Angular displacement isglbyjjed 12ct )0 fa 2*))ezgv usually express in units of

  Angular velocity is expressed in units of8 t3jf)6g af1,nh se vx-mfxkc9e*046j nqccz

  Angular acceleration is (r;ntw-i4g qn xa*l18jpnyx 7expressed in units of

  A boy and a girl are ridy45yc /zodqpqwku5:nv wot+-m7 o8l 3ing on a merry-go-round which is turning at a constant ra5 doomp y7wyq/5:4q+3o nvkuc8z lwt-te. The boy is near the 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 tfp g34f2q-aw nurning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater anguf2qw34-f pag nlar speed?

  A boy and a girl are riding onwi/ j/0iy(g c u;sxy;z a merry-go-round which is turning at a constant rate. The y c(i;g/wi/ szu;yj0xboy is near the outer 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 constantl+ udd.d n+g7t rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceled.7ldt+ug +dnration?

  A boy and a girl are riding a merry-go-rdh bg9 tkt lil)86*5rlound which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the centel5 *)8 g 9ihtlbd6rtlkr. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following dyk 6mk1r+5/ubnv(xt is an accurate statem/(1 nuy+k mdtxvr 56kbent?

  Rolling without slipping (fbpc7..jbgt*vms9y3dtgkf2 :a. n fdepends on

  Two equal forces are applied i -/1y 17d be ii2ghrlurey.x3to 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 perb/1i2e dyrxeuy.i 7g-i1 lhr3pendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the dx6x: m 4zm:7gfhz92j--tlm)wkbsubi oorknob. The first force is applied perpendicular to the door; the second force is appl6hz 4i-x:zx ft7:m2kmmw-gu9 )jlbb sied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, per3 ;ly xdc*tp+zpendicular to the door. The first force is twice as large as the second force. The;zd clxt+3yp* 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 edf.q- k5.n(aqjt8ischanges in rotati8 if sad(q .nk.etq5-jon?

  Consider two uniform solid vvm uh,vb:/jw:b ni8+spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smallevbvujiw8 +: /h:nv ,mbr moment of inertia is

  Two uniform solid spheres have the same mas1e duyskj91 6fs, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the k 1 6jey9sdu1fsmaller sphere is

  Consider two uniform solid spheres where one has twice the mass and tw,, ulhyhvj g.vh1h(1xice the diameter of the other. The ratio of1u .(h1y h ,vlxvhjgh, the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increasedbqd k0*r80e sk to 2M and 3R, what happens *80bks kerqd0to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wgkq:ru xi k45mo0n*n) ill

  The moment of inertia of ab h7(bhv* h3tf yh7aw*dg,e 5g solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of it h vbfgby,7te(h h* agdw5*h73s rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has auwt0)9 h,jmm w mass of 10 kg and a radius of 30 cm. What is the ratio m9tm) w 0w,juhof 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 roak py04a2lc14d . mlcadius R rolls without slipping down an inclkd4.mcl 401ycaoapl 2ined plane 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 R rolls wr-mx 6bq/ph*po -dk d w.i);upithout slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depend xbmu/ *op;q h)-priw pkd-6.ds on

  "The total angular momentum of a system of particles changesj wmiv 1-a)iqu/b/9 f4h+bu/ejn z50p(deocv when a net external force acts on the system." This 9pw/e bc1 vji 0v +o4(un-ia/dj5m/bfh z)uqestatement is

  In what circumstances can the angular velocity of system of p59k1 3milay+p8ag t(vflop3 l articles change without any iap8o yp3(35fatl+gm1l9 l kvchange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictio p .zbm38pm.3is9pqr qz:he-cn which may be present. What happens over time to the Earth's angulbp3mpp-8.zc9m3:hz .reiq sq ar momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As w9 su)572k*wv(b-g cj rwpcc dthe Earth moves close to the Sun, then which of the following best)p w2c *w(cvbg 9dku-rc w57js describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) byynap yf1qa+1 2b6jjngpgbiw8tn1 o 9qeu 60(/ pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotationjq(y1afaij8+1y26 1n/tnpnu eb qg 0b6o g 9wp?

  An ice skater performs a pirouette (a fast spin) by pulling i1a1 uarizodjx-l 28c,m-o 1uin his outstretched arms cl1ouo8ar i udj1 -xa2 im1l-c,zose 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 ijj 7/bw bryk 5*to,3ohis outstretched arms close to his body. What happensw3*ji/5b ,yo7o btkr j to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentubx 99 ;ceb jatnf)3.wum.

  What arc length does the Earth travel in a three month pe d bx1qk+ud5s8riod in its nearly circular orbit about ths + dkdq1xb58ue 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 82 zbo(l)fa wtdistance does the tip of the second hand sweep through in 3 minutes and 45 secondsot w8 l(f)zab2?

  How many rad/s is 25 revolutions per mi+ ,1ock je+ xmtu,kax.nute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 4 f ybjgds33+p What is the frequenc f3djg yp4s+b3y of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Theo a(eqhc/ 6fd, peri(c,a6eq dho /fod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn ie (o2n*fhkj od4/7hw dn 0.20 sw7od/*d4(f oe2hnj k h?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the oute,en6n o9g6b f)eggd 1br rim 1 6d9 ggg,efn6)ebbn omove in 2.1 s?

  A bicycle wheel rotates uniformly thrtow ,:pe2 y-tqough 2.0 revolutions in 4.0 s. What is the aver,ywt to-pe:q2 age angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 y+ p9 )o.d;uyeze2bx ds. What is the linear speed o2xdeuy;)ez bod9+. yp f a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers agzt * .9j5yb.5ksyvlt5 anx;j distance of 6.8 km. The cable which moves the car is driven by a pulley wt;g5 5ynl9x5j*yjs zvktab. .ith 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 constanrwn0:adfur nme8:rkn*7 m0nf1rs d7 . t angular speed of 2.0 rad/s. W:*7 r8 nmnnkf snru00 .:dmrrdf7w1ae hat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is)hgw e:qm2) :b4w b te.sy.syt 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of th4:.sge wh:sqeb.tmw)yb 2t)ye end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s. : h8crw*u 6rwa What is the centripetal acceleration of a point on the wheel's rhrawwu *86c: rim?

  What is the centripetal acceleration of a point on the perimeter of a bi6t9 5v3m.unalsshw d ,dy hm/y;*fw 0hcycle wheel of diameter 70.0 cm when the bike i3fhndy dtm6mu;s0w a v,.y*9 /hl5shws moving 8.00 m/s?

  How many revolutions per minute (rpm) must a cirv4a; 5p pel45uz: tby; m:pxuqcular, rotating space station (r = 1000 m) rotate to produce an artificial gravity yu 5bz5xuq;m;p:la p4e4: vtpof $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of e3dc n9x+,xipradius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by sta3 9+ xexndpci,tic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular ch3 x r11g;uejcurve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (3 gx ;jr1huc1eprovided 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-mhh afm ypa;6*v0,bgy1 string, is whirled around in a smooth level table. If the maximum tension that the string cangpa6 hvyb ,h* a01;mfy 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 kg and radius 9.0 cm rolls withoj1u-bzx2+5cmk ug s7 wu g;n7fut slipping 10 m down a lan;nkg+ ub -5fuu s7g1jzw7xm2ce 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 acceleration o/uq,9 )c mdygnf $4.5 rad/s^2$. 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 w 08iuc)c1 gzgwith 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 automobile t i1k; o ce8* fy a)zyz1yxxcml8.3/svxire rotate after starting from re )koyx1y1 ;*lfzzmsvexix.8c 3 /c8a yst 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 an angulawranyd .djwarzu9 ;j9cm-+e7 0yqv(yv; 6mc9r 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 x4kadvhg3la3 uzo qih /at/5oq 275 y4angular accelerakg/4hzt2/ h 3 x5qv4o od3qaayila 7u5tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest adf+f,ra*6g qdnd reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average ang,r* gqdf+fa6dular acceleration of the wheel?

  A wheel of diameter of v;xp5dd4r3d46 ;8 msp c8zofoyn ;a ly68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions thepmd;3y46ocy;rvazd;4pxdl5n o8fs 8 wheel rotates in coming to rest?

  A wheel of diameter mceg hr4gp h(wy36m zp0 2ja (0x1ckq3of 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the 3 megm kwjyqrg cpxhz0a03(46ph 2c 1(angular acceleration?

  A wheel of diameter of nyeo u. q++4 ork9i;-zqj 8eya68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to;u+9ork8zeqa yn -yqe+ 4. jio come to the stop?

  A centrifuge in a medical laboratory rotates at a rotation;i f scnd-2xq9al speed of 3600 rev/min. When sfs;qnc d-2 9xiwitched 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 3xu ,r:p9gevy-xiq1 (6u0zadsm fqf- 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 fo10u xu3dxq-qysae 6fmzri:9p,g fv (-rce is perpendicular to the wrench?

  The bolts on a car wheel require tighteningqw n3rycjz1y+( c. nvgs:nw/ fqsh15* to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forcernyc1gwnsfn( qzc :y /h+*s1q. j5wv3 applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertdvcdt,q,wpq1g7w7 r0ia $3.00 \; kgm^{2}$ 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 orig7b2qlql;hvv/h u 6 )nc7m:zvain, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment n6vzq /2h c7mq;l)7b vu :lvhaof inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a ,sk8hu gr8dsx xdbv,,yq47j: 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 exert ,u 7s8jx ,yk4d g,qs:drvbhx8s 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+dm 8 0hi1tvei 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. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts froth0e+ miid81v m rest?

  A 4.00-m long rod is vt 8d:t*tbs: bs2tx k4hinged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What i*x: kd:ttsvb2tsb4 8 ts 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 a ring of radius 30 cm anhe 8jor s).ewc.:qsi 2d mass 1.5 kg. Neglect the masje) wisr se2:qoc. .h8s 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 roduy 0h5+x 2pykpe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What iyk0+ u2dx pyh5s the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley ofwkg s7)i4yfu7h z;m m6 mass 7.07 kg and radius 66.0 cm. What is the acceleration of6if7 )z ;gw 7symmk4hu the mass?

  A rotating flywheel can be used to store ent 5z )8xw/bojyergy. 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 of e6p lhk du):yz:aif5-$5.00 \; kgm^{2}$ 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 tetl2t 3d6y9mo48g. po h6rpakg 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 the sphere when it reaches the m ptrp4gad3 6t6h8 29yotlo.ebottom of the inclined plane?

  A solid sphere of mass 1.0 kg d-q xnqfcq 3s),ro,(n and radius 0.010 m rolls with a speed of 10 m/s. How high up an on sr,,f(xqc-nqqd3) inclined 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 and6 y1irhhl,1fc allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distah hy61frl,i c1nce of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down axo4 9j5vp wyvdjwy:z+8zjvoq: y 4b41 35e incline o1 owzxjj4v 5y4wvj:9z 8vyq: 4pyd b+that is 7.0 m long. 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 m*w y6lwsoe .g-omentum 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 o2a(.k x5to ujjl-oye *nc5 pj4f 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 5.00 rad/s with arms extended has a mo75 b/7lb -o5nllpg,bs a zev6ka7(o ivment of inertivalb(o 6-niep5vog l5 7kalz,7 b7sb/a 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?