Angular displacement is usually express iis 3q30mrah icjx5bo.au32 (so:e/ c in units of

  Angular velocity is expressed in units w x*(:r9y9e)k lfdljtof

  Angular acceleration is expressed in uniz ) qyf3w6ocdy+x8k;gts of

  A boy and a girl are riding on a crfpo +i0 cy+ :9:vnnbmerry-go-round which is turning at a constant rate. The boy isr:f in:o9y+ vpbc0+cn near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are r.xtmyi( ecz53 iding on a merry-go-round which is turning at a constant rat 3y(ecx5.mzi te. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-gu9jbv /q b7.9n9yjy1l qoa l3qo-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. o3 a/bl9 jylv99.nqbq quy17jWho has the greater linear speed?

  A boy and a girl are riding a merry-go-round /fjwf , 4rkk(l :gxrf2-:ybzc which is turning at a constant rate::/kbfxz(rlwy, cg4 - fk2f rj. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are rb31w 5zk,1q1ty dkp zuiding a merry-go-round which is turning at a constant rate. The p t3z,udkq111ywz5kb 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. Which of the 5vfk2.vwr;le( 8an srqzb ww3 zm;7a: following is an accurate statementnrw5.za(;a s:e;278rbvlz fk3wwv mq ?

  Rolling without slipping o qb/g i98q2rsdepends on

  Two equal forces are applied to a door. The first force is applied at the .alce7- o zi+rwf d1r mfmc-39midpoint of the door; the second force is applied at the doorknob.-c+efdc 7o1.f3 rm9 zl -amwir Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the p v05( ,kfduuadoorknob. The first force is applied perda05fuvku ,p( pendicular 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. 1zx7z d;x p9rvw/w0 tr+rbw8qm*u 3wr The first force is twice as large as thrzm*bwr 1wz+r0 7xq/; 8wwurt9x3vp de 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 object's resistance to changfn2-gyqb6u nw5j :rrr0(m7 d nes in rotation?w( 2rn6rfr ybg5j:07-n q nmdu

  Consider two uniform solid spheres where both have the same diameter,/jiu,5 b()d-:svyar giaat;,owjm 8 a but one has twice the mass of the other. The ratio of the larger momeb-rsvgj d (i /auwta5:i ,,);oymaa8jnt 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 oa1 k*pb:yu ti4cm;ew 02gsx(jf the other. The ratio of the larger sphere's moment of inertia to ig *j t1p:xa( cy2; 4ebmk0uswthat of the smaller sphere is

  Consider two uniform solid sphern 4)jm5q ls.zwes 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 inertiam ln)sqz54jw. is

  A uniform solid sphere has mass M and 5ai0dt s5ai1 8f)u;ld hwa(hf radius R. If these are increased to 2M an shdd5 ;li)t0h5wuaa8(1a ffid 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is ap.8ag1h ymh.b qplied to an object, that object will

  The moment of inertia+ b r,6c2n uz)c d9su3wx,chjb of a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotcdj2unxcbuwb3c)s+ rz,h,6 9ational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of masw)yyh jip:6 h5s 150 kg, one wheel of which has a mass of 10 kg and a radius 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 6y:i w)j5hphywheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls wittdt7 pm41vn fet*ym9 yw1i7/twn1fi5hout slipping down an inclined plane starting fron dtipn*9ft71w14mi5 fvt e y1/y7m wtm rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radxq- ,egvyji*m vb+f7; 6w 6jdkius R rolls without slipping down an inclined plane starting fro7wfj v6*i mg,ed;k-q+xybv 6j m rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentu u9a6gap4wknz93 q/dy m of a system of particles changes when a net external force acts on the system." Thi 9g/q63auznw4 k ad9yps statement is

  In what circumstances can the angular velocity of system ocwyn,37 uwh)lqm( go*1t0ssh f particles change without any change in( hn) tw*lgucssq7 myo30 w,1h the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fri(j2xt jszvga; -rl5a2ction which may be present. What happenjs(gv t2 ;-rxa5jz al2s over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an vgjar90.71sstia ejs6* vf:8tf*uxr elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about thue0ts * :ag6fs1j8ts fvx.a*jr v9ir7e Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in f .o8yhkgl7 91d 8dglxm dk8*ghis outstretched arms close to his body. What happens to his angular momentu78fk1y8gxo mg kd*8l .l9gdhd m about the axis of rotation?

  An ice skater performs a pirouette cz, y*39o hxss(uui6sn6b1ia(a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotatii9zyohu *i 6 bcsn,6xa3s1 su(onal kinetic energy about the axis of rotation?

  An ice skater performs a y1.svt /, t9 9dyi93en naumfcpirouette (a fast spin) by pulling in his outstretched arms yfmv9dcy3u na9s9 et,1tin /. close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mor.dn7wc3ri+ z1l 1dz cmentum.

  What arc length does the Earth travel in a three month period in its nearl/1wy(m4ejo8 ex q4/pzr0go poy circular orbit about the Sun with a 0/e wq(4gyeo4porpmx1j/8ozradius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock hasbtt49 *upch, 6ufqb5ui(0xz w a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 se046uu*xb9 (zt ibufqptch 5 ,wconds?

  How many rad/s is 25 revolutions per minute equivalk ;pwwyc 8 ayr+grwc;;, a29flent to?

  A bicycle wheel rotates uniformly through + l.x89 fds5gky4v(+xcurh+qukb r4u 2.0 revolutions in 4.0 s. What is the frequency of the+rruf+cygx d k 9xl.bh5kuuv(+4q48s wheel's rotation?

  A pulsar (a rotating n kxnd(0jz1ib2xg5 otz(90 wdi eutron star) emits pulses at a frequency of 0.40 kHz. The period of its rotation(izx zd1bt29( xw00 5gjonkdi is

  A phonograph record rotates 89,j;bpztr 9yzlk:za7l d ;sqat 45 rpm. Through what angle does it turn in 0.20 s?da r8 zyjtq;z,l k:p9z97bs l;

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poin;i1ezajm.cm 4ju mxnk+z,,0 u9. c bmpt on the outer rim move .nx ,je;bup9m0zij,1kz +m ccm4a.um in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revoo6dj.*m64/osrc -bu0v t vd3 k ep*uuylutions in 4.0 s. What is the average angular spk6 vd c6 o0o*eujbum- rtd34 s.y/*uvpeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.sronjp 4fe.y: 6it7.xn.k7 pt0 s. What is the linear spee p.7n f4xk .rnt 67:oj.itpysed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers f vu; 72ec/zvtvvm9t;uu( :sva distance of 6.8 km. The cable which moves the car is driven by a pulley with diameteruvv9(t;s: 2etcvmu/ 7 vzfvu; 3.0 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 constant angular spee j/cl24 ou:sird of 2.0 rad/s. What is the linear speed of a point on the wh 4/o2li j:scureel's rim?

  The cutting cord on a gas-powered wee4m ayr;nrr(h45id5uld cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, whr(5 r lr;y4dah min4u5at is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constaur0sk3l( nvo0 nt angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel0 r v(03nusokl's rim?

  What is the centripetal acceleration of rm6gcvuxkg w1w 3 ti.e46pb m,o::g0xa point on the perimeter of a bicycle wheel of diametervbx ugw40m :3we:t,o.pcirxgm 66gk 1 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spacekisx w v py*o/2n(e w/1skq:y1 station (r = 1000 m) rotate to pwsexypn ov/s*2k k:i q( /11ywroduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m2x gjob u;fj ttb34v i: 2kxdto;.t/8z/s. The maximum centripetal force (pr2ik btv tu;j z2d4:tgxt o3;j/xfo.8b ovided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circulaez3zc/z1p/z vucify08 msp + 1r curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provid80szpmfiz u1e3py/zcv/ c1z+ed 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 string, is whiro-cdx el1ah es:jew,1l 0xoghm) -9li ,v,2l uled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear:j xc,-,oemeluel1-x290llhav1)h , woid sg speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm r3- +rn)p oy2eeau +lt:(/yl0rn ztceeolls without slipping 10 m down a lane at 4.3 m/s.y2e p lz)ate c(r/: -eol+enu yr0t+n3
(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 acae 1f /lhys0ez2:nbsk9nn1z (celeration 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 co9u)wvughm91n y )g5)intb bq;nstant 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 h 8g f.sx zbkx,usk2ix 6,c;7 h,dn0wxafter starting from red h6; x.uk x,fs8i7k0c2,x nbwzhsx,gst and 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 a. e6il -l 5)e:jpr,aqo:pmmdrn angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 5yi5ln)iv.kyv-xeh b) r 9a.k rad/s decelerates with a constant angular acceleration of 5.9k.)yiav nvei y)b5hxrk-l $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while u 86qhgrw iq c6ry1s o84;ae;tturning through 2.0 revolutions. What is the average angular accelw6e8c ury aqhsg1qio t8;r 6;4eration of the wheel?

  A wheel of diameter of 68.0 cm slows dow muy9 9z+h+nhy*-sp*jo lcxj* n uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates j9j*h m+on * cz9u+l*ysyp- xhin coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s-f)+hylu )pkgy .nkc / to rest over af -+ .lugcyykp))kh/n distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm sht d;te 7 ugvae//,4mg6-z) yf8qbwtolows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wh-t7etgheo8b ;amd u6,tfgz4 yw /q /)veel to come to the stop?

  A centrifuge in a medical laboratory rotates at a ro;+6bl ud.z )lqu-bpby tational speed of 3600 rev/min. )lbu+.lzd 6p u;bb y-qWhen 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 require tightening to a tvi,nmw 0gogmm-p kz,0v47 f6oorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of thmvom,6ok 0gpi70 , w -zvmgn4fe force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tic8dyr0dd 1+k/toy1hf k03eb mghtening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of t1bckth 800of /dk+ 1mdyrde3y he force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ikaglvs+s2*y/ .h5dey nertia $3.00 \; kgm^{2}$ 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 ro imp2- p/w:rorigin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the orp/pm-wr 2or :iigin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless ah-p/ (,pe5tuhp * jrhyxis 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.)hte/,p hy*jp- p(uhr5 What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionlq m7f*f4 5n2fhg vrs;hess axis 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 secf7q m4srng*h5vhf2f ;ond 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. T,,pm:ebfh pa4p wco /3he rod is initially held in the horizontal position, and then released/,fp e,wpc 4pb3m:hoa 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 b dl)l8o/ tiainl-j,l7e a ring of radius 30 cm and mass 1.5 kg. Neglect the masll)- 8l ji7,a/ dtiolns 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, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped aroun u 9r2 vx3r5f8ta/agbi7-wpz sd a frictionless disk pulley of mass 7.07 kg and3a5/ 72vrfagwit9pu zb sx 8-r radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped arkdj*9 rpstp2m uj/s 2nt78p+cound a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of thsu8jnttsp7 d kmp/j+p*r 2 c92e mass?

  A rotating flywheel can be us:/ tt2sh jcnz6ed to store energy. 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 inertia :lco5xu1u.gzof $5.00 \; kgm^{2}$ 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 0.01 krnlf 610vk,g 84b g6nze8cqo0 m starts from rest 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 the inclined pkqn6o6vzf,e48nr g 1l 0cbk8glane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10gy2 ,u8a- kd pomsc8t+ m/s. How high up an inclinem kgdsu8+yo, tcpa28- d plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and a(c af m)ur5e,qegv) ,lllowed to roll down an inclined plane. How fast is it moving after dropping a 5g,uer)(e) c mlfqv ,avertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping do/t m -sq xx,gv5l848iulvpr w)wn a 35e incline that is 7.0 m l slq 8x54vt/ )8m x-,vrliwugpong. Assume it 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 changesz (//bwzyjcfl/e*m,v 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 c km:5btoa io ng:/0b4of $5.0 \; kgm^{2}$ 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 incg d zt7i6t)k 6wg4te3ds.5ibertibkw5 4i edi6637tt .cg )ztdgsa 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?