Angular displacement is usually express in u rtv3j3x+zki .nits of

  Angular velocity is expresse6ir1(1 j gqwg -k7md lv(ubsw*d in units of

  Angular acceleration is expressed in units of*y) r/mnts.a f

  A boy and a girl are r9j k rxap4i4,h+)k;eq wv qu-piding 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 thqheuk4- ;a9pw)kv,xp +qjri4e center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant ob6 .hhq u 7 4x+o3kdssq9l7hgrate. The boy is near the outer edge, and the giq9xsh+. glb o4 o3 dk6hqs77uhrl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which f a1oy;8rdj3z+;saq ei14r no is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the + i8;yo eq1rraazs14do;j3 fngreater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constan bwirtop5t4 10s9mg b:t rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater :tp1 iwtbb5m09sg4rocentripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constantr:hgq c7 -i8nc rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greac7:g 8iqhn rc-ter tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an mlx jyfhlmr1e-osi3pqk4 , i/o(g-.,accurate statement?sq34i o.-imymg ( pol,jf1ek-/rxl h,

  Rolling without slipping depends ontl w:m /3)cssj

  Two equal forces are applied to a door. The first force is applied at tu+njww 4hj)1;wl-zr fhe midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Whiurzjnj-l4 fw )1+whw;ch force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is applc-a9;iv5hs ;i 6 pxz-j0cxk ihied perpendicular to the door; the second force is a60sxc p95zci v;a--xhhii kj ;pplied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the cv u+p28:qjfkdoor. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the sec 8pfuv:2kq+cjond is

  What is the quantity used to mey6zc 6c9, tcuscx0tv .ez5hj +asure an object's resistance to changes in rotatiojc0 htzz, c 6exu+6.v ct5ysc9n?

  Consider two uniform solid spheres where both have the same diameter,j:et 5eesf xr2 pj*pr *l4vbtw 1 x(ts6(1dfj, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the small jewf 42j1xe:6 1j *b5t(srdr t(ptp*,v efxsler moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius 3o:i j5 cv.xlkof the other. The ratio of the o5 lvjc:ix3 .klarger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the doq712osv2 o amass and twice the diame2s2 odav q7oo1ter of the other. The ratio of 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 increased to izkm- u/tp*6 a2M and 3R, what happens to the sphere's moment of inertia about a cenkt-zi u6* /maptral axis?

  If a constant net torqu gift 14rap4c/e is applied to an object, that object will

  The moment of inertia of a soli 4xr1qtq y av(xe73n9olpa e d-9/ok+jd 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 which ,kv-gylb n35vd 7a5jehas 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 the whee5b3-nkvgyj7ed, lv a 5ls are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping dz,gceg0m ,xo ,own an inclined plane starting from rest. The linear velocity of the sphere at thgx,,zo,0ceg m e bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down ahnyt,ir 6 ,y87h jrt:cn inclined plane starting from rest.6htrtnr hij7y,,8c y: The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whenjhn zi.e637i oj07bef a net external force acts on the system." Th 77 i0hjeb oi36e.njzfis statement is

  In what circumstances can the angular velocity of i4ux3b 9wm a9vsystem of particles change without any change in the sy394u9vaxiwm bstem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frm7lz r bb.;f8hiction which may be present. What happens over time to the Earth's angular momentum about the S7 8h rbfbml.;zun?

  The Earth moves abouk4lgcwb 8h2*qt the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the cb4kw8q2hg *lorbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast sz8qrd(j+otyz7vkd,m /e )e d*pin) by pulling in his outstretched arms close to his body. What happens7z+8,(qd)ke zjdrm vy /dt*e o to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstreqi9a. :a+fv nl g+ejd;8an 2hqtched arms close to his body. Wha.njql g 92eqiv: hd++; 8afanat happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) 2bx*wbo;fiv0 by pulling in his outstretched arms close to his body. What happens to his moment of inertia *bfw;b o 02ixvabout the axis of rotation?

State the law of conservation of angusm 5-1l 8i/hoj1z2xn,czp qqwlar momentum.

  What arc length does the Earth travel ij2k-rlhi hsp7yj3q o ml0/y 41n a three month period in its nearly circular orbit abo jlq/k-3 ysjyr024h1m hi p7lout 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. Whad l/kv wbg.9o1t distance does the tip of the second hand sweep through in vwb ko/9gd1.l3 minutes and 45 seconds?

  How many rad/s is 25 revolutions pe pk1s:8yy. wih ghbz +2+cldh:r minute equivalent to?

  A bicycle wheel rotates unifo-i/z tu v zy(gnm4pz9hed: u+3rmly through 2.0 revolutions in 4.0 s. What is the frequency of thz:v94eg-h y/+ 3u(uimdtzp nze wheel's rotation?

  A pulsar (a rotating neutroni6 3o b6fniyd wb9)gz: star) emits pulses at a frequency of 0.40 kHz. The period of its rotation ibnzigow9 yi d)f36 :6bs

  A phonograph record rotatesfuw+es q5t,1lqi 0qv3 at 45 rpm. Through what angle does it turn in 0.20 su+lteq, i13q vfq0sw5?

  A wheel of diameter 26 cm turns at 1500 rpm. Ho ijpu,5b1u7a/8a hkwiw far will a point on the outer rim move in 2.1 pah5b7jiw/i aku8u,1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutinct)t2v;jggf4z e5 d7ons in 4.0 s. What is the average an)g25z7gjd ett c4 nvf;gular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What e j5ad7d2j56j0irwswis the linear speed of a point 0.10 m from the cens0dd wwraj5j7j56i 2eter of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Tms6.f*r-i4 xudmao (fhe cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotaf ua4msr-oi* xd(f 6.mte for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotati)bh+n56m yypa ng with a constant angular speed of 2.0 rad/s. What is the lineara+ 6yh)b5mynp speed of a point on the wheel's rim?

  The cutting cord on a gas-pow 4yu,xy7)qpe(ec : vpqered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of thexuecp7qpe qy (4),y v: end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular sf;z rp0bcn p0,peed of 2.0 rad/s. What is the centripetal acceleration of a point on tr00z,pfnp c ;bhe wheel's rim?

  What is the centripetal acceleration of a point on the perimet zlebt0vhjf+ 64d 39keer of a bicycle wheel b0e t93k+jfedzl4vh 6of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpc)fq1qe r(l7u m) must a circular, rotating space station (r = 1000 m) rotat1 efr(q ulc7)qe to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of g5qslf l,7 aowf(na;*20 m/s. The maximum centripetal force (provided by static friction)7l a gs,f(*nf qa;olw5 is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a fla*uce l uadl;)8t circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by )ll*da8 ucue;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 a*fxz7 esw3uj 8+y./ef,v xo ztround in a smooth level table. If the maximum tension that the string can withstand is 250 N, th3we7e f.su xfv8y+z,x* j/zoten 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 tyi+j*- j mk44-aiwjv w j:*cl9.0 cm rolls without slipping 10 m down a lane at i*yjv*jlw-atwj :4 i +k4cm-j 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 constanjc167-+ s/5ews aqh qlxmpzp) t 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 a conshkmly/onge(l:0 s(5 wmsy 8mch ; k2*ytant 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 rotate after starting fro,qfe u+u.u (kqm rest and accelerating at a constant ae.q+(quu ,k ufngular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has a09rox 0 vxx*0 h(bdp4bvfwfn8n angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating a7*w39dg xy:voap yuxu +kj4)ot 20 rad/s decelerates with a constant angular acceleratu wa7y*ujpx:oxv3 4ogd9y+k) ion 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 speed of 6.0 rad/s while turni2dwf1 896i3 gpivd xcrng through 2.0 revolutions. What is the average angular acceleration of the whee3g2xpdrcvi8d6i9f w 1 l?

  A wheel of diameter of 68.0 cm slows doa-,itrqp:k5zl y73ehwn uniformly from 8.40 m/s to rest over a di3,t7 qkz p5:i lrye-ahstance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down x s,rhfov9on7 /4qlyn8jrunvo (t: wr:5(og3uniformly from 8.40 m/s to rest over a distance of 115 m. What is the aryv5(/3(q nwx,ls ut: rov94ronn f oo78jh:gngular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fa) o s3wmiq) j4 ti-+ ag1mllihs6s)t2rom 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel toq1jt)i 4mh+ai)l)im ss3ats2- ow 6lg come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of /w)zh *)-xz kz5ztmp j3600 rev/min. When switched off, it rotates 50.0 times at a -5xtkh*zz zmzw/ j p))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 tigakcu-,e)hb0kqn fk 6o 1lt )nwa)m;2dhtening to a torque of 90 Nm. If a 30 cm long wrench is used, what is thef,cob- w2)0kqehn )ad6nlu m) k1 kat; magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 9+x12ypgf l ya/0 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forly f+/pyg 12xace applied at $53^{\circ}$ to the wrench?

  A wheel with moment of 3nk -ckx r+ty 1d-n+ban1siw0inertia $3.00 \; kgm^{2}$ 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 or:-wwd 4)-c/edxed u uzigin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the oriu dwu/ -dxz-4eed:c) wgin?

  A solid cylinder of mict 4ocx a/4gd.pzl07rsts skq 91/ 80r*nifbass 10 kg is pivoted about a frictionless axis thought the center O. A rope wr0c0lf1kq9i crg/r4*o ttpn4sxis.a bs8 d 7z/apped 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 kzf )ws7xukv)-g is pivoted about a frictionless axis thought the center O. A rope wrapped around the ou uxfws-v7) kz)ter 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 th(it- v 8 , c*zn3htd99z dxobe6fv(jc9 0kqymce horizontal position, and then released as the free end is a9ccq * j9k9-(z,y8d ctd h0ft36 nvvmozbxei( llowed 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 be a ring of rckl mgu1:2u34ihuiq / adius 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 spromh2/k1g i u:qulc 34uicket 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 rope wrapped around a frictionless disk pulle f; i:twdg7t4 6ebe+.qympcf. y of mass 7.picee .f.w6 ;f7yg t t+4qm:bd07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aroundhc,j, 7z8m5tuhmkj m; a frictionless disk pulley of mass 7.07 kg and rad58 m7kuc,jtm;,z mhj hius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to kfn)m+*s -a-g u-8 cg-drvhugstore $1.00 \times 10^{6} \; J$ 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 inertb z)g xs+ca*u;ko j:d4ia 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 radiu97n bh7.w8 mcd zc-umbs 0.010 m starts from rest and rolls without slipping down a 1.07ccmw.dzuh nb8 b7-9m-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 speed ofzcafgn1cb7 5zn-*s f0 10 m/s. How 0 -nafgszz*bcc n157fhigh up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a maxb3 7o.nwqzq 3ss of 0.20 kg is released from rest and allowed to roll down an inclinqbo. xq3zn3w7ed 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 rolls without slip: uh2 r)q n,v(ittp1jtping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a supqt i)n:(2,1 tj vrhtphere 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 momentgb- nu* :qwmfnwj/x;+um 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 i:zqb: :6yu xrjh oo0dc:,c:e 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 e8hc-l*wrht5 3 u h8ihu6k1 yf+mguqy4 xtended has a moment of inertia o3q gkhhl+ u6fh1y hy8t-r* w5u 48cmuif
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?