Angular displacement is usually exprevzknm4-n ea+1ss in units of

  Angular velocity is expresq :icma6ae qsc7(v9n.sed in units of

  Angular acceleration is exr5 zh*7vv ry(mpb8qj(pressed in units of

  A boy and a girl are riding on a m5i 5i9wy4vj5oz tzue: erry-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 angueiz :y5w4 uj59vt 5ziolar displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a co5jl :qdjhc, 4fnstant rate. The boy is near the outer edge, and the girl is closer to the center. Who d 5f:hqlc4,jjhas the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constant rx m5ia(b6jsqdr3da+r3j7ne zt6 1e 4qate. The boy is near the outer edge, and r+b5 7m j ena3ae3itsqrd(d xqz64j61 the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are,no31)cykqf d riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, wh1)y nf3co ,kqdile 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 constant rz i gsu. -)+qjrfzx bzh)+)fi4ate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential accel) rgjff+xu-ihz z4qz.)+bi s) eration?

  Consider a rigid body that is rotating. Wh) pu,)3cinvf cich of the following is an accurate statement) )f pnc,uci3v?

  Rolling without slip(r hc-;cv;k iaqcos ua7*zldj 6-)8fdping depends on

  Two equal forces are applied to a door. The firsro +up,xwa06pwm0 iew/ . +khwh)uz d,t force is applied at the midpoint of the door; the second force is appliedk mwh0z06 howew,x)ra,/dwp uu+i .p+ at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a dooitvg 8pgngw54j8 -n q-r at the doorknob. The first force is applied perpendicular to the door; -g j8pnwqvg g-548nitthe second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a dec4vl )dmb6853 jpkqn.w 5w awoorknob, perpendicular to the door. The first force is twice as large as the second force. The r46lj 5v .bk)awwm cp35 eq8ndwatio 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 chan20n5ag b- qrvzges in rotati ngzb-avq5 2r0on?

  Consider two uniform solid spheres where both have the same diametermg ft 5gy.dh* j12qb0e, but one has twice the mass of the other. tg ydb 0 mj.*ef2qh1g5 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,tb* z 4wp4m ua)-ie 6or)ic+is but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that orm z) 6iu+4 -siatcbo *iep4w)f the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the di;hda ;zkk(tomb0y3 .eameter of the other. The ratio of the larger moment of inertiakb3 adh0ok( .ym ;et;z to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. I;xc)srr6 cb1sr u 3xh5g-8 ukaf these are increased to 2M and 3R, what happens to the sphere's mome8r5h3x)rsagc k;uu rc1-bxs 6nt of inertia about a central axis?

  If a constant net torque is applied to an objeh.u)h-l6 c qha7yvlh wo-(6gcct, that object will

  The moment of inertia ojc+3 vx 5pib xv4n,+6,pqvaih f a solid 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 whzg -c, e,foq721w+f9x ykxq wiich has a mass of 10 kg and a radius of 30 cm. Whaefkwqwo-1+, q7zy2 ,x9xc gfit 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 rolls, veu s2y(wb4x(,dw cf without slipping down an inclined plane starting from rest. The linear velocity of the sphere a y(d4(sw vub2wx,c f,et the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls wi tg9c 6qtgvi8 8ut* +mqx3ar:ythout slipping down an inclined p96:3qc+ggiv qm tta8uxt8ry* lane 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 particohc+;p +a1w f1,xzfcze+ 4rbrles changes when a net external force acts on the system." This sta ero+xcc;b,++1w h p zf4frza1tement is

  In what circumstances can the angular velocity of system of particle 4zakbg8na5s.;fy.sh s change without any change in the system's angular momenza.hfkg8ya;ss b n45.tum?

  The Earth orbits the Sun in an elliptical / cyy; vstrw6,orbit. Ignore any friction which may be present. What happens over time to the Ea;y/c,y6 swtvrrth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth move vryad4 .*iof (f:mcl6s close ylifa :cf o.*6(mr4dv to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched p0 tsbrqo84 j5arms close to his body. What happens to his angular momentum about the axis of rotatiopo0s8tb 5j4 qrn?

  An ice skater performs a pirouette (a fast spin) by pul3 (7 9inw l(dnmz2kdt 3kw9bd2ny0bqyling in his outstretched arms close to his body. What happens to his rotational kinetic energy ab32(9 kw3qbld d 0n2iby nty7km9nzd(wout the axis of rotation?

  An ice skater performs a pirouette ( 2 hdu ue6tfj y rs07l9bs-cpmqs3 umo*+z,4;ra fast spin) by pulling in his outstretched arms close to his body. What happens ; 7elu*tu-r6d r,4uscysj f sb h+zp3mm20oq9to his moment of inertia about the axis of rotation?

State the law of conserv+n*3 obfs fir sjml-i8g-e3*vation of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly cjob3;kg o5 x5x4z) lysircular orbit aboutkx x55sb34;o) lzgoyj 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 distanc zx*.v-7bde-fp c uga9e does the tip of the second -7d-9ucefg*b. zvpa xhand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per mi,8 w8 iw+zqbuenute equivalent to?

  A bicycle wheel rotates us- w vjcrm81a8niformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotatiom 8- svcwrja18n?

  A pulsar (a rotating neutron star) emits z)53/tfc5tk rhpb s9y pulses at a frequency of 0.40 kHz. The period zr3t )f5 h9k/yp5bts cof its rotation is

  A phonograph record /uk6q*epeeiq lp20z ;3cu)j jrotates at 45 rpm. Through what angle does it turn in 0.20 eq6)ce e2* u3zq;0ikl j/jup ps?

  A wheel of diameter 26 cm turns at q;2 -w4kd w* .xaghdhs1500 rpm. How far will a point on the outer rim move i *4d q. wdshxka-;h2gwn 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revo1 bghzh(jd( 9:5awg+ hweu gh4lutions in 4.0 s. What is the average angular speed of the guhz5g (d9w j4+ahh:( 1bhgewwheel?

  A bicycle wheel rotates uniformly through 2.0 rey,rhnn9m /);doh*idmvolutions in 4.0 s. What is the linear speed of a point rn 9)odm,h yn*;/md hi0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cabyslgkdey /1u+,*,hfm5kl xtmq3q99 y le which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate f1y , 3 ,9y+yktxlk e*dums/ qh5mg9lfqor the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular s;pqcyul )0u /vpeed of 2.0 rad/s. What is the linear speed of a point on thvl)u yqu0/c; pe wheel's rim?

  The cutting cord on a gzb x193bm3kn;vz+yq3muh h6+tkw h 8gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate o t;gymxn9huh z3+ 33k+mv8w1 qbkbz6hf 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 7 f a08kndp-fxjg9 l6mspeed of 2.0 rad/s. What is0k7a89jd -gn xf pl6fm the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicy.p.xh tos/e p)5z4aoucle wheel of diameter 70.0zat.p)o5xs. h u /op4e cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular,7- y4(d6a ,mz+n2pylsb zw bav rotating space station (r = 1000 m) rotate to produce an artificial gravity oa7wb(np-zab l s y4dv 26myz,+f $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50xsft*u8 0 7mjw m with a speed of 20 m/s. The maximum centri8x7st ujm fw0*petal 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 flssuljcd4if( s*,z0ows 20g2v at circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (prsdil4w g*u2(v,fz sjc0 2oss0ovided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached)obqf) qr83s ry3 bcs9 to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 bq9rbf srq83) 3o)cy sN, 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 radius 9.0 cm rolls without slipping 10 m d* ez2gvl(d rakc8c 1-kown a lake-(* g8ccr 2a1zkvldne 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 o 9+-1ikgv01crjr ascwith 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 i)z6 +/sblfhra 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 rotates1k6u5jb+ u ed(sdz(s after starting from rest anzbdjs6+s 1 (k5uue ds(d 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 an angular accelerat mb urxlp(;,x+ion 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 constant angular accelp jrdk97 l1q:qwj6cc wkwc1c*l +o (7gerationw :k7l(qkl1 6q+ c1 wdj7pgcw9* cjcor of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest aiqw*f-ngl6-v:, p heknd reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration g:, 6qvfplinw--k*eh of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformlymcdh75 d t+ kfc/ duoo20cjz0) from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel roo0kc0mddzfh )ctd /72 cjo5+utates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 p-/0 d p ve fwxaaypphz.*2c-+m/s to rest over a distance of 115 m. What is the angular acceleratioy0c-hp aw.p2a /x*-+pzpfe vd n?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40z8++tsnbbx l7w f)qc8 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to c +nxstb) +8 bfw7l8qzthe stop?

  A centrifuge in a medical laboratory rotatesnpo0i*w ,bq- 9 o+.t1lpwxmfd at a rotational speed of 3600 rev/min. Whe9plf-* t m0o1. nd,wiowq+pxbn 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/jb. el 2 2ge5jbgjc/v 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 force is perpendice/ c 5/jebg.jj22vglbular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 gtx53tm qu jol ,6dto 6vo/3)yz+k.maNm. If a 30 cm long,. u6 ot)3dty m 6x 3moov+ga5tlqzjk/ wrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia 4(a8iei x+7kt nv/qxk$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is moni ca57ige7a;deled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m5 i7 ;7acinaeg is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pzfqx jv2 .t-1divoted about a frictionless axis thought the center O. A ropezv1tj.q 2d-x f 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 pivoted about a frictionless axis .b7nl. 0,gaknb:aunu thought the center O. A ragn. ,.u0nu bkal 7n:bope 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) 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 horqvednux 50 7y:a- h3xrizontal position, and then released as the free end ixyv 5xq ae37:r -duh0ns 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 .pvx;6 )nj ,a2ezty osbe a ring of radius 30 cm 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 thyvo px;tz 2n. e6j,)ase wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrappekd ; l:,k5ewo.oe.pc ad around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of t. d:o clow5e;,.kpek ahe pulley?

  A 1.53-kg mass hangs on a rope wrapped aro7l)wluf cveli w :-f+*und a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whatfvu-)+7i wl:lce fwl* is the acceleration of the mass?

  A rotating flywheel can be used to store m2:/3:jed,rhpsp ak genergy. 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 inertoi h(wf0 sq7 2truf)x5ia 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 0.011 m(o dv-4jkov0 m starts from rest and rolls without1dk-v(v o 4omj slipping down a 1.0-m high inclined plane. What is the speed of 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 with a spe;d2f+ yozwcl) ed of 10 m/s. How high up an inclined plane can it climb before ccywz2f+ d )l;ooming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is release4y8f iz.yl zt2eyhe 0lg;m6 i2d from rest and allowed to roll down an inclined plane. How f g. l 4;6eyhi8y2l0yzzmt2eifast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping dows jk*e7xt -;xcs2t+ rgn a 35e incline that is 7.0 m long. Assume it started 7t*;kxtsecg +-rx s2jfrom 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 changes bxe- ax) fz)yhq k8n1f)y $20 \; kgm^{2}/s$ 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 inertirdgfu9: p(sgs sou2 5a2;hgu5a 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 rotavs5jxuc13 kieg .14:rjausc 9ting at 5.00 rad/s with arms extended has a moment of inertiajck: 4ej 3gav 9 .1usscr5xiu1 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?