Angular displacement is usually express in 6 a,3tdznmh nbr: 0*i2ih kus0units of

  Angular velocity is ubei7uk3 - 1icexpressed in units of

  Angular acceleration *ty-it- kz3 fgis expressed in units of

  A boy and a girl are riding on a merry-go-rop wblrk es. lu4oj-ks927.x1nund which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the pls2k.e4no s rjxu1lw79. -kbcenter. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is ta.qorno u )jp1 *bg(m(urning at a constant rate. The boy is near thpqg o am)(1on*r.ub (je 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 which is turninzde 9wy0c .r n,9on8xrg at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?n,n. e8xyorw0dz99 r c

  A boy and a girl are riding a merg c*pzmi)g4j( w rptd*s wry7- k8)gh0ry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Whor04 )dm hwrpggjwpyig *)zcs*8( kt7- has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a vg zcp2t )ve+w9iq b/-constant rate. The boy i)teb+9cpv g-wqvz 2/ is near the outer 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 accu pou r35 nhoia;c0newh7 n02u9rate statem0 uporc930uoh;hnaien7n 5w2ent?

  Rolling without slipping depocq ttss9 m);.ends on

  Two equal forces are applied to a door. +8wv+db2v uaj* -pq3vrv0 apm The first force is applied at the midpoint of the door; the second force is applied at the do-pm+d2 vvaauw3 8vr*vbj0qp + orknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The fio 3gqrlsvo+rk1*d:9: rw/q ac rst force is applied perpendicular to the door; the second force is applied at 30e to the plane of the doow3g rq+oqlk*o9 cvr/d::rs1 a r. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Thec))i edtd c108ooohw*. ezxe*1 k wd+,vynq 0s first force is twice as large as thkw.0c1 ywd0 * e+ )oqdvs),*eozhxn18citod e e second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's p2 dtr6smlut+5he4+ lresistance to changes in rotatio6p5s2++ t rumdle 4hltn?

  Consider two uniform solid spheres where both hs3fn2th gr- o )xvq(*xave the same diameter, but one has twice the mass of the other. The ratio of the larger moment * v-)2tx3 nhxfog sq(rof inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of t6 jc 9/tefm-rzrf(0 b3 xesu/uhe other. The ratio of the larger sphere's moment of inertia to that of the smaller sph3r0efts(urux/c 6eb-/f j z9mere is

  Consider two uniform solid spheres where one has t+8gl1gdm g jat.knj1ra 61kq9wice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller momr.k8 djlnmjk1ag16 q 9 gtag+1ent of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased t193t fq.aax iso 2M and 3R, what happens to the spher.s xfa3tq9 ai1e's moment of inertia about a central axis?

  If a constant net torque k.t6 uxnqdbk 4(ie g;/is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is gismyx5)e9n (mt2kly f- ven 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 ofkmg b 1m.a/st: which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic 1/gsma:.mbt kenergy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and rad19xa:4j b ujioius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the botto1o94a jjiu:x bm of the incline depends on

  Suppose a solid sphere o2z t;a1c/st le+ 7gfntf mass M and radius R rolls without slipping down an inclined plan/ nt7 s2l1ate;cgt+z fe starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular m5bju nkf4m*f) omentum of a system of particles changes when a net external fonju fkbmf45)*rce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles chanvi8nsa ; *7sfege without any change n ;a s87fsve*iin the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictih )5g+ otfv 5 izd1//rt5jfhvuon which may be present. What happens ovhfg /tj)z5 i5uv 1rd/+th5 ofver time to the Earth's angular momentum about the Sun?

  The Earth moves about tkrpwqib kin27*5h.4 whe Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of th*iwwn5kiq24k7 .hrp be following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a )jcy lo/j: ii98(p(wsx 3bf ;fu0i kuofast spin) by pulling in his outstretched arms close to his body. What happens to his angular momo byx8isw((o/kcl ;uj0uipf f 9:3)ijentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outs c9op-wcv9*y ..kl9hma tm7zq :oc wr4tretched arms close to his body. What happens to his rotational kinetic energy about the axis ol:at.y o 7qm9c z4rwkowp *9mcchv.-9f rotation?

  An ice skater performs a pirouette (a fast spinrn4vs1vm ohodd 2k*ft8 iy:;4 ) by pulling in his outstretched arms close to his body. What happens to his moment of inertia a8;d ny1:vh *kro2 dsmvf4i to4bout the axis of rotation?

State the law of conservation of angug r:e1 rxzv+c*lar momentum.

  What arc length does the Earth travel in a three month period in its nearly cv2xkxl mx888kpu3p 6z ircxukkpx v xpml682388 zular orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.3kn i 4xac;4vvu i*c-6a0 m. What distance does the tip of the second hand sweepc 4cnv4uk a-*6aixi;v through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivale8jzkpck8 fo 3+epu +)g;qwr6t nt to?

  A bicycle wheel rotates uniformly through 2.0 revolutd ,+ues;;mfy rions in 4.0 s. What is the frequency fye; s r,u+m;dof the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. t 9l3wva;fdo;; hgdg)The periavgo)ldw ;3fdh;9 t ;god of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn i d1h:pqyd: yvcfk1q 6;n 0.20 s?ky dc1q;v1yp:6fhd: q

  A wheel of diameter 26 cdg ym4:wj7o;) v*it5v /jqco sm turns at 1500 rpm. How far will a point on the outer );j j oqwytvm:*vgsi 74/ odc5rim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in7x wpr5lethzi at3+(,v *k.ct 4.0 s. What is the average angular speed of the whatr5zew*.itt+v7, (lc xk3p heel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0oxx. luc3sd 0+gckc)5 s. What is the linear speed of a point 0.10 m from the cenocdx)kgc3 5l+c x su0.ter of the wheel?

  A cable car at a ski resort carries skier1qko lbv2; rb5y1u bz qnp f2)8u 3j*frbwwf1)s 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 in 12 minutesrj*ubwwq qno3)pf f1urf2 l5b b yz2 ;1vkb8)1?

  A wheel of radius 1.0 m is roxmu8a:aln.)xhy 68fe6v43 ;uf w lemetating with a constant angular speed of 2.0 rad/s. What is the lineaxfl y 4x v.fe3ul6e8ae6w u;m:8nm ah)r speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length..(jdd 0 z9)q2t-eipfznmrx af q:1h0g If the motor ro-nxgj0d z.)ft9h:i01fqp ar d m (e2qztates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a co l )co,4y6zy)xv s)a;ahbqx n,nstant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's rioa;) ly6xbyh n cv)4,axs,)z qm?

  What is the centripetal acceleration of a point on the perimeter of a bicyccqh3 8xq;h- zjle wheel of diameter 70.0 cm when the bikhj8; hz- xcqq3e is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rj63dep oee3 y.y 09ykn )z(y8t* vgfeeotating space station (r = 13e)ye(otp.ve y0 defy9gz n6e38jk *y000 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 wic:fe d 8nr 80ju2pjj2cth a speed of 20 m/s. The maximum centripetal force (provided by static friction) is d:r2j jncej88 f2pcu 0$1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m with a speed oflab:u*d7 4dme bnxc0dg7,cy4hbj2 h e/kkj3- 20 m/s. The maximum cendjc bku4n3cxgebd-ayl *m ,/: 7 4k 02hjhdbe7tripetal 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 0.7(a as hh-boy-hbet*;j+ay2 +2ldif .q50-m string, 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 mab2oys +b -.-2hd ahhaie(q j+ylf *at;ss have if the string is not to break?

  A bowling ball of mass 2 5zc -gx w8u:t/b2t2eqcv ibpm7pmp+7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane a7b-b2 : w2v qcxmz pg2+8upi5tp/ectmt 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 ang,azmt 1w. rk+i.mzf- cewh48xular 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 wh l3ko:t ,e4qyith a constant angular 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 starting froy-m bj2v(ts;8e+ )im : fuepyi 6r*noom rest andmibe82tou: jnpor;(my vyf*eis+-)6 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 angularl *.)d4 jjvy6s fen (,l amf3z6gkf6gl acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerat7ez: j/ 2-cnojhsyr;les with a constant angular accelera7 :zo/r2 ny-js;lhcejtion 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 of 6.08vtmkza5j6(hdk ;7l0qw:n/ pzbo 6wk rad/s while turning through 2.0 revolutions. What is the average angular awzb thz6 dvop 0k6(ja8n mw5/lkq:7 k;cceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down ujo9gz*thnbr32x t 2cjc(62; hsyoo8cniformly from 8.40 m/s to rest over a distance of 115 m. What is the tota8gtonhy2x ;o jt9rcj3 (bs2z2ho 6cc*l number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/sj 7 du2c-+sjas to rest over a distance of 115 m. What 7sd+ a2jus cj-is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down nfw oc- 8dqsxg9 v uvk354 yd*;23ddphuniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for t cxqy3sv dd8hvg2ud*p;n-f 5 3d9k4wo he wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a )8 7cj*r6istwpyk c(q rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accelerari8 ( c6s7jyw)cqkp*ttion 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 wheeg*(omgm*j( o,kf il;el require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required whem (*kmog *oegj(;,lf in the force is perpendicular to the wrench?

  The bolts on a car wheel requ sal6g*n8t y:wvv)g+uire 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 applied *v vgnu: 8st+g )wlay6at $53^{\circ}$ to the wrench?

  A wheel with moment o d* m-jpkmk,vsz -+s9of inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as followsoite(8;27 vet- pcy 1k m0xe; cuhl:.* mfljlw: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. kmejfvwm7eu( 1t-oc;80ce plxt2ll ih *y;. : What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about arp*yu -:nf7i3uu6 kelv ru*r8 frictionless axis thought the center O. A rope wrapu*-y3uvu:k r r i86pu nrf7*leped 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 pivoted about a frcikh o 65ktmm:t:l6gwr 0g, t2ictionless axis thought the cent2l:wtr 5k g ,k6:mio6cm0tht ger 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 onhvg uu7wf/ 3;ne end. The rod is initially held in the horizontal positi/3 v7uwnu hfg;on, 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 one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. b8j-z 3sc c7bxy .wn8dNeglect the masb.y jx-nzd cwcb3878 ss 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 without slipping?

  A 1.53-kg mass hangs on nq ;ux kbctw.zi49l e:369jyqa rope wrapped around a frictionless disk pulley of mass 7.07 kne w 4;q.lui 3kb6 jytzcqx9:9g 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 disk pulley om2l9hf.ys(zpn86 v+ j nmydx4 f mass 7.07 kg and radius 66.0 cm. What is the acvnf2+my z. (l6yj ndsx h9m84pceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required y, pq;1( mgnj3qo4j*k jt8ov qto 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 inertia of wn1rr.janzzn(0x1d ,v/ats *$5.00 \; kgm^{2}$ 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 andybu (f3c i4/;8v1kr+ooqlhtf radius 0.010 m starts from rest and rolls without slipping down a 1.0-m higry8/vfu+i(b f q4;o1ctklh3oh inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kgcu4 ( kn9x6,m8 ngnjmu and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climbm6n98nj ugk x ,4ucnm( before coming to rest?

  A hoop of radius 0.50 - ;yjm ep/ rii/dunump0 r1v.5m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined pl50r//mvipm ni.uupe d r1jy;-ane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 3 hj(l* ct.l09 tz akyb:r4l agt7s,nicjb89akg 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 is givl 30aht:(abbtkjy4sn9 7ll9 zjag8* .tc ,icren 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 changes b4 avp8fs ;dl(ay $20 \; kgm^{2}/s$ 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 l/2am g6v gp4 (3vnvpy$5.0 \; kgm^{2}$ 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 7tn 5a6 .krhn(oho pz jbt,*e(arms extended has a moment of inertia ohzt . ,nr*o7kntbph j(56a e(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?