Angular displacement is usually expresv;i88 zxs scg8s in units of

  Angular velocity is exp:t)ykei ch 7)rd6 t6bqlrt ,v0ressed in units of

  Angular acceleration is expressed in unit7td d;.hrg5 ows of

  A boy and a girl are riding on a merry-go-rounzotrk+70 uy ,vm 3f*jhd 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 greaymu*7+z fk03trj vh,oter angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning a) ijyo9 dozdw21rz :ltsr/(m9t a constant rate. The boy is near the outer edge, and the girl is ozr1:i 9jr sy2dltm/ dz)w9(o closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on rn:o jj3doqz:ze957 vv ; opiy5qt -l4a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer todjo5753q q:z;:4 vjp9oet-zilr o v ny the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which isz n o5hrpx6 r024e/ jnkdx,y.tb/w10 z-a pwwj turning at a constant rate. The boy is near the outer edge, while the girl isa-5xej1 2bwzd6,pz40ro0nnjrx /wkpw / yt h. closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-gc;2vhg h b)8 m/rgmmtj,gmpb+i8m z99o-round which is turning at a constant rate. The boy is near the outer edge, while the ggimg9mb/j mhg c bz,m9 2) tr8ph8v;m+irl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body th(f w+6zet9cxzcxgcl mla 4up7jh7; .-at is rotating. Which of the following is an accurate statemezc+4f xxu7lt e7mh g a;- w.69zc(lcpjnt?

  Rolling without slipping depenyitmm:y l177y khll7lw0; r..ke8jq mds on

  Two equal forces are applied to a door. The first force id ml6 5-uz)mivd2w)2grj ce3as applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendiculaze g)3l w2cm6jra-diu) 25dmvr to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doo vpb ;rvsn02-jrknob. The first force is applied perpendicular to the dovn-rjvs;2p 0bor; the second 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 first fsh)j +;hw jj jiwvgoba* (pj**0 g6b0xorce is tjow*gbjgj*h*a(+wxb j 0pjihs);60 v wice as large as the second force. The 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 changes in r a odhty3o .9q6t(sh)bcojx(7otatiot3)x.6jdt7scqoy9(o( h bhaon?

  Consider two uniform solid spheres whe. 3jppycxt:5jt 9y8qv re both have the same diameter, but one has twice the mass of thetjxcpp. y3y j8t9:qv 5 other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have thehl hrr+)di 7d8 same mass, but one has twice the radius of the+7 8rrhdhd)il other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniformx:v,en 3x+ggqb g. /fh solid spheres where one has twice the mass and twice the diqgg nfvbgh :/x.e,3+xameter 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. Ith(eayrw45e ; v4vd u5o j*+gmf these are increased to 2M and 3R,eo* (4 rwv;+4dajyugmev5t5h what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, /hwq5jr(+wxo u:qy 3t9ve1ov xf)ov (that object will

  The moment of inertia of a sc0ng go qvd)zgm,/ ,st,34ycz olid 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+mm8+0ukerw ; 4ua(typbt,i r 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 k(i t rmw 4y;p+0m8 b+taurke,uinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls wiw)z +fy/ 21gmzr2kr-gch b 7githout slipping down an inclined plane staf/2r y)k2 hi r17bczwgmg-z+ grting 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 without slippw. l9slm;guxn( ;;sqding down an inclined plane starting from res gdswls9ml;x;n( .;qut. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of f8;i* 5 y)bvyde(bket 1vx 89vcfcn 1bparticles changes when a net external force af e kin8df8yb(1b*e 9yccvt x15vbv);cts on the system." This statement is

  In what circumstances can the angular velocity of system of particles changz)edv; mjhd2a7l*-k ce without any change in the system's angular mom-k; dd)h7*zm 2 ecalvjentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore anp5 wy)0ewqkq +fm/j7yy friction which may be present. What happens ovekpw+y f7 myq5q/0j w)er time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As7 j kqq:-,gvix+klyc) om42 jj the Earth moves close to the Sun, then which of the following best describes the orbiting speei,jg c) 4km7o q-j+:qkj2y xlvd of the Earth about the Sun?

  An ice skater performs a pir*aeyd. )cxog 9ouette (a fast spin) by pulling in his outstretched arms close to his body. What happenc yg9a)do*.e xs to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretb6x3 (ipvu;) hyteic*ched arms close to his body. vxuic(i eb *;3y)pt h6 What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchedku+ . p g*v.lqg+;/gcs eodt0n arms close to his body. What h le*kvoqg+gcu.p dnt.0+;g s/appens to his moment of inertia about the axis of rotation?

State the law of conservation of ang :bt:ck mp yz.e3hyr5*ular momentum.

  What arc length does the Earth travel in a three month period in itk1b od b6ehqm-)bbg( *c/p r u.lxi)t;s nearly circular orbit about the Sun wix b;tb cbog1-l/(dr*bih k6) qpu.e)mth a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distq1s *ig,5kc rvance does the tip of the 5v*qgrck1s i, second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions peroy4b:9iow ep) minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions is1 giq* n67v nbb9sudhi da/s*mx( v8:n 4.0 s. What is the frequency of the wheel's r6(*19 mbx:/qsn ag* uibn7ds sdvv i8hotation?

  A pulsar (a rotating neutron star) emits pulses at1 bg5+o 1es*axh xjtd1 a frequency of 0.40 kHz. The period of itx5h*eo+gxjbt1s1d a 1s rotation is

  A phonograph record rotates at f7mbxj** edjl6vv j*fw4 9r b245 rpm. Through what angle does it turn in 0.20 s?b mj2rjl vv*d*6bjfw*f 7xe94

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a pointwl:b* k5516u q;2smnm4* sgwaa aelqx on the outer rim move in 2.1 s :25w 4a*bss6 qe aq5l;1u xwa*kmlgnm?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4v ipk3l;3xv 3t.0 s. What is the average angular sp3tx vkpli3; v3eed of the wheel?

  A bicycle wheel rotates uniformly througi+h k o4.(dqk 7ai1z bk.cmd2ph 2.0 revolutions in 4.0 s. What is the linekcddb+7ih .za( o km2iq.p41kar speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8:jcw18hs6s7m 0k ay3io ;kcsg km. The cable which moves the car is driven by a pul;sc :j kac0yh7sk63owm1si 8gley 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 rs qui*e90qgm -otating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the 0 msquq*9i-gewheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. o w1qxb bu(a79If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?(7 w9obaxb1q u

  A wheel of radius 1.0 m is rotating with a constant ang(:rtynz85p tbular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the bt5ry tz(:np 8wheel's rim?

  What is the centripetal acceleration of a / k k.vm qmmzw,uw73*apoint on the perimeter of a bicycle wheel of diameter 70.m kkq z,wm*3vmu/w7a. 0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spap+mqr bb06a f,whg +wa saw0) *7hx0duce station (r = 1000 m) rotate to produce an artificial gravityax*wbw+ u7,)rd6mwapqaf0 0+0s hgbh of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 mpxpb3)1fmv *1gu eev,jo cbj0:viu4-/s. The maximum centripetal force (provided by 10p3bm4 ef:xv,uovpugji *-j )vbec1 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 with a speed of 20 m:vx2hch.ix y2/s. The maximum centripetalxycx2:h2. hi v force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, atta 7w /+nafkwxd38k0na .sbsfd0ched to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, th/+0ks fd0axba wdnn7 s38 .wkfen what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 k: yj6lyh9f hm-y6dfca a6 9ldctkpr 0 t*z1-1sg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.f11h9az c-f yj 6sty*p 0y 6l9ck6a rt:ddm-lh3 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 accelerajcw r-d(sr 1eafvq(2x 9:cj6htion 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 angularhr f+qonrr 54. 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 fvnl1::nd:uhijf s x.:ac m93aixxd-7rom rest and accelerating at a constant angular acceleration da-3x7f:lni dxajis.h: :9m:c x1vunof $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratiokxm7+jb0(bs et53y nz/ x+u01klipj x n 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 cons0608n5zzaoor( w rqck tant angular acceleration of ro0aoc qrnz8(56w 0kz $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of d+nfvs6t,m ,s/lw+ql 6.0 rad/s while turning through 2.0 revolutiom,w+ /ssftndv +q6,llns. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from sn1j8:nh,e g w8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to re j1g, hnenw8s:st?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovet nuux.2cb(m,qi6/o,xavs zj 89 f-nkr a s -8kzmo,qt.jcui 2,u b6(axfnn9v /x distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from g:s*8pr3rjm9ik- qcn 8tj5rw 8.40 m/s to rest over a distance of 115 m. How lk98rq-g8 wmn rspc5*rj 3t:jiong does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a p6yl1hwod 3 8rnx.3k mrotational speed of 3600 rev/min. When switched off, it rotates 50.0 tim1 83 r3ld6h.y ponwxkmes 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 tightenin5p c+ gdrd x+iqw)/ew(. g2mhqg 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 is perpen.gdqhmde cg+q 2r( 5/ ww+ip)xdicular to the wrench?

  The bolts on a car whe0db+w jih+m./. g izlzel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of zw/j+zm.bi+ lgdh0 i.the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertio7iaev8e g5yc k:d2cmt03-zosv 9i , ta $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as followsbug-frd 661m (lm)rw i: mass m is at the origin, mass 2m is at x = a, 6b 1-(wuilfr rdmmg)6and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pi qnb; co6qs0)avoted about a frictionless axis thought the center O. A rope wrapped around the outer rad;cna0 b6qqos)ius $R_1$ = 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 frictug*( (eku8cy3v dbs ,kionless axis thought the center O. A rope wrapped around tdk8(3se *uuvyk b(g ,che 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 hi /7xmaz2u+tn*l3om r fnged at one end. The rod is initially held in the horizontal position, and then release7l/2*ao3uz mtm+ xnr fd 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 radi8g92v7cqg lulok3n i+a9rn7xus 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force o7 x9cq+23 ignvrkl ga98u7lo nf 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 rope wrapped around a fricti.ve w7, bem . nn:pl5z-atg:tubf5r7 monless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angulare7. m,az5t lwmn n5re -v7tfbgb:.u:p acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrappm(zkii//x8h1z xter0ed around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. mx(r /h8t /zizeik10x What is the acceleration of the mass?

  A rotating flywheel can be .8cui/srh9 asused to 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 of489k/w)p a ytrex1 iin inertia 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 s72awbox*6rqi.unvri 3 4 5aj ctarts from rest and rolls without slipping down a 1.0-m high inclined plane. *awq3o x iuab5ic7r4r n.j2v6What 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 ;4xdu;g rr1unjb6/r:q t uz)ta speed of 10 m/s. How high up an inclined plane rur6 1ubnqx;zd );trt:/g4 ujcan it climb before coming to rest?

  A hoop of radius 0.50 m 0wn1 uss) my-pand a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. Ho)s1uw0-pnsy mw fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kf nin0*c goo 0o+xsf;n2an/2d g and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertiac 0oa o2nixfgon2 ;nn/fds0 +* 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 momenrr)+cs- elt tr*50toetum 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 momeafd) ob+*hr;/9j ty1p*e ga eant 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 5.00 rad/s with armi1q7z *rhyyk *s extended has a moment of inertiah*kr *yq1z7 yi 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?