Angular displacement is usually express in p5.n7q-zsyca units of

  Angular velocity is ex:f.x)m8 pfv*p mup-kfpressed in units of

  Angular acceleration isbc07 ic fdi0c*4g nujvwqj,a+9moh46 expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning atiy*h w;( gfe+u a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greauh ;fe (y*gwi+ter angular displacement?

  A boy and a girl are riding on a merry-go-round wu*/,9r.f i-fsr*t6p r wmfgp(a igcm/ hich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater afpmrgr tp/,aui mwfg9( f- isr*c*./6 ngular speed?

  A boy and a girl are riding on a merry-go-round which is n w:/:y2l hj3btf7h b+swo ta.turning at a constant rate. The boy is near the outerl2hw jbha:. f:n7soy/t w+bt3 edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are um.-e4 838b a7c rmlg cj(wkjh.n7r kyriding a merry-go-round which is turning at a constant rate. The boy is near the bje w rncr lg8h3(m4ack 87.k.-7myjuouter 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 con c9towq1nh6 c-stant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration qwcc91htn- 6o?

  Consider a rigid body that is rotating. Which of the following is an n2u;n r8h 7od+0fxo: 06qqlax edzk ,,8gbxon accurate statementxkz aobu +6:dx7h2nnro0g e8,l8f x onqd0,q;?

  Rolling without slipping depends ot/8r-w3o;al w,trqn: v yx)y gn

  Two equal forces are applied to a door. Thyh: /ner1m k0de first force is applied at the midpoint of the d1:rm 0/dn ekhyoor; 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 appddad / 63uiy8 1ghry4v3c;oiglied to a door at the doorknob. The first force is applied perpendicular to the door; the second force i/;gi336yado4 vducgr8hi 1dys applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Them3) lzwiv3re q88y 3ls first force is twice as large as the second force. Th yqr e )ls3i8lvm3zw38e ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistpucsq q p.;7mjnw1xep/kn4*a1r-i3 qance to changes in rotatio p/34qap-qr nj wcxes;imq1 n.k1pu*7 n?

  Consider two uniform solid spheres where bhs h)*7n mb) ;.njjskroth 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 smaller moment of inerth;7sj)n kmjs*h )br.nia is

  Two uniform solid spheres have the same mass, but one has twice t rzt)tz00fq ;7ka ,khzhe radius of the other. The ratio of the larger sphere's moment of iz7) t,k fhzz0;rqat0k nertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the di9r-ov*yf-c2xqg iuy5 wy-2 k lam-iv c-y29 ruyyf* lw 25-oqkxgeter 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 raf8)u isvcfg /g;ka.j6dius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a) ic8uf; g6.jfaskg/v central axis?

  If a constant net torque is a h/7e 8l-s7baquia/h applied to an object, that object will

  The moment of inertia of a solid cylinder abacfx6c /-msmv39 juj3out its axis is given 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 of which 5. kmw thpuh( s(wozb+qzc 1js-xu+:x o1 u;k*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 the total translational kinetic energy of the bike? Assume the wheels are uniform disks.u*s11k h.st ;qu oz 5c w:( p+hzuxmx-(+wbkjo

  Suppose a solid sphere of msh v pyp;8fk-.c -)oggass M and radius R rolls without slipping down an inclined p h gps-ko);f.yg 8vc-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 slipping dow4x(z de.0e umin an inclined plane starting from rest. The angular velocity ofmdix(u .e4z0e the sphere at the bottom of the incline depends on

  "The total angular momentum of a syspzdw8+ kul(+t ,3rmbmtem of particles changes when a net external force au(t+l ,wp3+ dmrmb8kz cts on the system." This statement is

  In what circumstances can the angular veloc8p)5u x 2onruvy 6t/wwity of system of particles change without any change in the system's angular mu82xw /6)v ryu t5npowomentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore a/ukat/ tmm+oy7ef -;f ny friction which may be present. What happens over time to the Earth's angular momentum abk-t;ffo mmaey/7/ u+ tout the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Eartew 2zpyr0w4uv72o yh8h moves close to the Sun, then which of the following best describes the orbiting speedez8wvw72 42p 0yuryho of the Earth about the Sun?

  An ice skater performs a pirouu(vuk -q et,3gette (a fast spin) by pulling in his outstretched arms close to his bqgt k(ev3u-u,ody. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchedmj/4+ 0wuldy ;zp rwai1.r5h eh+gx xbjs,;q5 arms close to his body. What happens to his rotational kinetic energy about bd + jwxpl01gia.4sz;;eyx,5urmh5wqr/ hj+ the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulr rslqi ;wg)p 1fk,x/,ling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotation?1,/, pqiwsfl) krr gx;

State the law of conservation of angular momentum.9tr1c6 (prk gsr2i.kj

  What arc length does the Earth travel in cerm po+a8o wl:; ms+0:t(gnq iec x/,a three month period in its nearly circular orbit about the Sun with a radius o 0 c:8seolopx+c(,grm e iwam/ ;q+:tnf $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dis lc.u ;0 e7gfjis2 x+8xtca )eex4w4d7q;rdattance does the tip of the second hand sweep through in 3 minutes and xac + tteau lrdf0e7g4qdx;7 wxj4)s.8e2; ic45 seconds?

  How many rad/s is 25 revolutions p iurt m73o3.heer minute equivalent to?

  A bicycle wheel rotates uniformly through cz.;r 5iy*i/udukb ,u 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotatio/ rd5 i;*,b uuzy.uickn?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Thc5 -a9 hwebc*ve period of its rc c-v95 *ewabhotation is

  A phonograph record rotates at 45 rpm. Through what angle does it;-lbwftpmb fw-d gz8z d0/c4 . turn in 0.20 s?/ b- 4ff0 pzcblgdwdwmz;8 t.-

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point vzzm80e 0.,z o qc6:5fsrfzwxxgas,8on the outer rim mo: vzz8s6cfx,rsqgzo.50 exzm af,80wve in 2.1 s?

  A bicycle wheel rotates uniformly t/ fan f0;2avnkhrough 2.0 revolutions in 4.0 s. What is the average angular speed a;kn an/ff2 v0of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.+q-iq;6qg 7xwlo8hf v What is the linear speed of a point 0.10 m from the center of the wheellfog+hi qx7w6v-q; q8?

  A cable car at a ski resort carries skiers a dist 9 la-fszs)4hsance 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 s)ssfah- z4l9 make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a conswvsp ;1m3 pd1qtant angular speed of 2.0 rad/s. What is the linear speed of a point onp vq1 dp;s1mw3 the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m inaz1on()nr* pli z;yl 2 length. If the motor rotates at the n;)i lzoy1zar*p (n l2rate 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 w wid /zb9s:1 sfzex0iwko. m)+ith a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point x:bozfw91 zi0smdwk e/s.)i + on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a b8y;312bim mojow8tnq icycle wheel of diameter 70.0 cm when the mitby8 q3oj8mn;w o12bike is moving 8.00 m/s?

  How many revolutions per t e-w95egccs)rp h:2p minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an a5 c2re:9tw -ce)hspgprtificial gravity of $9.80 \; m/s^2$?

  A car is negotiating ayeq ;esp9dq/w-+mf n( flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stat /qm f;wq9ns-(+ypdee ic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat czbv g k;xj52*cf *(nt2 8/rsqudpz8 hoircular curve of radius 50 m with a speed of 20 m/s. The maximum c(sf *zhqn8 z;k* td2/cj5vubx p 8g2roentripetal 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, is whirled m 8dr e 2hog( ,(f7d0mr1qapiuaround in a smooth level table. If the maximum tension that the string cano(f 0d rpd(82,u a7ime1rqhm g 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 cm rolls wkkv n8zrm gv, /(dg5 j1n7yhxny +bz58ithout slipping 10 m downn 5 m8vyrzx+yn1(hkgjn, 8dbz/ v75kg a lane 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(xuo j1whhk6+ a constant 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 cx e/j(ky l8,la 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 radiueij.,g*gt*4og u )dlopk t0n7 s automobile tire rotate after starting from rest and accelej*pon .ti u og70d k,*gleg4t)rating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and,+)yo)s uewlv 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 witpj95 xp;fq bubs7c/( qh a constant angular acceleration of q95p/ b(cxfsj;b7q pu$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an xi v2n1024. qkkrn ;6h+ pymoisa4jv rangular speed of 6.0 rad/s while turning through 2.0 revolutions. What is;v2.+240 pii4h o6ynvrxkmkr snqaj 1 the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uni+ k;n+ynl5o3x2lm ostformly from 8.40 m/s to rest over a d xynkootl+ns5;m+ 23listance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly fron,dzk+t+ tjjbs8 4wzh.ud-+km 8.40 m/s to rest over a distance of 115 m. What i jhd8s 4 z t+b,ukzd.kwj+-+nts the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from .hizlw e;l/v2 8.40 m/s to rest over a distance of 115 m. How long does it take for the whee/l.lv;w zeih2l to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speeq+ ss+m:cik4 z:nby(id of 3600 rev/min. When switched off, it rotates 50.0 times ati:: kc+my(sb 4qns+zi a 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 tighteni; q5hd p:yti8*3uflv)c+bhyd s: bar1ng to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requ 5:qs8rhb+b adlhit;uv)*1f:pc3ydy ired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening tocjyl 0:k4. t0v jfk2lm a torque of 90 Nm. If a 30 cm long wrench is used, what is the ma0yl42fmkt. k:c ljv0jgnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inlu b7; xr9cuett,bb85 ertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows:rw o4snp3he vp) 9gto/b :cr3. mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia abou 4rp3gp:h.ocrot e3b vsn/w)9 t the origin?

  A solid cylinder of mass 10 kg i u+ sg0i4d6qfsw6tkb: s pivoted about a frictionless axis thought the center O. A rope:sbqwutgi d4 f6k+06s 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictio81a/dq7 i fmyynless axis thought the center O. A ropey 1aqmd8fy7/i 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 hinge(4+ )aqgv*c trh:eti gd 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 angular acceleration as it is released? (The moment of inertia of a rod a4(cvht qt:)e*arggi+bout one end is ML2/3.)

  Consider a bicycle wheel f6 + )xjxc)zejf y(h8uto 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 sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel a+f(fh86 e xyx)juzcj)chieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a ropeyy b );9t2cmay wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is b2 a;y tcm)yy9the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulxw jja+.a 1t+ pn;qj.ws20bnh ley of mass 7.07 kg and radius 66.0 cm. a+.njsn2j wwh; 1+ xpqt0.abj What is the acceleration of the mass?

  A rotating flywheel can be o s6oogon)5t9used to store 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 inertia of pdy 2sq7vrj,9$5.00 \; kgm^{2}$ 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 masse,wpvx 19*k:ya e /ot,rr nij,t7afc2 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down wa9,p*, fetj2:ce, x1ktravoi/ry7n a 1.0-m high 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 kg and radius 0.010 m rolls with a spew spydq 0t,8n2ed of 10 m/s. How high up an inclined plane can it climb before comdyn,qst p02 8wing to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is rel lv1 yhx,l.eto86w7no a99w ppeased from rest and allowed to roll down an inclined plane. How fa918p h,y 6wvl7x9oewp l.ntaost is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kravdn ++ ql-liur)u.0dwk +fm(,b/ec g and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The mome, lb+u) lc-vd(q +ar kew uin./fdm0r+nt 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 chasg y7j06(uk7uog7 eu) dp8yaenges 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 inermy eukvx0t10tc 0+z +m ee6-jstia 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 armw v 7ql8p5u3k n.gq2d1u bhxe3s extended has a moment of inertia of 2gql3k15 vu nqpuxd.ew3bh87
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?