Angular displacement is usubq u1r*2dbrm365zso+/ t/i tpmsg yi +ally express in units of

  Angular velocity is expressed in un8 v9w rz,0t hb/f6dgcy/jk;f sits of

  Angular acceleration is expressrdftiu98(cy g.vpcf, 3g m3y7 ed in units of

  A boy and a girl are riding on a merry-go-round which is turnux-w5qgi- vq 7ing at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who hg -vqu5qi7w- xas the greater angular displacement?

  A boy and a girl are riding on a merry-go-roundeexujz,0w / s; which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the centez ,ujs/e;e0 xwr. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turnins w4iw7+r5le eg at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear 74iweel ws +r5speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant rasage*x(9 y/eujff n s5v0t1d. te. The boy is near the outer edge, w*1 n(es fa9 /s5e x0.tyujgfdvhile the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-72x ny) t,pn68ikcy xqround which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangentianxy yn)i76c 8tqk p,2xl acceleration?

  Consider a rigid body that is rotating. Which of t-0k+5y s i1wl wiq1j8piwgxqx0bb+k9he following is an accurate statem+-09 xypiw1iwqxs +1 ibkgqwb0l 85 jkent?

  Rolling without slipping depend u4nr ( m0 kl9z7cae(s68thfvms on

  Two equal forces are applied to a door. The first forcuw c6h0d+n9th6m lmzul 1 r/9pe is applied at the midpoin1rl+thzm6u / 69mw0d9 n luphct of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the9azyt )hg l. 7i+ db4w,wltr-q doorknob. The first force is applied perpendicular to thlwdi4)7g+wlzt ,ha 9tqy.-r be door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendiculbi orinbrtbft) 96/)7 ar to the door. The first force is twice as largi)b6)b9/binto7 rt r fe 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 mez*s7jx dp61butn pn 7i(+3fqiasure an object's resistance to changes in rotatioqjiu 7b dp1ift(x7n6p*z+n 3sn?

  Consider two uniform solid spheres where both have the same diameter, but one hcanyo 00u3 8tmcj9x( roi4+ dhas twice the mass of the other. tyixh(o4 c03o aucn +d0jr m98 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 onjdbr fx(c( o5(5tb j3we has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the j(3d t(rxj 5(5bfc owbsmaller sphere is

  Consider two uniform solid spheres w;c8f2tpjc u+ shere one has twice the mass and twice the diameter of the other2 8;upjtcfs+c . 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. s9fv xf+lnm)6e+g n8 nIf these are increased to 2M and 3R, what happens to the sphere's moment of inertia about esfl9 68v+nx+m nng)fa central axis?

  If a constant net torque is applied to an object, that object ibwf/mq f2*c t r9lvc zo5,x8i3 s+ad3will

  The moment of inertia of a 79ourwpuy1sm*n )ov( solid cylinder about its axis is given by 0.5 MR2. If this (o7*s 9vpur mo)wnyu1cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150ntxg)n;r 1q4xts s-b, kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratbt1xs, xgtn;4r- s )qnio of the rotational kinetic energy 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 radius R rolls without slipping down an injfg as-x/*q +xclined plane starting frogfxxa*j s-/q+ m rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and rf0ad6pb0 4b03oyff9lxwmu q8adius R rolls without slipping down an inclined plane s mb400lubf0wqf8 p y9 6doxf3atarting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a kn.9 3zsr8d).dl t nq*eckrxvyj4,k opl9 /0fsystem of particles changes when a net external force acts on the system." This sta*y.kxr,t zq9/) p0j 9kr 4ok8nvl sn 3cldf.edtement is

  In what circumstances cay9m2b9kdl,-8lkq ll biyqj7 ad -qe(,n the angular velocity of system of particles change without any change in the(72 elbl- -99i,d,bqldky jlkqayq8m system's angular momentum?

  The Earth orbits the Sun in an ellip:l9 mz: o5epjgtical orbit. Ignore any friction which may be present. What happens o5jg:zm l 9o:pever time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical ogut*2j) h hba3m3c )ocq:/l dbrbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting )/2*hblmqca3c:ojut b gh d 3)speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outre/2phzm 7*in( 1kypfraa 4g+stretched arms close to his body. What happens to his angular momentum p r2*f(aa r4e/gh zpmkn7+i1y about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretch7 th q;,0zgjtxed arms close to his body. What happens to his rot;x0t7 j, ztqghational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling5i)vxc e6a2 +5wsmuo q in his outstretched arms close to his body. What hap xcqmv65+aoi5w)2su e pens to his moment of inertia about the axis of rotation?

State the law of conservatio7x 5*gtbe9ytm izk8 .pn of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly ccvx qh7w hgrr,54tx/w 3)pm 4jirc7gq)hp/ xh cjxtm wv5r44r3w,ular 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. Wh j)2gjkr 2b0isat distance does the tip of the second hand sweep through in 3 minutes 0r2i k)sj gb2jand 45 seconds?

  How many rad/s is 25 rej-1c qfrtdge 2fo-h;l(b us -6volutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What i )uvi6a qn+mi(s the frequency of the aniq+ ()i6vumwheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0. 677,yujx ks 8rlcsec240 kHz. The period of its2xy7 jc8r kss7eu,lc6 rotation is

  A phonograph record rotates at 45 rpm. Through what ang0wadn;n/)m5d9 9 njnilvq*v fle does it turn in 0.20 dqa ;il/5n) nw*n0vmndf9jv 9s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outerf+t yohp b,; wpid2a;)w7:i+idmt 4d d rim7p:ia+tiwh +ofp4d ),t byd;2dw;m id move in 2.1 s?

  A bicycle wheel rotates uw spvwk7 tqzb h+7u 4w2*:eeo6niformly through 2.0 revolutions in 4.0 s. What is the average angular spee77q 26s*owe kph: t+uwvwze4b d of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is+ ozf-jws/d*a the linear speed of a point 0.10 m from th wd +ajo*f/z-se center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6 obd 9t959ols(y nba3s.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 the9sy(obod9n3s tba5l 9 cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating withuia1: c w tumby; tg*4dw,gsz227:djg a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel'suwdia*4 m,2 1t:z7bcwd2:ugggs ;t jy rim?

  The cutting cord on a gas-powergj8axa,mo ( l8ed weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, wh(m agx la8o,j8at is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 r;5tvo/. +j/v(v 3c,xly s(gqkodi tbn ad/s. What is the centripetal acceleration o svjy+(k /3(tb;lotv,nigc/d qo.xv5f a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a biv3s sr)hh )f.mvt p,xsohg)6) cycle wheel of diameter 7fr hg3p)v),6. xt)ohs)h v sms0.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circe1j a1gokpp; + op.,g/-y,bqa7 erpypular, rotating space station (r = 1000 m) rotate to produce an artificialregp yppy,bp1k1+peajao-; o /. g7q, gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed qjx;,g :sicsa nz902u of 20 m/s. The maximum centripetal force (provided by static frin :9,zx cssgju;iq20 action) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circul4 p3 rwgjdy :1o9+qvgpm 7g+(owwj)vyar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal forc vgwm3qvdgj(yj+p:7oo)w9 p4ywg 1r+e (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 en5wct; ir1hb;yshfu6 dosmg.;u i th3xr7 k,+9d of a 0.750-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 linearbi5hdy u x;sk;.w mu+t3c,gr;sft 917 oirh h6 speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and ra 86zl6:pecad adius 9.0 cm rolls without slipping 10 m down a laned6lc 8ape6 az: 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 constant angular accele .vtq3b-exs.rration 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 coxva5 .7-sl ln*-pwe uqnstant 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 startiiv+;9j r k7an7tz .kaing from rest a7;7z rk 9ta kvij+.niand accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at resq3j/zlx gtb2be v/k -zn5/egn :54mlh t, and has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating ubsctsxd, / 3j1hzd17at 20 rad/s decelerates with a constant angular accelerats 1bu,3zsx/t j7dc1d hion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angularpw:8qarq-;:tg wj*fl speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the t:qw-j;:8qf ra g p*wlwheel?

  A wheel of diameter of 68: jb s): t fx- 4kmngh4wdcs0wv3h5qz lh.)v;w.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions thevw: hs) lw;.kc:nh )zvqwt4 g b0s-m453dfxhj wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unis tikq m:k8m*jw;hm3gm 2a fr5h)e0*hformly from 8.40 m/s to rest over a distance of 115 m. What is the angular 2k mamhw :5h)3r g0kfmimjhq*8;*e tsacceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to 7g k96cmfd nhn6mep(e6)/ q rhrest over a distance of 115 m. How long does it t67)hpm9/e 6qe cnd6 hfrngmk (ake for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotatesj2ovrnb1w 5wl .j+p3n at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to l won+b5j.n 23vjprw 1rest.
(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 tighten4.2/r zag u xjb5)qvwi )u9qdying to a torque of 90 Nm. If a 30 cm lo g49)jau 5q.xr yiu)w/d2zvqbng wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighteni:51 zlqv* m )tmag23) bodj4iweb2c ting to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requi j2 a4qibgw)lmtmz :t)dvc2e53boi1*red when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o4 yq6k;x p n5oja7ks9 uwjw9rbsas:6; c)ud5yf 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 follows: mass m 8t9u.iffh gmsmb2: n8 is at the origin, mass 2m is at :9 f b2m8fsu8.mhigtnx = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg i 51 ;4zzzuq x.dsr0 bjmmgc.y4*dda;uuk/a9b s 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. 8-1.) What is the angular acceleration of the cyli0 ;.daq mj4cgr *a9.x/zmys1z5; bbuudd k zu4nder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless a +)8dr+pp by aquh.d/sxis 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 the cylindeh8p u)brd+qpdsa.+/ yr rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged ic: h1/nn hx:yat one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is then xy::hc n1h/i 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 3usj0:v j q8;hi0 cm and mass 1.5 kg. Neglect the mass of the axle and sprocij:sv8q ;0juh ket. 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 a rope wrapped aroun l;kl 1wv(8 o6xmj9ybxd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratiovw16l (9o8x xj ;mklbyn of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless dx-*39 odo4)xe e fzqlaisk pulley of mass 7.07 kg and radius 66.0 cm. What is the accele lzx3oqea)9-ofx 4*deration of the mass?

  A rotating flywheel can be used to store energy. yn +v8 g+gd01r jyc7y/)bzqo oIf 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 bh09nq 1r s5gminertia 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 rest and row* 8du bnsrw;+lls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom oru ;8ws*dbn+wf the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 1c-jqkpzdau8n md.*1)0 m/s. How high up an inclinezpm.jc k8n *)au 1dq-dd plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kn wak(n80w+w.p. ,es qt/oieng is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3pw8 tikw/no. we(,n qs0 en.+a.0 m?

A solid sphere of mass 1.5 kg an -+ ez54zynobtt8a 3le 4jdbx+d radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it xn z5eleto4jbty4++ 8zb3- dastarted 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 cy1 tzcc7,gr*lhanges 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 :89du;k )eb1jl2 hgfbc /ndduof inertia 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 extermsov*o:ur(1 q6ngl)-* rsv onded has a moment of inerti)r n o o(16slv*g-uovrq:sr*m a 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?