Angular displacement is usually express in un: wf5az 5.xxiuits of

  Angular velocity is expres5mtu/ .uec, qxsed in units of

  Angular acceleration is expresset y+a r07c xvzprj h--+o:h:k)7vzzqfd in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constantota;eq(if+ c 0a6dwy( rate. The boy is near the outer edge, andcaqa6 ft(i yo(+we;0d the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a 1ser6 2of/j jmmerry-go-round which is turning at a constant ratefe2om 16/j rsj. 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-go-round which is turning at a constanj:r)* wtqplhzx k10b3t rate. The boy is near the outelthw 30*xk:rj1pz qb) r 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-round which is turning at a constant rale c5fu.e7a0 zte. Th u cle.zf7a0e5e 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 riding a merry-go-rounlu. gwtg(nt+9d which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. ut .n+9wglgt ( Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which ofn l:srf/)3ki e:rmdsh+; s;ps the following is an accurate statement?n/s3kf:lpsemi+ r s ;rh ;d)s:

  Rolling without slipping5.;c: ch qujso depends on

  Two equal forces are applied0 osm i1/exn;a ca8e 24ate,wy to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknoxtn2oi,ae4me e/c;y 1w80s aa b. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the dl. 8r m372ui dz+emxotoorknob. The first force is applied perpendicular to the door; the7dmrl.e28 utz + i3xmo 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. The b2xmhge6,3 y lfirst force is twice as large as the lb3y 2,m xeh6gsecond 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 chalutpelfw-b*,oh /209 5x8irsjdr ;vhnges in rotation?5 - *0pxvwu 2r9ie fhstl8rd/hljb;o,

  Consider two uniform solid spheres where both ha7d9bg )7qt0nun k 4:zu dce3vgve the same diameter, but one has twice the mass of t k:ue47u 0gzqt gdvn nb79)dc3he other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have t d15+ykljv -i venom8-he same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smald-i8+ knv 1oljme5-vyler sphere is

  Consider two uniform solid spheres wherexe/ycexm 62 nlwc6/ 3y one has twice the mass and twice the diameter of the other. The ratio of the lnw3/ eyc6cm 6e/yl2x xarger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius /t1/ oipdlsb 3R. If these are increased to 2M and 3R, what hoi1/ 3/pl bstdappens to the sphere's moment of inertia about a central axis?

  If a constant net torque m:bt* zg:kr)ois applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by:kb: u+n5z )v1gauqyd 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational1qg+5und :k: yzu)avb kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which hi ;scb/8w2h y8e /ieofas 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 ;ywe28eh8/si fico/bthe wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without sl u7p7ka5 et4zeipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline ta745z u7kepedepends on

  Suppose a solid sphere of mass M + ib2/2aa h+ebhmj*fsand radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at +2efb+*2 /jbasimahh the bottom of the incline depends on

  "The total angular momentum of a system of partiwrvw ;sn f58 lv:u)5 m2tsco7qcles changes when a net external force acts on the ssnmqt52:lo );u8vv 75wcfw rsystem." This statement is

  In what circumstances can the angular velocity:k ir+ rf: cuc:jgd2*mfg7j+ v of system of particles change without any change in thei7jfrcmvf:gjd:g *cru 2+k+: system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit.3k5n 2l8wgw)pti( cogx 7gj3kq0g6ro Ignore any friction which may be presk683r wg57g2kgwxnt) p3ij ool c0(gqent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the 2x2o+g, dkaayxar0 w3dy.a *yEarth moves close to the Sun, then which of the followiyd rgaao2 *k wx3a2 ,+d0.ayyxng best describes the orbiting speed of the Earth about the Sun?

  An ice skater perfor:plv6r: :p u jayr(no3ms a pirouette (a fast spin) by pulling in his outstretched arms close 3:ppl 6najru y :(o:vrto his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling inh2 65ut 88pt iz)uc7vtd2evuo his outstretched arms cloeuozptivu2uc8t8 52h7 vt6) d se to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstreec 0q 7wbah.s1eoc/l*tched arms close to his body. What happens to his mol0 7he*.wce q sc1a/boment of inertia about the axis of rotation?

State the law of conservation of an6( 7 ynl.dlbb sk07dwj7w,gohy7e 0kguzj f: .gular momentum.

  What arc length does the Earth travel in a thre32arqh :m5hbh e month period in its nearly circular orbit about the Sun with mh2:h5h 3rbq aa radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distan)f)vq;i: 9 gr8aeuqyice does the tip of the second hand sw afqg8i9) yv: ureq)i;eep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolq/8u en (tdciy2n(0vwcrzy,8utions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 9; zxy:xx ,e.er-c fic What is the frequexc.c ;9,z ryie-xexf: ncy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequenr xc 22ie (bz40wa2f8ih,zopecy of 0.40 kHz. The period of its rotatizwebi2 hpo2 fe4i0(cx2a8z,r on is

  A phonograph record rotates at 45 rpm. Through whc1hos ts.( x.kat angle does it turn in 0.20 sht1o.cs .(sk x?

  A wheel of diameter 26 cm turns at 1500 rpm. Horq69wol5r 2aa0kr ie(w far will a point on the outer eo9 akq250rr ra 6iwl(rim move in 2.1 s?

  A bicycle wheel rotatesnk69uus;b +tk uniformly through 2.0 revolutions in 4.0 s. What is the average au9k+k; nbu6s tngular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 rejzzwacs)wcclhbv 7,r.3 jp:)0b lb 0:volutions in 4.0 s. What is the linear speed of a point 0.10 m from the center ofb0rpcz0 ba. chjw: wslj):3 l,zcb 7)v the wheel?

  A cable car at a ski resort carries skiers a distance of oiwk w8:+popul9)r1 q6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to 1o:+l)p9ow qwpik 8rumake the trip in 12 minutes?

  A wheel of radius 1.0 mw*u1m/ucer5 e bo 8l;c is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed ofl/;*r8u1eeoc 5 cmwb u a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lengt xz)yqf . btl:53xvl2wh. If the motor rotates at tybft2)z llxwx:5.q3 vhe rate of 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 speed of 2.o e1ws+352 gq yblg0m39xm1frj-q ca w0 rad/s. What is the centripetal accelerationf+qqmr0mesagw 1jg xo31-y2l 3c w5b9 of a point on the wheel's rim?

  What is the centripetal acceleration of mge( z0hb((e la point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike izehl(((b g0 mes moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stationu6zkh u5ab0f2/p .wj ) z3lxfq (r = 1000 m) rotate to produce an artificial ghu .jfq26w /ufk0l)zazb px53ravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 mz+pu78z/em8ndv3 r xb. fc,xl with a speed of 20 m/s. The maximum cef l8xn ,7cuz.3zv8redm+p x b/ntripetal 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 circulk-,vu 7zw : tpl(bx2m0o.sfyqar curve of radius 50 m with a speed of 20 m/s. The maxiq.x2l py z st:,mvwob7-(0ufkmum centripetal 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 en6wp6r*we0 un9) vmuwvd 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 N, then what maximum linear speed can the mass have if tv)we6r vpm9ww u*n6 0uhe string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls wi6cm9te yugrfg*18 0r tthout slipping 10 m down081c rgg6f9ur *mytte a lane 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 acceleratijkr(71kqn5 x fon 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 cs- j;q8xwlj: 2ntc d:yonstant 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 0.30bm43 pw cibs/)0-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceleration wc)mp4 3is/bbof $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and ha6qlbwj o+z s i0z66zq4s an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates pu - -w:esgnwc61 qz025 gstk c8r:lc+dgx9irwith a constant angular accelerati1uxwgsicc6q-rgec rl9t g :n0p+8sd2 w k5z- :on 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 ogse6wk; -1 ckrna*ln e48 :zospeed of 6.0 rad/s while turning through 2.0 revolutions. What oe1 -*sn6o :weczkkn8g a lr4;is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.4mdjzi4+;elfw:rm ,9+ z,itp j0 m/s to rest over a distance of 115 m. What is the total number of 9el ; mjrp4mwz+z f,tid i:+,jrevolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.sfz ew)7e 6sl i+wui:)40 m/s to rest over a distance of 115 m. What is the angular accel+z67if )e :)uswielsw eration?

  A wheel of diameter of 68.0 cm slows down uniformly i5/0, yqpr orrfrom 8.40 m/s to rest over a distance of 11pr0 ,q5yrri/ o5 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotatesi4d+ p,5 e-lf in(xwbb at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant anguxn (5ilb,peifwd4-+b lar 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 tighte+34prhq iti /ining to a torque of 90 Nm. If a 30 cm long3/+h itqri4i p 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 ; b j-/19 kd nan*ludi6vf6;+tzigm afa torque of 90 Nm. If a 30 cm long wrench is used, what is the nm+1i f;audjdk g/z96*t bn;vil fa6- magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiarlq9-vxe1su x gax. 4tw u5/0a $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as fo+nkdnmt q6 th3bb* a17llows: mass m is at the origin, mass 2m is at x = a, and, mass 3m6*q+hn3md 7ant1bk t b is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis though0eezc :ug 7(zdt the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0zueg (c z:de70 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.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought th mm zc:5doee/- m44biqpa4v1de center O. A rope wrapped a4/q:ae44 mivdb 5cpmm d1z-eo round 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. 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. bnvsrow )+5x),7nde a The rod is initially held in the horizontal position, and then released as the free end is allowed tor dvbe)n,+w)75sa nox 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 altx1wfswui 7b8zj:) g /u+h7n 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 the wheel achieve, assuming it rolls withou u8suwxj:+ n /wibzl7g1 h7t)ft slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pul403pi r,8zi zupszh --.dop) z,r abmhley of mass 7.07 kg rzipi30muo,d. )-z z-hr8 p 4azsh p,band 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 5 c e+.xdi0djl db+w/ipulley of mass 7d.i elbxi/j wc +5dd0+.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be us)wdzv pp*4 0rb2hnql/ed 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 k0ma /43dkzpvof $5.00 \; kgm^{2}$ 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 from rest t7cx x1 gnctg;)7oo4j6gfc: xand rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when ic xx co:x4 f1t;t7ggg)c6ojn7t reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a uple cx/ g gw)c7(y9 -u-vt2lrspeed of 10 m/s. How high up an inclined plane can it climb before coming tut7xu rlc-9 pwcey2g- l)g(/v o rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowednu(q7/t 70dcisa1l hl to roll down an inclined cu l07i/ stadh7 lnq(1plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 lwh, ow um) k8iaffq4: e b.mi-hs7)w:kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Ahuwse:k -i7)hwf.w)4q,mabo8 if: lmssume 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+2 .tygya1iq0q9drie3y5 uqn 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 in-eeg9/+qc3f r 4uhszbo5g8o dertia 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/ip,qp s wc g--xm 68g6f gn05gizvx7nw c0y6t at 5.00 rad/s with arms extended has a moment of inertia ncm0/6- s wx xy6gg6igq5 78,zwigfp-p ctn v0of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?