Angular displacement is usually express inmalrnr30y w :0 c1iy 6wp8xy;q units of

  Angular velocity is expressed in unic+c28 zvi(xs s6zol0its of

  Angular acceleration c ::r6mfl ded(pn7(0i(g mgqwis expressed in units of

  A boy and a girl are riding on a merry-go-round which is turniyb8j o jx*4 et*w:o-ting at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greae4io-ywt:j*t*box j8 ter angular displacement?

  A boy and a girl are riding on a merry-go-round which esa,s0- /pgde bbrj2*is turning at a constant rate. The boy is near the outer edge, and the girl is closer to es,0/b ea dgsbr2 j-p*the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-99 n:liof./gotlxg5b o pl5zjn2p4b2round which is turning at a constant rate. The boy is near the outer52ootln /og5j:g2l x l bb99f zinp4p. 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 turnl.1 fc1 b4gbqxob:ed8ing at a constant rate. The boy is near the outer edge, w8:xcbqd1b bl1feg 4 o.hile the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding ua,oa ;*zhb ylnk73r8a merry-go-round which is turning at a constant rate. The boy is nearr7yl*uh8z;o b na ,ka3 the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rota9ny6y7j h jf 3rs *ce)s+tg+la*vdg.dwkh 8( iting. Which of the following is an accurate statejyhg.a7er3 c k9t6ls n)+vds*+ihy*8dfw j(gment?

  Rolling without slipping depends oqah;p x9ut/2hv dq .p:n

  Two equal forces are applied to a door. The first force is applied at the midpot/gc8(( cn06 al cysjuint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exe(ts(6 0u jcga ccyn/l8rts the greater torque?

  Two equal forces are applied to a door at the doorknob. The firs 7l8 dd.vy0ywbt force is applied perpendicular to the door; the second force is apd0l8wb.vdy 7y plied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicularsqwwp :2y jp( b6czyn gp0v3)4hr ft:6 to the door. The first force is twice as large as the second force. The ratio of thegp pqbhvr036f:syw(ptnc2j:6y) z w 4 torque of the first to the torque of the second is

  What is the quantity used to measure an h1f7m urx+tum ,;3zry object's resistance to changes in rotation;m7 3tm fr 1u+hy,uxzr?

  Consider two uniform solid spheres where both have the samybx aq:9 x eb1(g0zdp6e diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the small6dg b9aqxe1bx0zp: y (er moment of inertia is

  Two uniform solid spheres have the sampbfurf o5;.:u e mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that o:5b; rf puf.uof the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass ;c5zam. v(dau+6t a; lrskm d(and twice the diameter of the other. The ratio of the larger mome;zt( 6rldc+ ;a5u(asam .k vmdnt of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has ma rf2ec8bi, bkcm 7a,x8ss M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inermf cke8,b 82acxri7b, tia about a central axis?

  If a constant net torq *exfkclyk4: zie*;8m9nq q .vue is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. If +qb1kmx4xg5lr/* e xf this cylinder rolls without slipping, the ratio of its rotational kinetic energy 5/mkxx x gl qe*41r+fbto its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 1a4 hkifw9ug+7kpd0fd9k, 2 cn0 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 the bike? Assume thecdpk a9kdw0ugff n+i9h 2,74 k wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls withouy-i*eotv t ).jt slipping down an incline.jev o -y)t*itd plane 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 s*)y+c0 ynzyrn lipping down an inclined plane starting y *rz+)0n yyncfrom rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes v9d l yj3kt4()seysjd 1/0 sbxwhen a net external fo 9 yyd 4(1)d3sjbv0/sxktsel jrce acts on the system." This statement is

  In what circumstances can 9ld m:y0bcf +1hdon) o pvzl.l6alk4)the angular velocity of system of particles change without aklz6 l:fn)y bap dld)m0vc.1hl9+oo4ny change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ign64g2p5 txmkfp+o1b z yore any friction which may be present. 6yztx1kp bm+o52 4gp f What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves qng , v/l6hm zdjwf (9ulf)u89close to the Sun, then which of the following best describes the orbiting speed of the8 unqvlu d)m9h, fg(/fzj 69lw Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hiw(sam: j8 j0qw)axm kllem-63 s outstretched arms close to his body. What happens to his angular momentum about the axis of rk)j3qx6mma -amww 8 :l0(lejs otation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outs;y:e1fxvde2 oq4 fel +tretched arms close to his body. What happens to his fd 1ef:l2o+qy eve4x;rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) byk/ w 3+nx6zfv4gl:wqg pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axisg6 knl+ gz3f4/:vww xq of rotation?

State the law of conservation of angular momeu k0yt5zp1 ys9ntum.

  What arc length does the Earth travel in a three mp p3zo3pfl a4(nfnnp65dv* u 3onth period in its nearly circular orbit about the Sun with anpld6von fa*4 5u3z3p pn3(pf radius of $1.5 \times 10^{11} \; m$?

  The second hand of a 02 tiu m;cs/unclock has a length of 0.30 m. What distance does the tip of the second hand sweep throug ut0s2uc;/m inh in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minuteo:d:m i hi,1ju equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whai 1:-bc*(krzbnf po4 5bc6cys t is the frequency of the wheel's rotation?(cbb1skrb 4zi y:*p c-fo6n5 c

  A pulsar (a rotating neutron star) emits pulses at a frequency of7,e i3ee 2lwvs 0.40 kHz. The period of its rotation is7e 3w,vei2ls e

  A phonograph record rotates :2ny2- lyon( xil fh(xat 45 rpm. Through what angle does it turn in 0.20 s-n(f h:lx ixyyl2(n2o?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outeux e 3- hwrjtzd3.)oe6r rim move itej. 3or)whex u 3d6-zn 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutionh0 ok)y*)q gvss in 4.0 s. What is the aver s0q oh*)vygk)age angular speed of the wheel?

  A bicycle wheel rotates uniformly thrc w*67zdy qm zt7bb.k)ough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 *b 7wk mqbdc6.ty7z)zm from the center of the wheel?

  A cable car at a ski resort carries skiers a distance 7ay3r.v frmni( 4xto 39gu,rgof 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 f,tmnoiu(rg v.y339fr rx47 a gor the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a conscsye+ f qo+zqr 4;fs,l./2 hdctant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheelc++ds4c/rs f2z,e fq.q;hl o y's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m ia71:p+ - f4cgsourdt jn length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of j ofducas:r4 1g+7-pt the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2ap jd0c-f.h zvo8ty0r (l5p4h.0 rad/s. What is the centripetal ac (fl 04h-tyajp.o0d5pzhc8r v celeration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on tc)dpp ml97 9az 8np*y1nf-mpche perimeter of a bicycle wheel o)za1mcmdn97p9lnf8yc -* p p pf diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating sp 1 hm omb.42eh*ew1knt2alq;wace station (r = 1wahme*kmbt2 o lh1 .w2eq;1n4 000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speeddbs e e/3 y j/wb,;+ 2ojv)dpvr-n:sjr of 20 m/s. The maximum centripetal force (provided by static f,/: 2+ e;-)n3yjv bs/srbde dpwjjorv riction) 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 speeez7hw +xn-29sz;d ,in e3xsf td of 20 m/s. The maximum centripetal force (provide2zn;hz+wf, 39sexe7t xsnd i-d 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,c9(b -ozevyhhm g8 8v1 is whirled around 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 not to break8 -z1c m(vgby98vh eho?

  A bowling ball of mass: scwsyk4229ja 3 puvbc7nb;m 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/sk pu 2yas c;2j3c 97mvbbsw4n:.
(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 anfb+mauxv d2)/j+ j3h ngular 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 anje h *e- z()in;)yb5-jb ziu qauf)hu.gular 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 0.erviho 64dyautomobile tire rotate after starting from rest and accelerating at a constant angular acceleration ofeodyhi406.vr $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angub 5;j w;dt*cqs6 tb,xwlar 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 with a constant angular 2je d p2va0g :0nckwr*kl:jz,acceleratwj0kr*pdg c,: a02 jl:vk 2zenion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and redj hru/fbpmu:: 4, vr)aches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the wheel?m4jdvr: )bpf r/:,uh u

  A wheel of diameter of 68.0 cm slows3knw*. rz8u mi.srf 1zpufa4/ 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 zs3.kr rm*u f z48a uwi.f1/pncoming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to 9lql5srw.ds0:2nmzikc qf ). rest over a dimqk.dq nw0flslc2i9)sr: . z5 stance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovw* 9 vlapxs(hdc:lc p:8bha.0--jnwrer a distance of 115 m. How long does it take for the wheel to come to vw-c(nxh-l:rp9 la:c0p *abs8 .dwhj the stop?

  A centrifuge in a medicdm ww5m +lg0 jhnk9fiu: :8o)aal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before comind95lo :0fwkiu8)mm hwga+:n jg 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 req1,.q:n3 igp z,qas6x. e: t5sk)jy j.zmy iigguire 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 ...ymgki,j:i6gxtnpq 3 :i ,zje)y5z1gaqss force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a tor9lti vmk6 hkk+lg*63d que of 90 Nm. If a 30 cm long wrench is used, what is the magnid lg6kk m3v6l+9tkh*itude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerf .zkcoo76h5:fwd) xt tia $3.00 \; kgm^{2}$ 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 thq5avqy- xb:g )hes/2 ze origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia avh/y-zqgxae 2:sq) 5b bout the origin?

  A solid cylinder of mfe:h 6po5t ad,e mk/mbxt: p/,ass 10 kg is pivoted about 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 section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. ppe:t 6ot:5aemxh,/ b,mf /kd8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless ax 1rw zyb2v3au h7au; axr-dakd/1t0.kis 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 section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does t 0d 3yzr/ k1a vud1rhawaa2.kx-7u;bt he 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 held in the hxin7d+r c(1us;pna)ttjnqgy 6+9 wq2orizontal position, and then released as the free end is allowed to fall. What is )yqr+tng;u 6pjct2xans(d 91+ qniw7the angular acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel r y9 iz.wvip1:ql1s1l:i 4m9ohl a(jfr5 mav(to be a ring of radius 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 spiwz.(omlahqlv ly54prs 9 9 ia(1ji:1vf:mr1rocket 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 frictsal6h.vgx9;t no cm*4x 8m7zoionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acce.ca 7 tso8hx*mzg 4nov9;lm x6leration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a f6ct g:.,snrht rictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of tttcr6nh s,g:.he mass?

  A rotating flywheel can be used to szhn6qol*g.3dg4 m1;c;ty e:w 2rp iwjtore 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 of ipl10il15em2 8km jpu.l,ao q/ 4fy jbjnertia 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 uh0w f488zwt8y -3/r dovs edlradius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined pla- 8 wte0d/w 83 8sodhul4vyzrfne. 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 s-,rzi-)s ;b dndp9 tiypeed of 10 m/s. How high up an inclined plane can it climb before coming d;iips d)rznb9,y-- t to rest?

  A hoop of radius 0.50 m and a mass of (qunzxu/6vqf)u 9 f/bkvg la76 j44qz0.20 kg is released from rest and allowed to roll down)a nzqvu6q6u 9z4jx fv lg(/7k4fb/uq an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 ;4ft; cq6nkm -xcd qebyi(a2: cm rolls without slipping down a 35e incline that is 7.0 d6y c;(kcxe tam-b4:2niqq ; fm long. Assume 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 momenxgsng 1mnv+ 24tum 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 of 7ks5ch c6k8aw$5.0 \; kgm^{2}$ 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 mok,8wer67mj p2b1 , u gtlivos:ment of inertia ofw8 t:, 7kosm61 e,jrpilug2vb
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?