Angular displacement is 4kl 3)o1me-p6 v3gj 8kpc4bzfulqz /ousually express in units of

  Angular velocity is express+ bkx50mz )xx xe1zglba4hj2(ed in units of

  Angular acceleration is expressed ;h,m:, )qfizx)3w4pjr kxhogr 8q5r w in units of

  A boy and a girl are riding on a merry-go-round which is turningvzt igp -5ph (zpoa* o-iee: v1:wh:2d at a constant rate. The boy is near the outer edge, and the gih oaepoh-*vpp:1: :t2zz vd(eiig5w -rl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a k m3jq0/trgqequ,-6jki 1u r*merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to thrjiqj10kgu/ m36-krte, uqq* e center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is tu ,.yc8gr;o: z y(ntkv6;upwaqrning at a constant rate. The boy is near the outer edge, and thek:r cyuvn.yp 6;ow g,;8azq t( 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 cck2-05rdk gdmonstant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centrik5 d-rd2c0 gkmpetal acceleration?

  A boy and a girl are riding a s-2j gxr,)y k4lyd ru)merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to yy4jgl drrx)-s 2k,u) the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. 3/hbf05iq*r(t ,bpse uih,ru Which of the following is an accurate stb( q5hu, ir0rut3*ep hs,bf/i atement?

  Rolling without slippia,l2bkq(4)3y jg t wzing depends on

  Two equal forces are applied to a door. The first force is applied7 /w6d cuq;p70li -vbs7dlw mm at the midpoint of the door; the second fwm7pw7m/s 67d0qd lvcli -b u;orce is 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 door at the doorknob. The figugv-l). (zz p,vw2ue rst force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts thw(g uzv) v .l2eg-p,zue greater torque?

  Two forces are applied q ,jhi-,n3q+srmp- ybto a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque oi jq p,3-qm,rsbyn+ h-f the second is

  What is the quantity use1*z0)a mfyg,jk, ih+0vb vzhad6)c ko +e3nja d to measure an object's resistance to changes in rotatikd*ve vj0a6 jymkg,anh oa0+h) +,z1f3)bzi con?

  Consider two uniform solid spheres where both have the fk.v fpd22(ncjl 33pl same diameter, but one has twice pf k.lp2nfvdj cl33( 2the mass of the other. 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 twice the radi yrii7g4 st5 lm:va er5,6v-clus of the 55tamicrl,ev4v 7 sr y6g-:l iother. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solidp+jpg4gp )2md spheres where one has twice the mass and twice the diameter of the p4pm2dpgj+ g )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 thesr .(0x77q xqe:e*qg; kiflzeve are increased to 2M and 3R, what happens to the sphere's moment of ine;l7g.qz*e rv:f7x (xeie qk0 qrtia about a central axis?

  If a constant net torque is applied to an objechspl1kcx7dl ) p seld (;-6hi2t, that object will

  The moment of inertia of a solid cylinder about its a19v/jf7(./ +eone jk7k0nmyk mlbbfy xis 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 wh ;ge5w 1ap3,opjk: mg6 lhmr f*dz4i7oich 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 of themlo 1m,d g:zgew75oajp3krip4h * 6;f bike? Assume the wheels are uniform disks.

  Suppose a solid sphere 9al)cy1o hj7j of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocy9 alh)71ojjcity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slij:km n89of9scpping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline do f8cm9k:js9 nepends on

  "The total angular momentum of a system of particles changes when any7+xj3ml ianc8 7lk5 net external force acts on the system." This statekil nx3 c8ay7+j ml75nment is

  In what circumstances can the anguwf6 jw vdlxy8e((( nr1lar velocity of system of particles change without any change in the system's angular momen1ewr v(wj n6yx8f(d(ltum?

  The Earth orbits the Sun i d. bkruzl*)+c5 isysvj/ax:.vs*zs 1n an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum aboux5.jyskb*s zzs) .d+ arsv ci* vul/:1t the Sun?

  The Earth moves about the -qpal 9+tg .hbSun in an elliptical orbit. As the Earth moves close to the Sun, then which of thb ahqltp.+g 9-e following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his o*/ 0g,fr,h xogknb 8chutstretched arms close to his body. What happens to his angular momenthx f*g0,ko rcb,g8hn/um about the axis of rotation?

  An ice skater performs a pirouette (a 48+i*+ pwi4anfd yp6spji,t p fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic eia+ps684yi ,nf*ijd4 p ptw+pnergy about the axis of rotation?

  An ice skater performso v-+t;g5ilbn a pirouette (a fast spin) by pulling in his outstretched arms close to his bot-ob+ln;i 5v gdy. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentumgotkqo7,:wy2h/u5c l 1oc k+z.

  What arc length does the Earth travel in a three month 3md9rt9t9v s hperiod in its nearly circular o99vthms d3r 9trbit about 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. What distance does thei y9vgzxt9 )o/2sx v9e tip of the second hand sweep through in 3 minutes and 45 sexxg o2ie9vt9s 9yz/)v conds?

  How many rad/s is 25 revolutions per mibvj cuqv02l95 nute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutiq(j/xd2 e5 hb+skqel 9ons in 4.0 s. What is the frequency of2hq (bkj xsl/e9eq+5d the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulse nwqndlv.)4ub m1f5o3s at a frequency of 0.40 kHz. The period of its rotatiolm3 n oquf)4vdn w15.bn is

  A phonograph record rotates at 45 rpm. Through what angle does it turn k6mddqbr9hb*c dyu+2h +r25ain 0.20 s?+umh2 9ba+ 56d*dc2dqh brykr

  A wheel of diameter 26 cm w t2uj1jj41r,xp)rnq6n g w8eturns at 1500 rpm. How far will a point on the outer rim1, jx4 nj81jw r6gr twuen2)pq move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions f bvllbe lo.c b46e7zy(:1 lq2in 4.0 s. What is the average angular speed of the whe2(41zlv .o fcl:l b7yb6el qbeel?

  A bicycle wheel rotates uneq5-b 6fqrevu, o;h*(fx c5obiformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the wheel?b56bvqe o;ue5f f,- qxrhc*(o

  A cable car at a ski resort carries skiers a distance of 6.8 km. The ca goi-jb.(sqi3,g1 png ble which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the ( j.o- nspgb1,igq 3igpulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotati) kue6s 6xbxhm8 :u:nbng with a constant angular speed of 2.0 rad/s. What ib8xuenuh6: xmbsk: 6)s the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If thtg (nl -r-4ddt4 3 aqxat.nuo,e motor rotates at the rate of 20 rev/s, g4tqra,.xu3o n d( ltt-4a n-dwhat is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angularmm-)e6yp92b gnr rx, j speed of 2.0 rad/s. What is the centripetgn, p 6m-2emyxrrjb 9)al acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a po l36ukf c2b8s o8f7tofint on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike isb3t6u 2kf78lofc sof8 moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spaceah; s rj hb1 :v*lm62p6itvue9 station (r = 1000 m) rotate to produce ajt 6v9:ls6ahbm1 v2hruei* p;n artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of49j c0vu:rg pnumte:dzy0;k0 radius 50 m with a speed of 20 m/s. u09y 0u md ekr::t0zp n;jgcv4The maximum centripetal 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 circular curve of radius 50 m with a speed of 20 m/s sm)/ .o:ve ;nh-xgius. The maximum centripetal force (provided by static fx-io/v hgm;):.e s sunriction) 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 arouztwp3lz ( tc*ggnf22 2l 9zs+p7qe cskl.,9jynd 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 string is not2 p2 g3e z+p.lnql*ktg2fw,( t9j 7sc9zlcyzs to break?

  A bowling ball of mass 7.5 kg and radius 9.0 +h40 eohkne 2wcm rolls without slipping 10 m down a lane at 4.3 m/s.e en4 0khw2o+h
(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 ar 5ui):.d dei(t/q srfngular 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 rbq;pq/x eh*p,n,r w z2 ,9dvow.(j bfwith 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 au y oy*l;l,u zs m6oulz( :bfi7schr/;0tomobile tire rotate after starting from rest *i6fz7sboz:l/ mcsh l; yu r; yol,u(0and 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 angulo2d pe2b:xptydk+)(3 um.p4bkkq :zc ar 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 witv7 f+dhbahq+n2jd8wcq vp. 3vc ;/sj)h a constant angular acceleration +/vafv2 j b dv7whq c8+cds; .3hqnj)pof $-5.0 \; rad/s^2$. 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 whrar1n n604z xaile turning through 2.0 revolutions. What is the average angular acceleration of the whnnr arzx1a064eel?

  A wheel of diameter of 68.0 cm slows down unifort+: xdfxvqsf14g ,r: omly from 8.40 m/s to rest over a distance of 115 rvtdfq s4o,x gfx 1+::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 uniformly from 7v2 s ich16ieokuck528.40 m/s to rest over a distance of 115 m. What is the angular acceusoikv25h6ec 2ki7 c 1leration?

  A wheel of diameter of 68.0 -:f ;mdvmel:mcm 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 come to the s;lmm-dmf:: evtop?

  A centrifuge in a medical laboratory rotates at a rotati499k8u o o005z on5lkmdh1 pmpwsjpq+ onal speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before cool5m9k +p pp k04 um10shwoz8jo5qn9dming 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 torque of 9un+mir7k u nbre2576u0 Nm. If a 30 cm long wrench is used, what is the magnitude of the force n7eu+u2m 7rnib 6u5krrequired when the force is perpendicular to the wrench?

  The bolts on a car wh;p+b,tr-x by d;k09flviyw kx6f 34lleel require tightening to a torque of 90 Nm. If a 30 cm long wrench is us 3r;6ltbkff9 4ll0v pxxy-d k+w,bi y;ed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ocd8ga9 s*es*mf inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modelen1q h rd4ro00fd as follows: mass m is at the origin, mass 2m is at x = a, and, maso4 nrh0f0 qrd1s 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about ab-6k/ /vmlznt ;/bk tk frictionless axis thought the center O. A rope wrapped around the outern k/;lv//k-mttb kz6 b 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 frz oby, armeea2 *35an;ec:7rwictionless axis thought the center O. :ar2ae o3n,cba75;e*mwzy e r A rope 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 on)s- vi8hn/py duj/1 jai),mgl e end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall.m/gs jadh j 8u-)v1i/nlp,y)i 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 rh oe63:mb)6,nl47bpdt hzkryadius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially t74 3n:mdezot rhhk 6lby6b,p)o 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 rmma g272xmv2)cg g7dr2 uhae/ ope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 662ge)h2c2m am7d/ mgrxvg u2a7.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around ypox+d 7 y5rs7a frictionless disk pulley of mass 7.07 kg and7spxr5+oy d7y radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is(lnxl-3cd a2mvuab) wq5c 0;qt 3l*cn 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 in)7 o6s 4l9kujkl+iekfertia 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 7 qw*zjyi0(dk 5w/uhhm starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it re kw/wq5i7hy0d h*(ujzaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of grb;xzy.v0 wn)dfu1 210 m/s. How high nd z)by; rg1w20ux .fvup an inclined plane can it climb before coming to rest?

  A hoop of radius 0.5* w sc)ly: 0yu+txhl2 5kbgbu/0 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined planwtblhy) u0l 52kuy/c:s+xg b*e. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radiuj7m .urt it**m u1l9v 9ccve)ss 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it cu9 t7.tumjci*sm9erl*1 vv )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 8: l yw:ly9qikmomentum 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 inertia ofyetszu 8.01+zp 9ujdm $5.0 \; kgm^{2}$ 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 a c zml484 rw4qk;y4csnt 5.00 rad/s with arms extended has a moment of inertia 4sqc4r;8cz mlwn44 ykof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?