Angular displacement is usually ec1 rpt.s0jk,d/jbmp 3xpress in units of

  Angular velocity is exp fj y3eg 8woehp(p3*-oressed in units of

  Angular acceleration is exprepejd3; g;c .u ad-8sjk ej-x0essed in units of

  A boy and a girl are riding on a merry-g u 9sp8-y,c2gy4nwjc ro-round 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 greater anwrun42j- ypc s gcy8,9gular displacement?

  A boy and a girl are riding on a merry-go-round which is c 5l7;og (anmrturning at a constant rate. The boy is near the oute7l;amc5rn g (or edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a con4p3 brm5svm h oje. 1-v-(c2qvdhx+j estant rate. The boy is near the outer edge, and the girl is closer to the cv.1(pxceds-3+ jevvrq 4hojh m mb-52enter. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning d*xgpto 7+a* ()tn ycx 1r0r)nqonuqk df(y-8at a constant rate. The boy is near the oute8 q+(o7nrqfy*dynx))-cd( a kx0 tr1tupng* or edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is tu/gp,vonysp8*dhpv) o;t:x 2k rning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greatesp2 ,v/pgyho8nt);*xpvk d:or tangential acceleration?

  Consider a rigid body tk2 1v4ig a6ffhhat is rotating. Which of the following is an accurate statemeng6f14 2hivkfa t?

  Rolling without slipping depj;*ah;,ilb x9(v0lb ydv7 s lzends on

  Two equal forces are applied to a door. The .ta ys)-nb3y6ra cg,.0y )f wgy ebd0qh+na1 bfirst force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts th g3ay+-bw)n b 0,0enhr1d yys6c fatyg.q.b)ae greater torque?

  Two equal forces are applied to a door at the doorknob. The fi; r(mlz now5j72kf6i 4oaj;wkdh7 v0m rst force is applied perpendicular to the door; the lmo a6hn(kozj;4kf5djwr m77w2 ;vi0 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. gvx 9hb2cs-g( d 0rn,c The first force is twice as large axs g,-0hvcd2 grbc n(9s 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 anyo(9 niq+fy g, object's resistance to changes in rotatio,y+fy i 9gn(oqn?

  Consider two uniform sol8d9lgd6n;vwa*m3 ) dikjpz1u id spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger u 9dpld*zni)gmv63 djwka18; moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same nw, hsr y; ba,56).msaosndq )mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphereqn aa.,6b,; r)w 5mysoshdsn) is

  Consider two uniform solid spheres wherub2h5vn-l-e d e one has twice the mass and twice the diameter of the other. The ratio of the hb52ne--ud l vlarger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these areg6ylw41xi/ u h3ajouf ;;p 6ua increased to 2M and 3R, what happens to the sphere's moment of6gy af3uua ; ;xujo4h wi61lp/ inertia about a central axis?

  If a constant net torque is applied to an object, 20duee jt*bu/qa 4sw xp52+ nqthat object will

  The moment of inertia of a solid cs/h f)0d yhsg9ea f8hq+,7wxkylinder about its axis is given by 0.5 MR2. If this cyl/ h q,gewfax+f8 )sd0k s7y9hhinder 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 h32u zk*bka 9leb7b6 ezas 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 to kzbe37 96b2ub ka*leztal translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere ozzz g2l- 1ibv7f mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom ofl217 z gzzi-bv the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an4if lm24,-. lfnnrh dm5bik;d inclineh-imi n ;2blf.45rmd4kf l ,dnd plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum orcsin 1p8fu81oc+m2euw t;: jf a system of particles changes when a net external force acts tjs: i2cw 1;p 8urn+fe om18ucon the system." This statement is

  In what circumstances can knbna4 -ps +unpl/37r s,kw2pthe angular velocity of system of particles change without any chk+apn2wsnr7skpnb,4 3 l-u/pange in the system's angular momentum?

  The Earth orbits the Sun li* o9rv4pn v7in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's vn*vl rio 47p9angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves clo(g2hb ,0(2b vei1d+s 5utgaxcquqtmn t9 j)5fse to the Sun, then which of the following best describes the orbiv ct0 5bq t9g+)in5qx2( bd(t1 fusague2,mhjting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulli 78mm fl+u)burng in his outstretched arms close to his body. What happens to his angular momentum abbul7m8 +f m)ruout the axis of rotation?

  An ice skater performs a piroq.1.pm,qc ws v,/pqpkuette (a fast spin) by pulling in his outstretched arms close,.m,qk pws/. 1qcv qpp to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a piros6q -xr5bg8equette (a fast spin) by pulling in his outstretched arms close tgserxb-q 8q5 6o his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of an:g 8 1kbjs/gp 0cjk u:kwumn:)gular momentum.

  What arc length does the Earth travel iniefd.29sl b)/p.r4ux-vkfmc a three month period in its nearly circular orbit about the Sb idxfsp.lvm. f-kc2eru9/) 4un 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 ther 6 yp3aster npj uurm2i08v+8;o-m38 vsqbh, tip of the second hand sweep through in 3 mio p 6j2-i ehsn0vru3y+,ms8m;rq38vpbu t8ra nutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivaa4*wxb7 ch7ri lent to?

  A bicycle wheel rotates uniformly throug7kw lw6uhzqfl;.na3 g+ rt8a)h 2.0 revolutions in 4.0 s. What is the frequency k8 uz.hr q3twlf6a7gn; la)w+of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Tvqk80tv: g ;hk*st8a she period of its rot ah08 gv*kstqsk; v8:tation is

  A phonograph record rotates at 45 rpm. Through what angle do g6re*jv /af;w(g ;yqez.w.saes it turn in 0.20 s? v6j qf;zw;./*sggera aw .(ye

  A wheel of diameter 26 cb( nwl:puka 25m turns at 1500 rpm. How far will a point on the outer rim mo5nwb l:pa2 uk(ve in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in+ jh7)yus*vs r 4.0 s. What is the s* vh7)ys+urjaverage angular speed of the wheel?

  A bicycle wheel rotates un+3as gqopk:7t iformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point oq+ 7a tskp3g:0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distan guj:3 yhp1ei0ce of 6.8 km. The cable which moves the car is driven by a pulley with diamete 0jy:1ipe3uh gr 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(dd3. v+,e0dkk5juf au kv: cp m is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a pointv.+kf (3ap ,ddj0u5dkk:v uce on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lengthqok;hr)d y :07ofyycrei a:)- . If the motor rotates at the rate of 20 rev/s, what is the approximate lineq:7 fcoa)o k0i; yh:d)-yryerar speed of the end of the cord?

  A wheel of radius 1.0 m iba l:dg5l9)kiqj 9.eb d1/jdcs rotating with a constant angular speed of 2.0 rad/s. djblde j:9qa91 d.cbilg5k)/What is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on t nixj wdpp*bo49gan) qx,e7 s-b*+gv/ he perimeter of a bicycle wheel of diameter 70.0 cm when the bike is movinjbg p9 b*dsq+*x74/paxnov-) e , nigwg 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotbrjd f,,b r:t*ox0xv 2ating space station (r = 1000 m) rotate to produce an artificial gravity ofrox*, vdbb2 :tx0r,fj $9.80 \; m/s^2$?

  A car is negotiating a flat em1w+x gz( h.;t,cuxscircular curve of radius 50 m with a speed of 20 m/s. The1(x.ech twm, ;ux+g sz 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 speec6/2mnqd djf/ (nl( nnd of 20 m/s. The maj(nn6/c2 n(l md/ qnfdximum centripetal force (provided 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:1iy/ lm; sz. 9ekjbgw in a smooth level tabs9 bkz:gj1 /;yei. lmwle. 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 not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slippiq up:4y6 - wgs/*zu yrcf7jai:ng 10 m down a u *a-/gfry::pcq sw 47jyuzi 6lane 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 accer( v ddz /i+u/ xxwgpq- u59;sr6ec-luleration 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 angulaf5-mzym* qiu e tw5ry.4. rn.ar 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 s o:4oj n6vf,yrtarting from rest and accelerating at a constant angular acy v:f4rojn6,o celeration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hadz)ylr6qf . c5sf(tgi8yc p ;+s an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 2gu9+hu v+0v(w7t. k/fb cjld a0 rad/s decelerates with a constant angular accelera(7jcfa vt gbukl+0 dw.9 h+/vution 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 o5qsfl:t bb0g94l 7wpp l v(dr7f 6.0 rad/s while turning through 2.0 re 5b7(p t:vdrws9l47pql0lfbg volutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unif7 pqo y)2sw qni6u,ai:ormly from 8.40 m/s to rest over a distanc:oiw6ip)y u,q 7n2qas e 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 dcxe3kb97au1rz x5y u( own uniformly from 8.40 m/s to rest over a distance of 115 m. W(yu zc ab75k3e1r xxu9hat is the angular acceleration?

  A wheel of diameter of 68.0 cm sl* ,wy orz, 7q ap+r:eqc+a*xuvows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take f, *uxe+vow ,c7ay *q:zqarp +ror the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotaticma1jultp:id62g 37pi *dj ufc68w 0ional speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coti8lwjipjg6mcd1pu2 uf7 cd6 i 3*0a: ming 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 ti im phae z):my+-f0fq0ghtening 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 perpendicul0 +apm)hmq y f-:zi0efar to the wrench?

  The bolts on a car wheel jt1p:ozeg;h: require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required tjh z;:1ep:g owhen the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ir49 rlwh:ff a2nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as ak.)ddyqkq.r; );xav oj 6f+j follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia abf; qj )..v)ya ak;6ojkrq xdd+out the origin?

  A solid cylinder of mass 10 kg is ;(e0c/ i70l*puddxp0fr4e, bp ttsxcpivoted about a frictionless axis thought the center O. A rope wrapped around ccx*4rpx,fubs7de pt dp (l0i0;/t0e 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted a4k) .415kgqkbkn kf- 0uars zebout a 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 sek-nfke a4 q r)1.ug0kbksz54k ction 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 from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially heldbtocc835 nzy9 in the horizontal position, and then released as the free end is allowed to fall. nb8t53 oczcy9What 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 k0f) ;vr ;2kfg wwmlwv3cf55q hg. Neglect the mass 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 wit f5fq wvf hcwv3;l)2m;r wg0k5hout slipping?

  A 1.53-kg mass hangs on a rope wrappms0k ( )+ffsihed around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. ) (iss hffmk0+What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on 1t;r7nm0m8 (ni za9certy0)jq-kdub a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the a1e ny; 8czadk bqjn90()rr t 7m-im0utcceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requi uv z/sfbze7zjw2 n)cut/b):1red 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 i2j uj0)57;rgn1w( gfnxwphq ml,52z sdivof5nertia 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 kii +kmzw80rf x6 ym t9:r7telir.-h,and rolls without slipping down a 1.0-m high imhirtek l -,0ixi+wzkmy78 9tf.r 6r :nclined 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 of 10 +:w d h9m o*g8vucd5qfm/s. How high upo*5 mq +uw8 hcdvf9:gd an 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 an.l.us+tyc it mfqg+(* d allowed to roll down an inclined plane. How fast is it moving after drfq+g.+tlt .*u cm i(syopping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slip;m,97rq*sesa mqcp *( vz7xupping down a 35e incline that is 7.0 m long. Amqqpcx* ( s7smrv9 z;*a,pue 7ssume 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 mo5jq keo5bnc :r35wxo8sz6qi 8mentum 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 o1b,/t j8hscbmf 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 momes-j;ybv0yc ;y nt of inertiyysyc jb-0v; ;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?