Angular displacement is usually express in uni h1kg,5vb/c ksts of

  Angular velocity is expresjmk:p. wfp5q6,3pp9,en btb ksed in units of

  Angular acceleration is e7z )vvfjcs4 l1g* ,fzizav; o7xpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a/,i -rhvsjc5lr5) :/eug rl ay constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater ang g usi55l:rec/)v/rh arly,- jular displacement?

  A boy and a girl are riding on a merry-go-round which is turnin5(ip y*pn/ox5 mt ez(ug at a constant rate. The boy is near the outer edge, and the girl5 (t*/mzop(enyi5pu x is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-roungz2 ;ko k0rbbussd :(8d 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 linear speed?(kzsr0 8bgs od2b;:uk

  A boy and a girl are ri3e6a oq-gnw3rtt lu*8ding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while tgqol8- et3rau n*w63 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 conshrtiem w4r -3v1 +x6pytant rate. The boy is near the outer edge, while the girl is closer to the center. Who h6+pmh4yvirxr1e w3- tas the greater tangential acceleration?

  Consider a rigid body tesl -gi1 u uwojc/ v8ha+ ix32x911yqyhat is rotating. Which of the following is an accurate statement?8y9xgsu + quivh/iowx 1ec1 32lja-1 y

  Rolling without slipping d *om*t9x9h4 itwz(m2qkcnw-sp +j r1wepends on

  Two equal forces are appliedo6et(fbk/j24 wa,h *k d7v5 3zdxhv cc to a door. The first 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. Which fjdato(zfc khw 7dxbehv2, *k4c65/v3 orce exerts the greater torque?

  Two equal forces are applied to a door at the doorknob.zf 3qq9q qxg1nruv -3isnruy04 .n-w 4 The first force is applied perpendicular to the door; the seco9-zqf r0nnnvg.s qxy rwqq4 i3uu-134nd 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 firs: .6pw fuv w. nfb)lb ativc))r8cy5x9t force is twice as large as the second force. xwv. fb8blr).tw56 a):iy fc9)upn vc The ratio of the torque of the first to the torque of the second is

  What is the quantity used tl+; u .clwlb /y:ep.kdo measure an object's resistance to changes in rotationl./u;.b kly cp l:wed+?

  Consider two uniform solid spheres where +hx;)ylya+cvboth have the same diameter, but one has twice the mass of the othe yxv++h)cl ay;r. 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, but one has tl*rx1gfi 4t3a wice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller spher1tg3xiraf4 *le is

  Consider two uniform solid spheres why15j. l s0buk-am 3 kmv1dfas1ere one has twice the mass and twice the diameter of the other. The rat3v0fm1sk5amj-.u l1kasb d1yio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius /lblri*n4 9/q.qmg wbR. If these are increased to 2M and 3R, what happens to the sphere's moment of inerti gi9mb*q/wnrq . /4lbla about a central axis?

  If a constant net torque is applied to an obje,v belna;, z(jg5l j0ect, that object will

  The moment of inertia of a solid cylinder about its axis is gm1l4 )pqqabr*)kz; o miven by 0.5 MR2. If this cylinder rol k)aoml*zm;) rbq4 qp1ls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of m*h dfbm0htcr9,+ c;l mass 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 lchtb;mc* ,9m0 h+d rfof the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of m. ef3xs//g 8hflkn (zo--zbsuass M and radius R rolls without slipping down an inclined plane starting from rest/lk.z3(8--esxz hsunob ffg /. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an izo6x824eztmj q;ajf 6s( 0zz+ v xa3mnnclined plane starting from rest. The angular velocity of the sphere at thznfo+x6 zm; t 02azjexm3s(z qj84v a6e bottom of the incline depends on

  "The total angular momentum of a-1 kjrye wob,(sd: -yh system of particles changes when a net external force acts on the system." This statement is1e ob: ywr ,s-dkj-y(h

  In what circumstances can the angul1lo jp+w**6y2ijf)ue hrvm3d2,euza ar velocity of system of particles change without any change in *e j *j+l 2vd iu21u ,owyz3haf)ep6rmthe system's angular momentum?

  The Earth orbits the Sun in an elliptical orjqbp.pmq- yb4lp68k3bit. Ignore any friction which may be present. What happens36bby4pqq pk8lpm-. j over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbio6.bmq2, tnswj 2q h2nt. As the Earth moves close to the Sun, then which of the following best describes th2hn2 bm to6qwsq, j2.ne orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fastyh8(r al *8bgk spin) by pulling in his outstretched arms close to his body.y(ak lrghb8*8 What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hi2s4k aw9+s p knhcsz5)s outstretched arms close to 9ck apzws+k2snh)s 5 4his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast s.ne9r0 aupl x-pin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the nar e0lp-.9xu axis of rotation?

State the law of conk yv)mabt54-ngy q4c) servation of angular momentum.

  What arc length does the Earth travel in a three month period in its ns 5t1af)untg4early circular orbit fg t1n)5ta4usabout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clocp0-18s;rxek zwg5a9kqh as s8 k has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 a0ksrse8p 891;w5 xgaq -kh szminutes and 45 seconds?

  How many rad/s is 25 revolutions per minute eqf.iogmk ;x:1uczn u m:ry d-4zn72y4mv j.2 zauivalent to?

  A bicycle wheel rotates uniformly t/3ku13fxpf:4ip fjv4b mt7xbhrough 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotkb tuvmf/ :pp xi434x3j17ffbation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz.ckv g+el,qb r+l+ dp;q5+zn f9 The peric+ p 5q+rz9gbve;+ k+n, dqllfod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turi-lyvfs gureb 2v h f.u/3w:.1n in 0.20 eus-u2 h3v/lg f.b y viw:.rf1s?

  A wheel of diameter 26 cm turns at 1500 rpm. How f /+q5e xj.kno16d+;urt 0p:al ldjlrvar will a point on the outer riml l +a+rre:j6l dv/kj pt;qo5n 0x.ud1 move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. jc yufm)/8j7 cj9z7xr What is the average angular speed of the 7y7/ 9zfxjrmju8c)jcwheel?

  A bicycle wheel rotates uniformly thro ue zj( e 4vdm//a c46ak4poad5ecbo3g8;s0yuugh 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the wu ;5kpb 0( aa464odseozdg /aj84uyev3/ec mcheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable w/o5ob y/) 1e*ijjoe rahich moves the car is driven by a pulley with diameter 3.rbjio j )y*1e// eo5ao0 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 angf, g-lauhh c24ular speed of 2.0 rad/s. What is the linear speed of a point on the wh, 4hgfhu2a-c leel's rim?

  The cutting cord on a gas-powered weed cutter is,5g)xw y 4jcee 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approxi,y g wce4j5xe)mate linear speed of the end of the cord?

  A wheel of radius 1.0 m iv6 l/fsd9*e rcs rotating with a constant angular speed of 2.0 rad/s. What isrc/v6fd * e9ls the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal sbrn t*l.i /83nwo aj7acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cmsj/*83nbr.7 a io tnwl when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station099rgfpf t f1spz4e3 ;n.y7tgvly2lh (r = 1000 m) rotate to0n g4 f l27fyg1l;9er.sphtytp z 39fv produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m witgp6ae4u 5qz y5h a speed of 20 m/s. The maximum a 5zg5u4p qye6centripetal 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 ck ygxwb8lk x tfr77440ircular curve of radius 50 m with a speed of 20 m/s. The maximum centripetl87fb4x kwkt g0r7y4x al 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 aroundn3maiu3wd rq-b 4,jd+ 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 the strinr db, d+um-aqn4jwi33 g is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 m fqx 9cupi ht0im:81kt7 bax64down a lane at 4.3 m btqk 94i0:7 iha8 mcxtupx1f6/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 angu :sndkptw*b5w g2*c-db)5zh zvs xc -4lar 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 a constant angular accelerahnw8cdac 6y*/p fau nf 2w:e-;tion 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 after s 3e0 hmwgwqt -31:3zo; csrlyn7 h1wujtarting from rest and accelerating at y 0o7 ethw;w jsq13hrngzl13 :mu-w3ca constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accele(yb.n 7l.i xg5 1nvbosration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 2xuvib* 5ekh coh*fp) +,x ei5+0 rad/s decelerates with a constant angular acceleration of *h ku xo+xpb5*5evfich,+i )e$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an ag6)tkt y z vypkj+h882ngular speed of 6.0 rad/s while turning through 28zk6+tjyk yt) vgh8p2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformlyn6 -gq-bvx/lwfhwq 34 from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rota6vf/qh-4gb nlwwq-3x tes in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ove uoqr5zm*bac3jel ) 7y)w t+j9f+h/ yhr a distance of 115 m. +cjyh7w bheaf9o5q)z)r/ ly *j t+um3What is the angular acceleration?

  A wheel of diameter os: pl:yagu9h7,yq r6cf 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long dor :yg:s7h6cp y a,lqu9es it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of -do1 )fv11r9w 57mywv vta ykhl8m6 y(qgsl4y 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to rk6d 8-5ymh v)1(rvl1y wy yw9la14ts 7fovqmg est.
(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 reqmica 0)41 2wo6czlg/1uu z 1as flbi5ouire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the au bs1ziw01 goc6c)ui lo5m /a4 lzf21force required when the force is perpendicular to the wrench?

  The bolts on a car wheel req+o tpj;jg3rt pq 9br b4per2 .dx9gt*8uire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what p2g;3djg .bp* rpet9rr jx89o ttq+b 4is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of 8i110omn 3hooxbw mhp :vz0u4 )y3f rjinertia $3.00 \; kgm^{2}$ 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 origin, m5jvcut-l(;u sn vd:)fass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia aboudj s-v:tl vfu5cn (;)ut the origin?

  A solid cylinder of mass 10 k e( ua+(2e/x(se6i 8z h(hyzrhngimd.g is pivoted about a frictionless 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 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 accelerah ius/8ze(e+x(6z2ema( d.hygrn (hition of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis85d6 jp3 jwhdyi vl*snv: pqa(+3 hg5d 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. How many radians does the cylinder rotate through in the first 5.0 seconds, if it *s+hhn8jjp6 pd5 i(w3 lvv yd3:5aqgdstarts from rest?

  A 4.00-m long rod is hinged at one end. The ru h 5sf ingb2f7-j4b7v-acuj.od is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration ahsc f a-5.4 fu7u-b gvj2ij7nbs 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 h gr2iza/4rtek o9pf01: in3anjh ;w3cm 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 ha;i /0fnk a 4ri9 zhnjrp3ot:12e3wgwheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrappezo hq j(/m2my8d around a frictionless disk pulley of mass 7.07 kg and radius 6/m2 h z(jqmyo86.0 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 masr k-k z,i- f6ok7s9vjcs 7.07 kg and radius 66.0 cm. Whsri-, 9ok6fzjv ck-k7at is the acceleration of the mass?

  A rotating flywheel can be used to stouz pv 2x5 th/.(rpidr, .vle1mre 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 ine, wi4;m j;f g6 ipec.1onyhz6yrtia 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 from rest and rolls wi +(mam 6qotsi2j( jx(cthout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reach6 mas2((+ jq(tjmixo ces the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radcw v-wfj,x o0;ius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane canvowcf j x,;0-w it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20t ruv3.447ololw q dv8 kg is released from rest and allowed uolq7vv 4o438lr dw.t to roll 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 rollauz */ n2x9kdxs without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere i ux*n9x2/kz das 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 chanczxw(zmk;h- lma4m 2:ges 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 ine/rwr52,k s dturtia 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 extended 8ba8k/ngfn/e q8xjhf(x 8 /r ahas a moment of inertia o(8/8fexh8q /rjng k a8xbf/n af
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?