Angular displacement is usually express in+bw0vp;0 kt qb units of

  Angular velocity is exprut4fn/tud zs1ehut0 . ley(./essed in units of

  Angular acceleration is99 nx(s,bbbefq/- + o+fkan tx expressed in units of

  A boy and a girl are r i pt9(:. qku(w0w7ooyq:srxfiding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is cquwrpfwi:yo (o qsk. (0x79t: loser to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning0b9o /: dprjcs48zlg*dk 2wjp1 pd,gr at a constant rate. The boy is nwp,dz 0jc o8rr1pbg*4 gljpk2ds/9 :dear the outer 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 whi*dxt)7jsmj 2b d6d4 myrvm,:och is turning at a constant rate. The j6yt*m:dd db4x7rj)s om2,mv boy is near the outer edge, and the 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 constant rate00tt lp x7l0v:4obb :xywr 1kv. The boy is near the outer edge, while the girl is closer to the center. 4 0t rlbx:lk y100:t vw7bxopvWho has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning +e+f es+y pgjq:6q h2tpmoc7qw0a:f4at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration? 0+qap m:e+pf4+f7jg6h 2oce wyqtsq:

  Consider a rigid body that is rotating. Which of the following e* 7bpdvl1 rxhq,5q6k is an accurate stat7 qvrx6h 5,b1lep*kdqement?

  Rolling without slippi:55u7//useicw ftgro ng depends on

  Two equal forces are applied to a door. The first force is applied at th20lsmsjdmb, gi p(9pl a/ n-r5e midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greaterg9m,l5 0a-nbl mp i/s s2p(djr torque?

  Two equal forces are applied to a door at t yauqqxu.r -xz+ f91aih8p(0khe doorknob. The first force is applied perpendicular to the door; the seia+r9 8zuq0q uk a.hx1yp-xf(cond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied tompio caaj7.hdj4/ j2z.v q 1l3 a doorknob, perpendicular to the door. The first force is twice as da.oima3p jj2 j .vc /hql1z47large 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 measureuu-1w, *fex hi w(x;qj an object's resistance to changes in rotatii1-w,uxex hjfqw (u*; on?

  Consider two uniform solid spheres where both have zjq0,k xh3-:xm mgv ;mthe same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia ism ;h : mxmkz-0vgxq3,j

  Two uniform solid spheres o .e kbo+;poh88r9uuphave the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inee8up pboh8r;oko. u+ 9rtia to that of the smaller sphere is

  Consider two uniform solid spheres whl0q apb0bq-k/ ere one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia 0qkbb/0lapq -is

  A uniform solid sphere has mass M a m ;emungl)oekx-9+ ,and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia abxmo+g ak;9,m n-eue) lout a central axis?

  If a constant net torq;zkzgeh:f ij 3 -za8k3c3o/gy5 qu6;xp. iczfue is applied to an object, that object will

  The moment of inerti :x 8;(hikjurya of a solid 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 has a mass ofkumda.3zq92 m0exc igk* l ;k( 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational .2megu0k;km ik( *39 cqa lxzdkinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphewobu() fle83 i38a1bj zrjhmvz 2vp-)re of mass M and radius R rolls without slipping down an inclined plane vvho e pbm1)lfi3uz3(r 88a) 2bzjw-j starting 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 slipping jny1arj)8 ye12dtbc) down an inclined plane starting from y)y8)tcaej1 1djn2br rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of; ysy/4ee(l t5b9 fx;gl9ooet igy 5v3 a system of particles changes when a net external force acts on the systemo v t(y g;ib ey5telsfegy95;ol9x3/ 4." This statement is

  In what circumstances can the angular velocity of system of particles chh 5s*y2wg )2 hbymesq )p6r. wurc2s:dange without anhqpc 2hb .) 5*du2emswyr :swsyg62) ry change in the system's angular momentum?

  The Earth orbits the Sun in cp qzh-gpqbj7.nl :4 75l1n tpan elliptical orbit. Ignore any friction which may be present. What happens over ti7pt1blh5g-nc.4pq7p q n lz:jme to the Earth's angular momentum about the Sun?

  The Earth moves about t(;po)c4f ql dtsz4t:l1vjus 2he Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of theo4vz ;4 1ss:d)qtt2f( upj llc following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hbv- ;9zirma/j rpbp (+is outstretched arms close to his body. What happens to hisv;b j ip9/rb(m -zpa+r angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) rc 9 + zu;yad8m:rg2hwby pulling in his outstretched arms close to hi+w hcu9: ydmgza8;rr2 s body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs. kllyc7u i/tbf *e .5zna;x-u a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to h /aux.yf tlz enl-cbiuk5*7.;is moment of inertia about the axis of rotation?

State the law of conservation of angular mogaq)3 hzyiw9,1 mvvg0 mentum.

  What arc length does the Earth travel in a three month period in il0jsz snm zf)q 9e64p-ts nearly circ j90z 4nlmszf-)pes6 qular orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does rs,yo/z h (lkfmgdn7hdw* /)2the tip of the second hand sweep through in 3 lnms,ghz / *kd/h( )dywf 72rominutes and 45 seconds?

  How many rad/s is 25 revolut siy)7tm jby, rol3kmq,cj,tt d0bj:c )/39neions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revo ophu vv9mn:b 9,:4gvplutions in 4.0 s. What is the frequency of the whe,9 nvvpovm9 u4p ::bghel's rotation?

  A pulsar (a rotating neutrofikev5 1n7 j*y* h/re.imhf4bn star) emits pulses at a frequency of 0.40 kHz. The period of its rot* *4 fmifiyevh k1nb/h.r5 7ejation is

  A phonograph record rotates at 45 rpm. Through wtm4 r 3rd8ar*jhat angle does it turn in 0.20 s?d8tr jrra* 34m

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on th 2qqbgv s1i8fif8rb85e outer rim move v 2ifqqb 5b1f 8gsri88in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions 4qclq9ylk e c twm/;8+in 4.0 s. What is the average angular sp+q8;/wc ety9c4lq mk leed of the wheel?

  A bicycle wheel rotates uniformly through 2.0ut-hibi5f -f 3sw4f l8 revolutions in 4.0 s. What is the lineau b34wt85fi i-lfhfs-r speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski rekcsjnmpemw 64-*4 oq7w4t ou0sort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip -s467*t4wn wemmo 0pqckuo4j in 12 minutes?

  A wheel of radius 1.0 u .y9s ub,z-xkm is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of ab. kzysx u-,9u point on the wheel's rim?

  The cutting cord on a gas-powered w2kw:3t)kdnwiilrp 2 3lrq-d- eed 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 the end of t3 wr3ln)w-rdtd-ki 22q l :kpihe cord?

  A wheel of radius 1.0 m is rotating with a constant anwc qipo -la 2;gpr5 37if f0g04om1ijvl,hx8pgular speed of 2.0 rad/s. 0iorg x7f-lq8v,i43wj0paic l2 h pp;gfo 15mWhat is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perime;3, jf/3*s8 aex agmld sgr.bzter of a bicycle wheel of diameter 3x.f; jzs8 bla/,sgdmre 3* ga70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circula)p gv) fk qs7iky3*f,nr, rotating space station (rfkyp) sf*v7, nkqi)3g = 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve oh.m)t vgp1 1qff radius 50 m with a speed of 20 m/s. The maximum centqm fv1g. ph1)tripetal 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 curv/ind lzk) (x+8b tr(tce of radius 50 m with a speed of 20 m/s. The maximum centripdcx/r n)8titl+zbk(( etal 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-;-.ac ph5e(5 imaizgrm string, is whirled around in a smooth level a;g.ie h5raimc-p5 z(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 not to break?

  A bowling ball of mass 7.5 kg anjx (rcb(y.t i*d radius 9.0 cm rolls without slipping 10 m down a lane at 4b yxci*r(j t.(.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 accelersgvig-t,2 dg1ation 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 accelerat(sampux,*fe 6 ion 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 rjav9 hsphh31(- s6z8,ugr+qm fe o 4peotate after starting from rest and accelerating at a9vu,3s8 j6m fzprhe-ha(1hp g+e q o4s constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an a+k8- in mxb4ji/hg 1kyngular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s dem-y0g4/mx0:;q usbt9fv/bx4y(wru) l kep l rcelerates with a constant angular acceleration ofw/b9p0xulx umrm y v0-eg;r/ k4(tfbq )4:ls y $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from reit iev;9 sf)f92w 8vbc89p rqest and reaches an angular speed of 6.0 rad/s while turning through 8w f)pr99vie; cietvs 82fbq92.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly / )w/k0 ycfi)q mcv8ikfrom 8.40 m/s to rest over a distance of 115 m. What isic8wkkq0/y v)icm) f/ the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8m5a;z, c3. j6nk6r wquke4pn x.40 m/s to rest over a distance of 115 m. We.xjpw z 5 6ma;n,cnq u4k36krhat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 1);hcigtqz6 a8.40 m/s to rest over a distance of 115 m. How aqi;1t6 )gzchlong does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotat tzq,f0ekd((aqtn6x 7es at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before comingdtq67 k (exfa(z0,tnq 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 requixg)f a( s7c3uhre tightening 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 ua)7xhf(c3gs is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm guip:n ki/,gqd y of1lwkpx8q /7w15 ;long wrench is used, what gp7wi1,g o8dxkwy 5/qn /lkiqu; 1f:pis the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inert1fa -k3o+ui isz*q+dn ia $3.00 \; kgm^{2}$ 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 ori cz4 zh9kdt)f;k5no*jgin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about tj9z ck k*hodz5 nt)f;4he origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionlemaqf;dp+ qr 5zel+:oog-kc 46 ss axis thought the center O. A rope wrapped around the outer radigl:qkq4; - 5mcdre poo fa6++zus $R_1$ = 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.o4rb1s,pp ds5w6ne 2.)gf qo qvv(wv thought the center O. A rope wrapped around the o5 6.(rvd2 ovs ,gnw .qebsqwpv op)14futer 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 initiaw wg4vu,lb )9dlly held in the horizontal position, and then released as the free end is allowed to fa ,)wgw4d b9ulvll. 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 1nmuue )t2p)kl qyy)9ain2 wac(ll/ 22 .5 kg. 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 achiev( )ik )u/ut)2allapl2 y29me wnyn2qce, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disc/0;kosl+w y ak pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the /;0+sk cywoa lpulley?

  A 1.53-kg mass hangs on0n z806ohq3n0jxlkn h qe( d+p a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acc0n0xqp nn(6d+3 8jh ezkoq0hleleration of the mass?

  A rotating flywheel can be used to store energy. If it is rel fzp)aupaxi/as(6h5*9bh( u9k yb2o quired 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 ine0x:(+9es-fw*xbftqw k 6n2j nt.ky dp rtia 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 andsq - hx8ukewrs ,:wn:46h6vsd 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 iu-:: wnk e6hqsxr s6w8hv,ds4nclined plane?

  A solid sphere of mass 1x (wi1t cgza9rk) n*/l.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up 9cknti/ (arl z*g)wx1 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 re bi tqz.pnr+aqsl 1261st and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical 6s21a rqnlq 1+zpitb. distance of 3.0 m?

A solid sphere of mass 1.5gb(063z 8gph 8u lbaur kg 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 inertia of a sphere lbz0a (6gpb8hgu3u8 r 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 momentum change/ wf jto(jezm3sa0 rbik:wt oj7 j:+.4s 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 ofcr f 1sh.:lhv: 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 v4vnigw :8g0d 5.00 rad/s with arms extended has a moment of inertia ofv g:giw4 8v0dn
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?