Angular displacement is usuowb 5vf ++4p/*wq jzrrally express in units of

  Angular velocity is eoncp wr+j f1d;0bzv9y-o k ;:dxpressed in units of

  Angular acceleration is expre 6m+ncddw 6-efug pq84ssed in units of

  A boy and a girl are riding on a f9q2q 5pko:nh 9yx;bjmerry-go-round which is turning at a constant rate. The boy is near the29po 9h: q;5 nyxjfkqb 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 is turning at oe*i tn,px5 3oa constant rate. The boy is near the outot,* x5po3einer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are ridings+q1lamp( lw vw5q9( r 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 has the greater lineaqlar51+vs(lw w 9(mqp r speed?

  A boy and a girl are riding a merry-go-rou9t4pzt ilc b3.nd which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the9t.3zblt pc4i greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which i3lc( o s6c frd0jsc()es turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration 3jf0( d()rl ocsces6c?

  Consider a rigid body that is rotating. Which of the followi;)f pyswnj8o: ng is an accurate stas) yfpwj ;:on8tement?

  Rolling without slipping depends on6 ,pu,m ezc.dn

  Two equal forces are applied to a door. The first jyk4r: n3mr *7vz;uhc force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Wck7;4r* rzy n v:j3muhhich force exerts the greater torque?

  Two equal forces are applied to a doow( gzdr/rwt f4fidkt1kl* / )+r at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the dodiwgf *t )4 t/r/rkzwlf+(k 1dor. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicula: 5v17autwlwd04g wv rxm4vbx)z2li* r to the door. The first force is twice as large as the second force. The ra:xd4amv*2xiw1 wl lu)v4b5 r7zv0 gtwtio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's rn0tq1 nth 5-kbesistance to changes in rotationkbqn5n1 th t-0?

  Consider two uniform solid spheres where both have the sam-bjb,cng 0f.te diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that-,bf 0cbn gj.t of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of t0oyg9lus j9-+ oj7bli he other. The ratio of the larger yil0ujs +j9lb-o9og7 sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres ww)s: su z,kfo3here one has twice the mass and twice the diameter of the other. The ratio of the larger moment o:k,3)fzuws sof inertia to that of the smaller moment of inertia is

  A uniform solid sphere rq5cyhk ;sew:v o1d;-w cl ..khas mass M and radius R. If these are increased to 2M and 3R, wha.q;swr vhcc e;:k5kdwo yl. -1t happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to h lqa2f7p*)b h -7x0xr/ii3lh 2bjtoxan object, that object will

  The moment of inertia of a solid cylinder about its axzeya57d8sc(fdipjyk v3 121 his is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy day18je7y3s1h2 d zkic(f pv5to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whicm4wcs7 d jjhd37 i2m xwka4w(.h 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 totalkh(.dwa ji4c7w2xm w7 s43mjd translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls witho .a 86decex0tput slipping down an inclined pe6tdap0x 8ce. lane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R0umibj.6c 3zj rolls without slipping down an inclined plane starting from rest. The angular velocjzmj ub .063icity of the sphere at the bottom of the incline depends on

  "The total angular momentum o ; apw)fkb2 mb98xnhx.f a system of particles changes when a net external force acts on the system." This statemenn x.x)bhmbkp9fa ;w82t is

  In what circumstances can t (rs;hu:x*6fp7 n7z,xu * pivjknrp/phe angular velocity of system of particles change without any change in the system's r *:huskxipp76 j ,(np;rxvfz/pnu*7angular momentum?

  The Earth orbits the * d *r(6au; jcfnzva h2t5vc;wSun in an elliptical orbit. Ignore any friction which may be present. What happens over time tc uj(6v*2 5tahfarwncdv ;*; zo the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves i uj9*t;a., gheozqh/close to the Sun, then which of the following best describes the orbiting speego/zjeqhut9a *h.;,i d of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spiyual .v 3kq4kq+)eoq)n) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the akue4lv )k.qyq a )3q+oxis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstf, zef j-2a(h9z9psmo hki: zw. .lmx*retched arms close to his body. What happens to his rotational k kzwf9hmf2* ,z sm.ljzi:o-9p (xe .ahinetic energy about the axis of rotation?

  An ice skater performs -:ffpvlfhc,jd og8 g 7w.u 3:ua pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to hisdg :3u.u v8wg7 l,fjp:fhfco- moment of inertia about the axis of rotation?

State the law of conserva 0wup6ju9p7ygq;r.a+ix ,tq gtion of angular momentum.

  What arc length does the Earth travel in q40+up bm*zh hoy3 .rhm(dnia 4xa 0/ja three month period in its nearly circulauim adyoajxhhr(b p/ qh +m4. 3n004*zr 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. What distance does the,r g0:1fuq (klxx wk8q tip o xql1 wrx 8qkkf0ug(,:f the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minutek:h:8w -koc 3x5r kgi, zxztsv(zji2 ( equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.4m)7a27kjlz pj(n eoz0p)se2 3qy mth0 s. What is the frequency of the wh(em zn kqplp4)70o 2zh3a)yj2m7ej steel's rotation?

  A pulsar (a rotating neutron b9g4x eq xb(3:k fhjl4bqnk 21oo1db3star) emits pulses at a frequency of 0.40 kHz. The per j4l2eqhx1fb4(:g bk 3xdbb 3konoq9 1iod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does gbtb,j x whjize,,xis593p;z+ 8 :mjvit turn in 0.20 s,8,;jm,g:zvpx+whj 3 9 tib xezi5 bjs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point onh0e 4sr;j0fus1 dv/sw the outer rim uj v 4hf/wssrse1;00dmove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 44:9td r5r dgak4ed*,a luuy7u)ct1cwa k5yz6 .0 s. What is the average ar uda7 w)6,ukc :ak4uyg*z4 dar 1yetc tl59d5ngular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolukksh9rhoyyhkd+2 :t9s+ (.uc)vs xc/tions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the wheyu .skty kr+ (/hodkv)s9cs +:9h2hxcel?

  A cable car at a ski resort carries s8w;q9g ygvjr,) lm )egkiers a distance of 6.8 km. The cable which moves the cayj)v8q;glew ) 9rg,g mr is driven by a pulley with diameter 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 constan ucozc7 jv0ufo,3iy **t angular speed of 2.0 rad/s. What is the l 0fuo7io uvc jzy*,c3*inear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cu ; jj2j1zftn* i6lgm(ltter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is(2;t1liz *gj6 n jjflm 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 6;uoqc bys:evb g9w 0i3.aj60 rad/s. What is the centripetal acceleration of a point on y3qusvao c0b6i:b ;joe6 g.w9the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter o)*7o + qnpo3wjv1 qdinf a bicycle wheel of di7 pn+qw on *31)vjidoqameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, roz p;pd)sykvx +c (ux39tating space station (r = 1000 m) rotate to produce an artv;3xsupdzkp)( y x 9c+ificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of rad/w4(7ai pf mrpius 50 m with a speed of 20 m/s. The maximum centripetal force (prov pwm 74fapir/(ided 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 curve of radius 50 m wit9,qo0 ut cpv1hh a speed of 20 m/s. Theuv t,ph91o0qc maximum 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 end of a 0.750-m string, is whirled aro5p2*htak5l x e b6-xz-+pl7jbp kegjr) *q -qound in a smoothh7qpebq k 5*- a+oz2-l -jgxpbpj )k5re*lx6t level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 :t(1oql :idcif- cr.wkg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/swit:lq:oc (.rfdic1- .
(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 angula//cjr2ta (jcd j5g hlqel; t,1r 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 wifcb- z659uzero m* *nith 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 agcyt/ (dvey7 :utomobile tire rotate after starting from rest and accelerating at a constant angular acceleration(:gvcd7 /yyte of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has ana(q jr,y: 8aiwx(( c3k k/wwer 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 with a constant angular acceleraotlo++j9 m4gw; zv ;f4rwo:t xtion off;gt+ z woor+;44m9 tovx lw:j $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular sptv4 d :x-8ctdcqiy)wtc5 :c7 8rk(la veed of 6.0 rad/s while turning through 2.0 revolutions. What ilr:v8dc7c: wtdq -tyvtxc)8 kc(5 a4is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over; *bwz)fx *ya 6b4hdeb a distance of 115 m. What is the total number of rebfbe *h6a zx;b*4wd)y volutions the wheel rotates in coming to rest?

  A wheel of diameter of3+x /k4xsnxzw3ym j) e 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m.n jx4mzs ewx 3)/3xyk+ What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformlb qn .0sjx)-gjh:7dvk9i na4ly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to n xn.0v-j7jg :slqabk9 4i)dh come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational spe)tbu 8atdb :4 cy1ime1ed of 3600 rev/min. When switched off, it rotates 50.0 times at a con4m)1i1 au:ty bbedc8tstant 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 torque of 90 Nm. If a 30 cm lp.8 zkaq )71vd :ik0,etttofqong wrench is used, what is the magnitude o0dvq ).qo at ,:1ki7ktf 8tpzef the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm l azu1 08 6/mji2 ;aqb76aivlgw jlvs*jong wrench is used, what is the magnitudes 7a6v62q jl*ijag z01i b;jm uvw8/la of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofnfn3sqj,m;lo 9n bh, 0 4q:2tnbd7ybx inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is hfd ruy57 69izmodeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. 9fyh6dzi 5u7r What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis , vi6/40 bjyyb m2g n45gvyspfthought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a 6y5s4y,bjfn0vm2p g vy i4 bg/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.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis ):mopwvs 5 )gbthought 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 sectiop)m5sbwgo ):v n 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 b0/9i lyp xymkp 8z,4fzq)si/ is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angu xkmi bq0izl p)/syzfp/49,8ylar 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.b. g be8 zo7x rpfj6-xsuv)9s7 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 s ).79 6o7bsz x-pfe8gxjubrv4.1 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,irfm 3g)fgt7zp yf2 c2d rt7/ionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular aczg g)r, 77f2rdyttm pf32i cf/celeration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pidk80 l3a vtg kv zkx*86fm7.hulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?k . k8z308dglvhma7i 6 t*xvfk

  A rotating flywheel can be used b6 vlbkbv: -nur00y9i unl;eil/p )6 vto 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 inejxjdf-o )/o 3.ffh1lyrtia 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 massrt1 i3t ku ij9x2ix7ix vd6)s9//ful c 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of theus9i) xj k uc/9vftx r1236lxidt 7i/i 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 speed of 10 m/s. e:sr-gg3r-j0 nrv mb -m i)hucylwb zm2.( -o0 How high up an inclined plam.y:(i3e0cwgrouh- - )0 vrb-jgn-bsz2 rm lmne can it climb before coming to rest?

  A hoop of radius 0.50 m and a ma: 2) eudysj3kt:,zrsxss of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping asks,2t 3)xyu:de:rj z vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg jcf(,- :9v 3nujol7ynzo2 sp pand radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The zyv9c( 7, u j-l2psjponf3: nomoment 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 mom;cjm*; cf hm: mbvz ss..;c1iventum 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 mom-en ue0oy v2v1ent 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 ib,fae4 6gz* - fe6tww5.00 rad/s with arms extended has a moment of inertia *bawfz6e, 6fge wt-4i 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?