Angular displacement is usually expr lm9s3 xfwwehyf.d56;j3g t8 jct-qi *ess in units of

  Angular velocity is expressed 5 gmlzxpqq d7 qx).nw/j h9y2e/yrb3-in units of

  Angular acceleration is 0z r2aessm;ruw*sk9(5 c:u x-nxlq 1 wexpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a con()jyu-+ 7j ddiz 5*fqtif en4wstant rate. The boy is near the outer edge, and the girl i)d-7i+tuf5zj dy e(j 4n fiqw*s closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-gm. 9f2tmwk 9qky4 zmh6o-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the g9m 2m9kqwf4m.6ztkyhreater angular speed?

  A boy and a girl are riding on a merrv gugqp /7xb5.31, siocipxh /y-go-round which is turning at a constant rapgq/ b1vs 3g.x x/ip5chio, 7ute. The 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 cd6lc zfxa 5/n5r4 jgp1onstant rate. The boy is near the d4gpjrx/az5lf c51 6n 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-go-round which is turning at a consto oz0 5bd;p;lbant rate. The boy is near the outer e5pzo d 0;lbb;odge, 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 ay79 amc 2hmfa.ccurate statement mya m927.cfah?

  Rolling without slipping dep udy04z13h.g29dqcac uz tzy*ends on

  Two equal forces are applied to a door.w h8f0ys7o+x6gnxwb3 The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which for6y+wwsxx 3n08fb7h ogce exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first forp vst ob(cag6quga6byyd 1p 2;6+2 a5hce is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which forcvb2ta6ago;yys qd (2c + g6b1hup5ap6e exerts the greater torque?

  Two forces are applied to a doork:r wn4ut/wv5y(gu g8enob, perpendicular to the door. The first forceg/w :85r u(yvntgewu 4 is twice as large 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 measure an object's resistance to changet mir1,j haa6,g .h;oes in rotatio6ahe goa1htj; .,,r min?

  Consider two uniform solid omcbr,)+dv6y+f0p hkspheres where both have the same diameter, but one has twice the mass of the other. ckb)p0rfvy 6+h+dm o , 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 onallp )98yno df9 )kv .p(-mkhbe has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of9.yakd8)kno p- f (hpm) blvl9 the smaller sphere is

  Consider two uniform solid spheres where one has twi3os q-6kr k9/3xs2 oqb; gscguce the mass and twice the diamet3gb3 gso-r qoxqsu;ks/9c2 6ker of 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 R. If these are increased to 2.u-8f / 2:q2tqg ryg+klw zofhM and 3R, what happens to the sphere's moment of inertia about a central axis f8u+f/qwytz rk:.2gg-hlqo2 ?

  If a constant net torque is applied to adfc93 cv.c+eyi o9jo9 n object, that object will

  The moment of inertia of a solid cylinder about its axis is given +q36p i )qorq:eo7m hbby 0.5 MR2. If thiim3rh 7e 6q)p oobq:q+s 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 hmug1mp *og*b -9hhl /rl pzu**as a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels 1*h zm9/pu-r hlbp gm *o*g*luto the 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 slippingpt4/jose ma64oui,n* - m0gzh down an inclined plane starting from rest. The linear velocity of the sphere at the bo ps04m /u 4onag*tejmo-hz6i, ttom of the incline depends on

  Suppose a solid sphere of mass M and radius R rop6yy,vt 2ss8olls without slipping down an inclined plane star ,vsp8yt6sy2 oting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a systeuia/wfv,m b5 5m of particles changes when a net external force acts on the system." wui, ma/fvb55 This statement is

  In what circumstances can the angular velocity of system of particles change wacpss6v 2: k;eby92wcmo 3io 6an8 -elithou3 c2v bpa;c:eiwo6kns 29-ey solm68at any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignor-t r)acyw0c uvz/by+,q0m c1je any friction which may be present. What happens over time to the Earth's angub 0z c,m 1t-/c0wyqvuyrc+aj)lar momentum about the Sun?

  The Earth moves about th1dv a jc 7m:m0zr rc,svvp)jsd9;, k:he Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?c, ms) dvzd0: rj;r:sacm 1h9,jvpk7v

  An ice skater performs a pirouette (a fa*1d )bmi u4 bo(ewvv ns6aby.;st spin) by pulling in his outstretched arms cv.b nd)iw1 sbo*;ubvyame46(lose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullnocdv+4 o1wd;w:jzt yww9; +e ing in his outstretched arms close to his body. What happens to his rotational kinetic energy about thw4+vo;oz w wy dn;9dwej1t+: ce axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstr6/nj+we a-ewd7*a tk z)quh8hnt3:x uetched arms close to his body. What happens to his moment of inertia about the axis ofx*8:ehu/7hnwjant6d-+ )etaw k q z 3u rotation?

State the law of conservation of angular momentumjq8-s.je1)d( d mxpnf4kw ;ht.

  What arc length does the Earth travel in a three mut9kz -5dc9p8rrae * wonth period in its nearly circular orbit ab9z9 c8puetrr -k* aw5dout 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 - 0/c b+qsy.4mfsievmdistance does the tip of the secos/m4y0+s imqc.fe-b v nd hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25(aduhh i.n7i 3 revolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whwi :;,dlzzv jy7h8 i* y8ryay8at is the freqy a8di zyw; :yrhj8yv7z* ,li8uency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at ju m3v.nykk ,7+*j ru t3uu)e2m2rfnva frequency of 0.40 kHz. The perik2kv. yu* mu j+n3 j2r fvr7m3unt)ue,od of its rotation is

  A phonograph record rotates at 45 rpm. Throo. 8; ntbs7a6ptm n+zek6ygd5ugh what angle does it turn in 0.20 s+y dz7.6k68mbt ptasgn no;e5?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will4rqdolnz7/- m g, ueg, a point on the outer rim move i du, 47lg,g/nomqr-ezn 2.1 s?

  A bicycle wheel rotates r/ys mzh2imh*7( 9( +sncfzmo uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of the wc7(mz ( 2+hs hmiyfzmr9on*/sheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions.* wl 9ojaah9-6q6orqaag,r*y ov4 li in 4.0 s. What is the linear speed of a poini q gaoawo-. jqr 964,v lhry9l*aoa*6t 0.10 m from the center of the wheel?

  A cable car at a ski resort carries yyt z ih7 n)x(ao,z3.gskiers a distance of 6.8 km. The cable which moves the car is driven by a hn7t) (izgya .o, x3yzpulley 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 of 2hsh7sok4a c .8.0 rad/s. What is the linearhc oa478 ss.hk speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.eshg3)p,af h sq(j:e +16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linearp3:ja she+h(gq )se f, speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angularl.z-f 7nlbb ka0: xe/k speed of 2.0 rad/s. What is the centripetal acceleratk.lb:0nb /zfk7l-ea xion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimet+ain.y.v gx1 ovs.)zc er of a bicycle wheel of diamet )yx vis+gnz.cavo1. .er 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station0jy0d8* rxbu n (r j 8xrud*0n0yb = 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat 1 oeu3o m:-nc4tzhz) bcircular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by z1to ben-: uz43m) hcostatic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat t;f)d*dj;g*p1ht oif kr9k8s circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetalsk; d kihrg81do)f; jtft*p9* 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.phn,y:)- uev8epm xa+750-m string, is whirled around in a smooth x)v,8 upp+mehyn e:a-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 break?

  A bowling ball of mass 7.5 kg andm(nrbak k0-(g ;a g/*8)r5deb cbpunm radius 9.0 cm rolls without slipping 10 m down a lane at 4./k)u-b;a0 (n mr(e8dnb5abc gr mg*kp3 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 accelerat(ned.o.3qq a(z qr no4ion 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 with2gi*xnu*(a * eg c9bsz 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 0.300t0 qb43-lyt )g( lpq bkv8wos5-m radius automobile tire rotate after starting from rest and accel(0-qk3q ptlbv8 swg) 5b 4loyterating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, lh0ct +f s 13prjj(,wdand has an angular 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 w*qu9 ht bsor (7ps6)xxith a constant angular acceleration obs 7xx)sq6*horu ( t9pf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of /x 9evta4jq2y6.0 rad/s while turning through 2.0 revolutions. ayxv92jte4q/ What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 p;; ,z9 u)mw3)zqc tk1mrmsh fcm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Whac9)qfm h wzpkm3m,urzt ;) s;1t is the total 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/s to rest ovefa m8.out*hzhf6dd+wc0 21tc utn) c: r a di1m8uz:dt c*)htwf+tdn.c 6a 0h cu 2ofstance 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 overv x18bt+8owl c a distwctbxo1v l+88 ance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600k/7moaq 6g/y g rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming yag kg/o/6 7mqto 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 y9n 9 f7;o q/flgmpw6zax0b 4atorque of 90 Nm. If a 30 cm long wrench is used, what is the magni a g0m/b4 w;fxn99o7pfzl6qaytude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel requ5g- .bkut- oz)3bs :y f7tgktwire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the fo5stg fy:7 -3t-k)k.tb wz bguorce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of8h(zq9 efipn :)o.xq e 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 follu03fx im. (cbb+i+ omp rots5.ows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of b spf.b o0+3ocrim5im+u xt( .inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought ,tau1f8n+ l8 pkwx-q q*q v-pythe 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 arounl - -x*yn81qapq+uft8pvwkq,d 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 10jvdx4i( es(/ w kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outis/(w j(ex4d ver 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 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. Td5ggbf: m7( bjhe rod 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 : bd(gm7fg bj5moment 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 gnafz9 1c0azo: ovh)o4pt )z (yci)4 0hcv+m lkg. 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, assuming it r: n)c1caz yc)tg(hz9op40v i )+ oomfhlaz40 volls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a friction2gv) bnty5b va0)4ryzless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelyyvn2zb v )r )g5tb0a4eration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fric80btt-ox;l3svung b , tionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration n-bxt u3to;lbv0,8s g of the mass?

  A rotating flywheel can be used to store energy. ,yi 6 7zbz4nuyq:up1hIf 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 inertia 0z(ho:69/ f:1(kwo qvb dnicnul kho0of $5.00 \; kgm^{2}$ 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 e,ny2lpg fz59; f7iqpfrom rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere fz, 975igp l2nqypef;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 speed of 10 m/s. vik .:r5xef8qjq: : npHow high up an inclined plane can it climb beforkn:q jx8r q.ip5ev::f e coming to rest?

  A hoop of radius 0.50 m and a mass op.bd ;n, s(zhbf 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it pzb .sh(d;bn,moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 sa1b bzstge9 yw+)+m 1cm rolls without slipping down a 35e incline that is 7.0 m ws+g1t1 ze)m s+9ybb along. 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 momentum ch0spjb i5wpb//anges 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 y1r)phda6bh r)k n59 uof $5.0 \; kgm^{2}$ 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 wi1ngq ;zgl-/s-hi qv e:th arms extended has a moment of inertia og-zqg;:eh s/n-vl1qif
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?