Angular displacement is uskzidxw9; -:x5i v3w*kj x7wavually express in units of

  Angular velocity is expressed in units odlp yzq 77kh4oh 6nm+.f

  Angular acceleration is expressed in units o 2 s9sst3 ld4pnn7t0azf

  A boy and a girl are riding on a merry-go-round which is turning at a constku/1y7x-fxlp bqs+(d/ zg 6enant rate. The boy is near the outer edge, and the girl is closer tnk6p/z /exq1dfgb ly( +us -7xo the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round 2d8o8/xpyidl t 7: 7w8g9af os +bkupowhich is turning at a constant rate. The boy is near the outer edge, and the gi 7s7wp 8 ad 9f+uyi/t8o:kdo8oxp2gbl rl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round wnd qmkup 96a2q( ;on6fhich is turning at a constant rate. The boy is near the outer edge, and the girl is unpq kqo;26m6f n 9ad(closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-rounc0fh 6w 7yxgmi4 r)r;qd which is turning at a constant rate. The boycr)hf7y4x;mr6 gi w 0q is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-gqm.nnr+ .fgp0mt ,ufw4 :5bsvo-round which is turning at a constant rate. The boy is near the outer edge,r4:+msft fvbum p.g q05n wn,. while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Wht-15 w (0p )jzudc,y w :e4wzzddu)ihhp mji;1ich of the following is an accurate statz,dc)zmi we;w5w -h1 tp41 :dyi j( pdz)uuh0jement?

  Rolling without slipping depevnq:nfb,+r :fnds on

  Two equal forces are applied to a door. The first force is applied at d1 x*sde79 rts5c vr+hthe midpoint of the door; the second force is applied at the doorknob. Both forces are1ts9rshv r xddc*5+7e applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorkno zl. kh6kz+2que7e*tgb. The first force is applied perpendicular to the door; the second force is applied at 30e to the plan+ q kzh7elt uz.g26ke*e of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Thfk3ujy+ei +q1apo04ae first force is twice as large as the second force. The ratioy1 q fapiuj+eo 0+3a4k of the torque of the first to the torque of the second is

  What is the quantity used to measure an objecs.)vwp t)b 4oemy 2kg5t's resistance to changes in rotation? ek)st.g5 oybm2w)v4 p

  Consider two uniform solid spheres where both have the sgbj f(5f i7ul.ame diameter, but one has twice the mass bl.u 7(5jgiffof 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 twicemud2u46 x:jnj6oku *u the radius of the othekj 2um6 u4ou*undj6x: r. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twas2t- 6/zby6 jh-b an2stc k)pice the mass and twice the diameter o 2bn hzj26/a-)6a-pbtscksytf 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 R7:a:fke ybtxr4t( :ch. If these are increased to 2M and 3R, what happens to the sphere's motcx7 4(:: r:yaft ebhkment of inertia about a central axis?

  If a constant net todd+9is jft tc8v8q-sg 88h-cmrque is applied to an object, that object will

  The moment of inertia d1qhe45al6,c;uwl u 5zv h ,ptof 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 motorcycl nke,(2mzu .vzndh0fn:;lw-5ogb if 1 e of mass 150 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 n01nu e fo2:gv(d m5niwz;hlf.b-,zk translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without sl b*g4jgsvii,;ic;m :e ipping down an inclined pgsm:bc;iji ,e;4v*gi lane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M anldwq g/ w.p+8vd radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of thegw qw +/pd8.lv sphere at the bottom of the incline depends on

  "The total angular momentumb*iy v2;: 9u)ysuqyf b+hgn- q of a system of particles changes when a net external forcgb:yufn)*hb +;9-qvuy q2isy e acts on the system." This statement is

  In what circumstances can the angular velocity of .;vrccb nv: vy+ xn4nuv0.ly +system of particles change without any change in the system's angular momen .vrnycl04.ycnv:;n vv+xbu+tum?

  The Earth orbits the Sun in an elliplmizub-d:0yn* , p :xmtical orbit. Ignore any friction which may be present. What happens over xmbl ,un *yzm:p0:di-time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an e u;:njh3vg p,plliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the or;upj,3 :gphnv biting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outoc4p4+h why-ti9sid+ stretched arms close toi4+c o4i9thd+wp shy - his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (ox2cel n14 jzl+yxq--q 5e-hra fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about 4-qnrc- x +2e- e5hozlyx1lq jthe axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrehkb5jqm- 56 di0-b5yfhd6 d yttched arms close to his body. What happens to his moment of inertia about the axqkdbh 5db66d-fmyi5 j-50tyhis of rotation?

State the law of conservation of anci9oas,+x8zq8x gr y xp2(-bm gular momentum.

  What arc length does the Earth t : krzt0+4/u xcvh2zlcravel in a three month period in its nearly circular orbit about the Sun with a r2vc 0+4x/l:kzc hr utzadius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance dotb j 91p9 5d:/oznio8wxccc/wes the tip of the second hand sweep through in 3 minutes andcbc//oxnp98wi 51wcjtz :d 9 o 45 seconds?

  How many rad/s is 25 revolutions per minute ed h5dbm3 c27kadr7rj8 quivalent to?

  A bicycle wheel rotates uniformly through 2.0 r ql/gr8sce.4wo/,x yb evolutions in 4.0 s. What is the fr w gy8,.4xreoq bc//lsequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40:wrg 7mv 1vnrmazt025 8p.pnl kHz. The period of its r 1vr:ta85 vwg0p7mn.p lr zn2motation is

  A phonograph record rotates bn /-w4x9rs ufat 45 rpm. Through what angle does it turn in 0.20 swu f9-sb4x/rn ?

  A wheel of diameter 26 cm turns at 1500 rpm. )yz 83pixbq ums13x *7l djb5pHow far will a point on the outer rim movex7lyp)izp1b*d3qm8 3x5 b jus in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in xzms5a2e,ls( 4.0 s. What is the average angulams,z alx(se25 r speed of the wheel?

  A bicycle wheel rotates uniformly tjl9 f 0l*7q1nkecd5)nbo f k,ihrough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from*n7n e5bko9lc) j, 0f1dqiflk the center of the wheel?

  A cable car at a ski resort carrie0v * 4y 0yk+ch7 vjlk;iyapxz+s skiers a distance of 6.8 km. The cable which moves the c+k; h0 7l+ ivy*0y jkacxz4pvyar 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 in 12 minutes?

  A wheel of radius 1.0 m is r.e4 0uqtwj 8t w,s*yafotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's rim?4ej 0tyu,fasq*w8wt .

  The cutting cord on a gas-powered weedr;2z7bu h.czg3m wnacd96 8ij cutter is 0.16 m in length. If the motor rotates at the hi.zd 2ag;38j r ubc cm96zwn7rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m vg.p x9a w(b/dis rotating with a constant angular speed of 2.0 rad/s. What ivbag( .x9pdw/ s the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleratwx r58r )l1 4;+kd sdfekqok6jion of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is 4fr 5;)jqd kwxsok1k8l6 red+moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spacev2bfvi h+bf/.-l * il2kohs b+ station (r = 1000 m) rotate to prfofvi +kih.l2*b/ hb-s2+ vbloduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m9 f bfg1 ymj/i7dx+w1s7h;em c with a speed of 20 m/s. The maximum centripetal force (provided by static friction) i ym7jmid1h7bs ;/x1fe+g fc9 ws $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a fla pug4p0++q1 sdhqjrmec; vg 1+t circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (providp4mp1++j1; uqc vg sredqhg+0ed 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 aroundflhnaf:np-la r6;x3+kt 1 0if in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed -ll:+t 0rfip a36fnnf kx1ah; can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and 4 q,1o4bj ix2vtxizz 7radius 9.0 cm rolls without slipping 10 m down a lane at 4. ,1tixizvj4q4x7z bo23 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 anguy *ps5oaz7i1sh (m6hwlar 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 with a constant angular accelerat,wvqx:0icz 9p 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 ragll9k vfjx/ mf/ *3be3dius automobile tire rotate after starting from restx9jf3m3 l*vlf//kbg e 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 angular acceleration p/b/ z)g tde /b1iifb)of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotat+ m1nq4k6cmgl ing at 20 rad/s decelerates with a constant angular acceleration of klc 4qg6 1n+mm$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an an8b kg 3t5, f1dgtbil5jgular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of t gj,b3b ttgkl1f5 id58he wheel?

  A wheel of diameter of 68.o-m 4kg xk44bg9 3fahw0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in comingo h4f4wxa4kggk m9 -b3 to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rivhu 13vl.6khv sh,+vest over a distance of 115 m. Whatvh1+vsihh,ku v3l 6. v is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 l6br/hsyjppbdz/874 m/s to rest over a distance of 115 m. How long doe8hrdpy76bljsp /z/b4s it take for the wheel to come to the stop?

  A centrifuge in a medical labor2v*nmfl 9jil ilfvz6*h x 4,;oatory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleratio *ix 2l*f6n,4olvf9 mjli hzv;n 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 tightening to a torque of 90 Nm. If aq9jq2, v4qkkk8ib e)d 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular t8b vji q9)kq 4k2,qedko the wrench?

  The bolts on a car wheel require tightening to a torque of 90 N a2kf7gaue l8z-:a) hvm. If a 30 cm long wrench is used, what is the ma2g al-7v he f)u:8kazagnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in*,sbdp mjk+o.a6c7a prm9 z,zertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is model.l -6ruj m*s4r gakvy(ed as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment omarurv g-sy*6k (j l4.f inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought ukt s+:5 jumg.nhrmyhcc689vq;m 5(p the center O. A rope wraph:5 q6cyc5+9muhst 8 mj;m gpv(.knruped 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivo es(xgk(a7:z)qnp u1nted about a frictionless axis thought the (xqu)(sk7g a1nep :nzcenter O. 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 one end. The rdwyb*) l8h)l/gg bd:vod is initially held in the horizontal position, 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 g vb:*lh)bdlwd8/yg) one end is ML2/3.)

  Consider a bicycle wheel to be a ring of rad/iz)3wh81ra hy qa7q wius 30 cm and mass 1.5 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 achieve, ai3az wyqr1h8h7w qa)/ ssuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fricg; 1hn ; -dnmyhfvjd83tionless disk pulley of mass 7.0njhfhd;-dnmy v1 83 ;g7 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless jxfp)wi,,; rbe-(l zn5uinx4a*d 8 swdisk pulley of mass( fwx,jbnsrw l) n*a-pd8zi5;4 ixu,e 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is rj g89jre1see/xm: hx 2equired 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 inerti+ ehy99brk zh2a 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 r2fkbkyg2c aa6z bfu/+ d )6j4d /*wdrkg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it bd6*gdw6 cr+fzrfj )abk day//k422ureaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rollsm9q8,nfn-sg6jd( +n,tl w x r k3dp3xi with a speed of 10 m/s. How high up an inclined plane can it climb before comingxr xg d8n9 3j nnmq-(f+kds3p,,6tilw to rest?

  A hoop of radius 0.50 m and a mass of 0.4bjcrt4.w l7mb(e ka ,20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m? mtb4ra,blj4 c.7 ekw(

A solid sphere of mass 1.5 kg and radius 15 cm roxx m0j)a-mr3c lls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. x 0)xjc 3mr-ma 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 3g.n+ hcyuh a-momentum 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 inertt8 y7ujs k9qmn+lq95r i,ns *9e:dlbuia 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 ha jp5 x1/r gc8bz;lu5ppkb q5w8qus :h1s a moment of inertia ofu gqlxqp8 hpk1 sujp;/bbz1 58r:5w5c
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?