Angular displacement is usualcjk-t5;vav fgmp 3-m1ly express in units of

  Angular velocity is expressed in unn:iax dsj,w4e:c xg0 qmen8w57: 4fpvits of

  Angular acceleration is expressed in unitsf/cxg y4kw;t: gms+h+ of

  A boy and a girl are riding on a merry-go-round which is turningv)1k kb,ryzm75g jiz+ at a constant rate. The boy is near the outm zgj7brk)z, i5 vk1+yer 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 whp9u5sk,bom g):bbd31 isuh k;ich is turning at a constant rate. The boy is near the outer eu 5i ph bsmbd,) 391s;gkubko:dge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding dv-ykt h05p5+to x(vu 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-+t dyv(t 50 5vhpxuok the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is t5. brdsx1 b*n tlbmo-liapv5 2- a(. +sfiq-lburning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetalf2 asmi-b*iso(d-ptl lrba-5.n5xbl+ .vq1b acceleration?

  A boy and a girl are riding a merry-go-round which icpl a8s38vz p7s turning at a constant rate. The boy is near the outer edge, while the girl i szpcv38a7lp8s closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. frt, lfr4v. g.h g)m ry2yj. iy)vz.4sWhich of the following is an accurate st44ri,lyv .fryvs)j yzh2tmrg.). . gfatement?

  Rolling without slippin jtq 95tq2i:zj(ku vj+g depends on

  Two equal forces are applieo *;b-3 fcbkbmd to a door. The first force is applied at the midpoint of the door; the second force io bm;- *3bfckbs applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a doodzi8f,82a yltd8 ml*lr at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which forc,l2d8d8y m ftzl8 li*ae exerts the greater torque?

  Two forces are applied to a dq:njy w;:bz y9oorknob, perpendicular to the door. The first force is twice as large as the second force. The r:b; yyzwj9 nq:atio of the torque of the first to the torque of the second is

  What is the quantity used to meaz4o0cyh q6x2o(+oli fsure an object's resistance to changes in rotatiofzqoico l2 6hx0o+4y(n?

  Consider two uniform solid spheresdb6ctyp hmqoyd9 k5)f;g 29b2 where both have the same diameter, but one has twice the mass of the other. The ratio hd96b o5d qy mgbpy9f;2c)t2kof 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 twice the radius ofkwa ra6i iz+x1+-hg7e the other. The ratio of the larger sphere's m7a +zki +rei6x1-a hgwoment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where o.0*k0pe;y,ap ko0 pao:orir nne has twice the mass and twice the diameter of the other. The ratio of the er;ia ko : r* yk0,opapp.on00larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M an oyii q10(f:l+kufjal- h+da2d radius R. If these are increased to 2M and 3R, what happens to f( + j0 h:2ayafl-ui+io dk1lqthe sphere's moment of inertia about a central axis?

  If a constant net toiie 7 k45l ut)cnv9*jj/n;u8ft2qhl x rque is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axi+ bn3 57z:t6g nibqcl3lky+fos 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 whee 8v u-d2wvc+pdl of which has a mass of 10 kg and a radius of dd uwv- c82+pv30 cm. What is the ratio of 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 radius R rolls without slf5z.r2kvjqol7m s3k +ipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends ovf .ko3m+7 lkz2qr5s jn

  Suppose a solid sphere of mass M and radius R rolls without .fc026d sqaow slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depeodw. a 6c2qs0fnds on

  "The total angular momentum of a system of particles changessslp43 ;3v0c hgj rtr6 when a net external36j4c;rv ght r3l ss0p force acts on the system." This statement is

  In what circumstances can the angui, ll u mhc-slb,//l)klar velocity of system of particles change without any change in m-sk hl/ uclil b),,l/the system's angular momentum?

  The Earth orbits the Subs(6u maz pf6rcs639a n in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the Sun (3a66zbsspm rac9f6u?

  The Earth moves about the Sun in an elliptical orbit. :2sm;)c6e vuopr (d lh* u.gdr As the Earth moves close to the Sun, then which of the following best describes the orbiting speed duves26rp*r h) (cdl;mo:.ugof the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretc0sfqc9t0l/8s 2xl sx; hpzsfng7-x ;i hed arms closel s i0s9;ffxzx82nxlt cs; p70-sq/gh to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a:rn 1.qw j*fmhrv(2tq fast spin) by pulling in his outstretched arms close to his body. What happens to h1r *n wq.2(q:htjfvmris rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hi, ak1 djrf-yw.ecl/b,s outstretched arms close to his body. What happens to his moment of inertia about the axis of rotati,klw crfe1-j.ay ,/bdon?

State the law of conservatio7c 7baw cm48kbn of angular momentum.

  What arc length does the Ea p1gxd4pza4go : v+yi5rth travel in a three month period in its nearly circula 4x1p:g5oa vz4pd gy+ir orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.3-9f3 pynf fxv-0 m. What distance does the tip of the second hand swe3vyp-xff-9 fn ep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutionf -)xv5of4( ky)ws ishs per minute equivalent to?

  A bicycle wheel rotates uniformly throupo .0zk)h :nen bi5,whgh 2.0 revolutions in 4.0 s. What is the frequencyk,:)pze0nn i b.oh w5h of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHzywy2c; ic- *2wzd) dgy. The period of *;c2dcdw- i2z ygyw)yits rotation is

  A phonograph record rotates at 45 rpm. Through what angt)h;l6 l zwon0le does it turn in 0.20 ) ;wl60hoznlt s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point5vzie) 5s+o q ezlt.n4 on the outer rim move in 2.1 )z zvt4+qi5.n oe5esl s?

  A bicycle wheel rotatxzlv.p (y( p5wpc/.ates uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of thatp pvp l( ..z/5wy(xce wheel?

  A bicycle wheel rotates uniformly through 2.0 c1/ ukd/ohj) crevolutions in 4.0 s. What is the linear speed of a point 0.10 m from kd)j ch//1 oucthe center of the wheel?

  A cable car at a ski resort carries skiers ap* cgp.ba6z sn 5r3k2x distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter p*gk63n rszpb.c5 x2a3.0 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 constant angular speed of 2.0 rad/s. aj d*4:ci eqa,mljo ** What is the linea4dja* eajc ol*iq,:*mr speed of a point on the wheel's rim?

  The cutting cord on a gas-powered we+/k h3efw se108bivy nt/ 6lrmed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the a//h+rlwem0e13t v 6fniyksb 8pproximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a c md4plmmyk1b6. rg)+ aonstant angular speed of 2.0 rad/s. What is the centripetal4b1k lg) +6madym mpr. acceleration of a point on the wheel's rim?

  What is the centripetal acceleration ofup p1;lg18+pobzf hu3 a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is mo+pg3 18pu bph;uoz1f lving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotau( a8fq,of) ieting space station (r = 1000 mfae,i8(fu q) o) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular cup tgm7 siaz fw-/1, adq+w4p/qrve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction w+a /p1g7,d4w/azmqtp-ifqs) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve o xdpl2:fc p-y.h66shkf radius 50 m with a speed of 20 m/s. The maximum centripetal force (proh :plcp sdx.k62y6- hfvided 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 around in ac0dva.n lnzd,9kv y+j t4 (/ja 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 string v, kat(d40y.ca/ d jj +n9zlvnis not to break?

  A bowling ball of mass 7.5 kg and raae:.ia m5p 3ain v6r4adius 9.0 cm rolls without slipping 10 m down a lane3 aip mr56e.a :4niaav 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 qcs e(wu 3t:)ve;mjrima0ylb v97 ;+bacceleration 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 acceleratiodjnnb7c871 8olxr -( ides8zc n 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 afterbg n( 7zpokt2a1oad,5 starting from rest(o ka1 b725pgd ao,ztn 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 a:x5 ylr k67vklz3 eo3jngular 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 withtgzzf+ny3gw+ 6)ok emom 7,gf9p2 ha. a constant angular acceleration of yg2+fowam kfe+z h7z),9 ntp mo.gg36 $-5.0 \; rad/s^2$. 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 wh1wxgn w -hpswnsa0u;v xeqn(xi,*57pw9/ o4wile turning through 2.0 revolutions. What is the average angular acceleration of the wwn(w h q4 o/*x-7visu0,wpw5g1s;pne9 naxxwheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 02tvf)m hvvg 9bv9e; g8.40 m/s to rest over a distance of 115 m. What is the total numb;g0bvm2v9h )v egtv9 fer of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unhug 16vd:y1reg,* e ojiformly from 8.40 m/s to rest over a distance of 115 m. What is the anh,uv61 ody1geejg : r*gular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over akwq ;/t *7rih((ofkd o distance of 115 m. How long does it take for the wheel to come to the otd kq((o/h*rkw7f ;i stop?

  A centrifuge in a medicaken7 ,thc1)l irhg4z-l laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration befh) 1inhkzctg7e 4, rl-ore 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 to+oq3 8for/ct ql ; o6dnn3j3mxrque of 90 Nm. If a 30 cm long wrench is used, wh/x6 3njqtfqol83n3r+mc d ;ooat is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightenv+ os 5w5dcy,ling to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force apc55 v,soy+ dlwplied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiae1uck--d 6d.wfgqv45oj6cq gr z:0h r $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modele3 igi ;uco2dtq( v( 5mbs.akz;d as follows: mass m is at the origin, mass 2m is at q idbtz; a2mvuk.ci sgo(53; (x = a, and, mass 3m 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 2o:1kp/0xzo.s zsf l-(ov cgg thought the center O. A rope wrapped around th.s(gc g/o zx0s zp-vlf21:kooe 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 kg is pivoted about a frictionless axis thou. z42p4h3ttf ,au5zw;a fcvtsght the center O. A ropeafzuvc w f2,4t3htt;.za5s 4p wrapped 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) 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 iv oub2 /dmzpn4v7 5sivqm3( z8nitially held in the horizontal posit2zdovib (svm 8qzp537u mv n4/ion, and then released as the free end is allowed 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 radius 30 cm and mass 1.5 kg. Neglect p3u /ba-c3htwdg,s6ww1rfm- the mass of the axle and sprocket. If a force of 20 N is agd-bcpmft1as/3w h3w 6 -rw u,pplied 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 rope wrapped around a frictionlessby 8 :7ua;ux) h(qqoed disk pulley of mass 7.07 kg and rad ehqy:d;8xu 7a bu(q)oius 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 pulley of m,8wm m :sms(5 ymllgb 0/nhab,ass 7.07 kg and radius 66.0 cm. What is the acceleration o0ag l/sbym( hm 85 bn,mwm,:lsf the mass?

  A rotating flywheel can be used to store energy qp ozc76l)aoxe(8p:zifj (0b9gy sw :. 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 b(oxaey i0.a tmp : 3f3sfrk20inertia 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 agxrzzbc l* 4k:t;n-4u nd rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plan;cx* gr-lkubt zz4:4 ne?

  A solid sphere of mass 1.0 p*0qrzg f(pwtt +p*n /kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb gq(0+p*prf/ *ttz p nwbefore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and alv sdjc.*zf;pr63mv(m: ajy :ylowed to roll down an inclined plane. How fast is it moving afteajf:dvz36j; .*: rpm(sc yv myr dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and rad:xv; twkvse;7ai(zmn,u1 , t zius 15 cm rolls without slipping down a 35e incline th;(u ,,v: tzkw;asx 7tem1 zvinat 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 momenttvhjw.7q/n *yzs..j/ ia +m(avfqkx :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 ofmveok+p1 dj 4*n m.p1k 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 aral3b s.n7 -,;/wyvghfvt5mv4 nywp4ems extended has a moment of inertia o,wly7 4ts. ;vnhv5fgy 4-pbmvaw ne /3f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?