Angular displacement is usually expre0* p cd/pbz4)l.mf52 x/owynd v*jvtgss in units of

  Angular velocity is expressed in units of6y yu0jxt*br +

  Angular acceleration is expressed i g dkqfyhd9 e ck4x092lmf52*on units of

  A boy and a girl are rf.r+on pu(zyq,cetd37gudp 43, e,mr iding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who h.t(3cpue ,pdrozgqfy, + 3dru7m e4n,as the greater angular displacement?

  A boy and a girl are riding on a merrypsnjmy a vix./-5)dq5 -go-round which is turning at a constant rate. The boy is near the outer edge, and the yqad5/m5 )js i -xnpv.girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding- 88n3v 1nnw;; cfk *ge8suxu qq(bkaj on a merry-go-round which is turning at a constant rate. The boy is near t;ncq8u -e*x831wsvb( kk8 a jgf;unnq he outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merryblukm4kmz-pre7:;f 5 -go-round which is turning at a constant rate. The boy is near the outer edge, while the giu p:7 r;em4klf zbm5k-rl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are nf /// tjc8sdsriding a merry-go-round which is turning at a constant rate. The boy is near the ou/jd/f tsc /s8nter edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate sq. pdx3h c0jy(tatem3 qd(0ycx .jphent?

  Rolling without slipp 5d//at wit+2nnya cfe0, zrl2ing depends on

  Two equal forces are appe7t+oiz*+p7oj : fpp xlied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular t:7po jo+pe+zx*fp7ito the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknooh 7c w;xwf6cff17 8kcb. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torckox1w;wf h fc8 767fcque?

  Two forces are appliee- tizu/3a6bkd to 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 of the second /bkueia6zt 3-is

  What is the quantity used to measure an object's resistance to ch(mz; k fz0uwp4yz6jxf-* s p/4d. nt uzi;7izlanges in rotatiop z;l (tj 7iyzzu/n0 4*wmuf p-.x4 z;d6izsfkn?

  Consider two uniform solid spheres where :-; zawhzak ,8 zttm3)tpo qh9both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the s h8 pz93zkat o,:twzqa-;ht)mmaller moment of inertia is

  Two uniform solid spher g/c0zmcoj+8lq k 2d:ses have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's mome:cms+ jgczd82q/l k 0ont of inertia to that of the smaller sphere is

  Consider two uniform sol2 lbnonkg/xcd vsm. w2;n( x).id spheres where one has twice the mass and twice the diameter of the other. T;.x(v nbgso.2dm2nlc w/kn) xhe ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M afeg2 / ta- m-klfye35xnd radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a centra/tay e- kfxlgf2-3m5el axis?

  If a constant net torque is applied to an object, thatq9(.p z3qya(h/br fa3 wlkcj 7 object will

  The moment of inertia of a solid cylinder about its axis is yykj8a4n, p7g bb0xo 4given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energygb7on0 8y4b4 jk,ypax to its translational kinetic energy is

  Consider a motorcycle od+e 1yr6r/fhck7jie 1 f 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 thdjkcerfe1/ + y16ir7h e total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping d.kedsd 8bw;l :own an inclined planwb8sldk:e;d . e 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 witwp-6 v w0vul4s) 2grzthout slipping down an inclined plane starting from rest. The angular velocity of the swp2v-)4l ugvwsz6 t0rphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles change tfth)+ g fn1n70ng x7ob;+uocs when a net external force acts on the system." Thifn) n 7gh1 ngo+xo+cf;u b7t0ts statement is

  In what circumstances can the angular velocity of system of particles c0gkb( :t hzz,)6zyluejhov 1.hange without anyhug6,j 1lzb: vh .)yet(k0zzo change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. I;ddotqm7uj/6 xo6 v3a gnore any friction which may be present. What happens over tio7/t;qa6 3vdu o mx6djme to the Earth's angular momentum about the Sun?

  The Earth moves abou p9a(4 qa5eutaa w5n3xt the Sun in an elliptical orbit. As the Earth moves close to the Sunuxw(ea3 qa5pa4t 59n a, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater perform7j) ih-oo4h7r v xf1xfs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotafv774x-f h rh1)x ijootion?

  An ice skater performs a pirouette (a fast spin) by pull*b; hwdeiz f1ro xd0rxaq-l if.)5 :k*ing in his outstretched arms c ewkd ihql0 *f)xx o*a :rzi5bfd;-r.1lose to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstreqa 7yauxb w-f7bh5.6 qz42lqn tched arms close to his body. What hqn-hu4.y aq q2wblx f 7z5ab67appens to his moment of inertia about the axis of rotation?

State the law of conservation of anga628l .o gj r r1kpcy5n34stumcsvz8; ular momentum.

  What arc length does the E/(inp:: 5 kf.l*ovp ry/ jqtucgz *qb. o;5ruzarth travel in a three month period in its nearly circugzu*t:vcprr .jo/yzn qp :k5bq5l(. /u; i*f olar 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 do30ctsln c* t, r.t2grves the tip of the selgtns v.0t tcr3rc,2*cond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revoluupwcrcct , ( b 9pm7un*,sgoodar;))7tions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatym ethk -6/3fd is they h/-3 demf6tk frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses pu 0vkk+p:(jk at a frequency of 0.40 kHz. The period of its rotati pv+0:u(kk kpjon is

  A phonograph record rotates a(x;)qkpf s7rx v+ipo-8kq ,szt 45 rpm. Through what angle does it turn in 0.20 ( q,qk7;s+ xsxirp z)fvo8- kps?

  A wheel of diameter 26 cm turns at 1 ,hltlnno ina d;5o8o /.g,*kh500 rpm. How far will a point on the outer rim move in 2.1 sih gnk ont,l.*,ona dh;ol/58?

  A bicycle wheel rotates uniformly through 2.0 revolphye,63 ; ddobutions in 4.0 s. What is the average angular speede od;b3d, hyp6 of the wheel?

  A bicycle wheel rotates uniformly th:7 :sb/p-n c.x+eta qshb 0a-hbqj bi8rough 2.0 revolutions in 4.0 s. What is the linear speed of a poisbj/0 epbhbcn7q:h8-sbi - +aat q:x.nt 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers4 as5jr sepw0xep8d12f (qvo oi5w dew:6.9xf a distance of 6.8 km. The cable which moves the car is driven pxsv1 j4eaodo0es5r6e pf .2w58wf q :d( 9wxiby 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 rotating with a constant angular speed h8r m2gnw7tt -of 2.0 rad/s. What is the linear speed of a ptgmhtr82w n 7-oint on the wheel's rim?

  The cutting cord on a gas-powered w ;o zgz847-1 jhdhcovoeed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate line7-ozg4;v1oh dhc8 oz jar speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rag/bbs 5p uyi:vb8 m9w y 8:xrt,af*jr.d/s. Whf8.9 b/u8b5vb:yapmgr * jxwyirt:,sat is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the per plv(qmr)r1 znh,s) 8fimeter of a bicycle wheel of diameter 70.0 cm when the bike is movin( rfhz ,v1srmnql)8)pg 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotat);3ie h6;u: nnkmos82.zqo ay tbla*j ing space station (r = 1000 m) rotate to producub a s62 zotnn;l:q.*e i ;o83hykma)je an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circq;x2vz p4rxlt-hg7ykea8m 5 4ular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) i gqh zm5;xar7v4 yt -kxe284pls $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m n+u fv9) (*kxzbrbfl3with a speed of 20 m/su(zk 3bf*bf x9)v+nlr. The maximum 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,oc,(o.44czdh .vx5kweas fo a7c j5n8 is whirled around in a smooth level table. If the maximum tension that the st,o 4 8wac4jz hn.fd7ocks.ocea(5 xv5ring 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 zu8ig;wkkg 3gq 5+zm2)yuc+x cm rolls without slipping 10 m down a lanugg2z8wmc3 g ik ;5+) uzqx+kye 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 conncb-: )9 yrvspstant angular 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 a0lnm yya/-;cnwj:wl nm1j/r- ngular 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 au6si5mbdzz ia z8c;16vtomobile tire rotate after starting from rest and accel85d;sci6 bzivm z6z a1erating 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 u69v+s +oygcaof $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatin/r:7a( k/o l ;tpxmutvg at 20 rad/s decelerates with a constant angular acceleratio :/ ;aluptkr( x/vmt7on 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 dbl)f,fdjsj+tz pxt -2f*)o:9k) neospeed of 6.0 rad/s while turning through 2.0 revolutions. What is the average anto9dk)je+l: p- d*z,otxffs2 ))b j fngular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8f-:8c ncvt xk..40 m/s to rest over a distance of 115 m. What is the total number of revolutions the whek v fcx:-t8nc.el rotates in coming to rest?

  A wheel of diameter of 68.0 axed.9myfi -* cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the ay x-f.9imd ae*ngular acceleration?

  A wheel of diameter of 68.0 cm slowsg x z7u2b*vb/k down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel tz2vu *kbxb 7/go come to the stop?

  A centrifuge in a medical laboratory rotogsoo :f-0w g:r1iu/6j bhk;lates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a :-go1 rook6jg;h:f s u i0wlb/constant angular acceleration 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 .*lgkmu,1-q k c(dyuytorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the fo-yk.yk(*mlu 1c ,qdu grce required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightenigmj*;8 f /abhwng to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of tgw;hjm fa*/8 bhe force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner* 8a zgy4uvf0gtia $3.00 \; kgm^{2}$ 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 origin, mas-d+b *)qvzo a cio:7tbs 2m is at x = a, and, mass o7a*bzvo +dct q:- i)b3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivote8xy zu+g u416e zu,dsid 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 z +eusx 8, 41zgudyi6uthe 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 k uvuqf bozexi7)8ds w2v.ekr042a:m;g is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m,8o47zvbsdqef vi02 muwkx ; )ae2u.:r 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 the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinni a4 j3b4uqnl syh,8y (ux):wged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angul3uai8xy4l uw) q,yh:nbjns4 (ar 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 rad ab/fv2h p,zn+hi89y/ +bp pee9u.mpmius 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, i h8e,b/h+/uz a m pmnb+vpefpyp9.92assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley/zjk .y/z*zsf of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratz.s//kyz *zf jion of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulle7 r( bfd.bq v8.wmnl3hy of mass 7.07 kg and radius 66.0 cm. What is the acceleration of (8hmvl7.d3b bnw rf.q the mass?

  A rotating flywheel can be used to sto yt/uklbvj+8b;n,i6 yre 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 ofumqs 1yj 5;j6t inertia 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 rest5i f.gwt7 d77tid(qnj-p.v ew and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphe7jtgd.5p7q.(w tw-v 7 fi iednre when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg au4 5wvb6/tku wnd radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming tobu6k4 tv /uww5 rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from res5/c7r su9u z /n2iectds2 /epkt and allowed to roll down an inclined plane. How fast is it movingzr2 7ntdsuiek 9 cu2//c5pes/ after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kgfu d 5:5yp6fuk/quouk b+)g e2 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 sphe gffu/5 u2po+ueb:y u k56kq)dre 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 c26h m-anvo9z.vmj 0 /3illnxjhanges 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 oftnoru;: k; oi,n1 ush: $5.0 \; kgm^{2}$ 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 armw+ ze8ido(4fr s extended has a moment of inertia o4efi8(w zor d+f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?