvt ; lbjgip9(*a0,v wkuo.rp d877t. 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 m(eo+op ((5 2 kos4fbwdhiyg5lomentum 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 of ine5/f(dtgfk)nv+zdfizr5 gt(i /9oy z.rtia 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 exne 63bt wv8-jl10heme4q9y iltended has a moment of inertin0b 8qe withy9e13m6ejllv 4-a 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?