Angular displacement is usually express inr) -ai,z2 hmzz units of

  Angular velocity is 3ayis((z4 9u9 7vvvlh;x8wd wrohr0aexpressed in units of

  Angular acceleration is exprejhm 6dn, tbomii* b 1px84kb7,ssed in units of

  A boy and a girl are riding on a, +,4pbv96v f.f *afzxcr/nsja- dq 0jty yb3n 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. ad ys-f0 . v/9fcn p zjxrb,,jf+t34nabq6y*vWho has the greater angular displacement?

  A boy and a girl are riding on a mervxo9d 6adr t-4ry-go-round which is turning at a constant rate. The -xrt64v a dod9boy is near the 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 me(zuz 60 hp.j)0sxiy zsrry-go-round which is turning at a constant rate. The bojpxu .0 zz0 s)(ihsy6zy 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 cz/ gv/, +;:ad buqwcva merry-go-round which is turning at a constant rate. The boy is near the o;cwbu ,a:+v/gz/cv d quter 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 isahb9-kai:rm z-6 xl glc j+8x1 turning at a constant rate. The boy is near 9zglciar-1 -m l8a kxjb xh:+6the 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 p tj54:m7nhtfufjy+)j1t(ri an accurate stat7jj +y)j t145( ihp:ftfurnmtement?

  Rolling without slipping deperke8p : f) dw92on6km+ ktxn+snds on

  Two equal forces are applied to a door.1af0e k5plo:3w+g7jevup:k w The first force is applied at the midpoint of th l5kjpu ewf+p0:3weoka v g1:7e 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 the doorknob. The , kd r8vmjmr+-rrs: i1q6f3 cb2ugzs;first force is applied perpendicular to the door; the second force is applied avg31 ,2rsuqrcr 8mri-:zm;sjf6dk +bt 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the zt;ll b:1r;yt door. The first force is twice asb;ly :lr ;zt1t 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' 4u*mf; sh8hgys resistance to changes in rotations8m hugy4f h;*?

  Consider two uniform solid spheres where both h yke*ujz-1t*qvzwy c(,e -im:md.zt -ave 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-zuze:tdvy-- i *q zmyj*t(.m,1ek wc of inertia is

  Two uniform solid spheres have i8;n+tnenka*2nkpys 4p z 83 lthe same mass, but one has twice the radius of th+knayz4sn8i pp3n *8en t2 ;kle other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice thsg:/t8,:c8 4sif nbj 8fcts6u.gol bee mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of in /bssgt i .ctfl8g8soce:,j nbuf64 :8ertia is

  A uniform solid sphere has mass M and radius R. If these are increaseds7ito+ 1lgtvox wg0/* to 2M and 3R, ti*to0xs1lv ogg7w/ +what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wilcil :ogvf6b)kbh4n( qd3 kv 0n,.qt5yl

  The moment of inertia of a solid cylinder about its axis icvi h 3ek oh58mwoe+*+s 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 *l5cjs9 gm9sywhich has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energ*5 m9c9y gjlssy 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 R3kr,w,m wlh;:3dqalt gyp( ,q rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline dm3lg(kq;,r,q aw l3pyd , w:htepends on

  Suppose a solid sphere of mass M and radius R row9lnqrucl .n::8j3pglls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline nuln jw 9g3:.:c8qlrpdepends on

  "The total angular momentum of a system of particles changes when a net externalbysk /9h +syq8 forcsyhsk8+/ b 9yqe acts on the system." This statement is

  In what circumstances can the angular vq9)9e h g;dfvdelocity of system of particles change without any change in the system's angular momentuh9deg 9q ;f)dvm?

  The Earth orbits the Sun in an el,l.uao4 :4ovtdmicvi.)l 6 nbliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the ,iiab)d lntoco6mv4:v 4.u .lSun?

  The Earth moves about the Sun in an elliptical orbit. As t5oi,wbn)d f*r he Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about tifb*ro )nw,d5he Sun?

  An ice skater performs a pirouette (a fasxf g4i2j19ozk6 reyp0 t spin) by pulling in his outstretched arms close to his bodyg y469orzi0fk jxep 12. What happens to his angular momentum about the axis of rotation?

  An ice skater performsdhzsp3-4) .fn j/ ci6r3shzdl a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy .pn chf3 jz)hz34 d-iss/l6dr about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullingpz i.ay9dy75s in his outstretched arms close to his body. What happens to his moment of inertia about the ax7y 5.dpizas9y is of rotation?

State the law of conservation of an1 )e n2eyml5ouqd26o jh,id p-teso8/gular momentum.

  What arc length does the Earth travel in a thoa:b o 3uad/-;/oon3 jqdnvf5ree month period in its nearly circular orbit about the Sun with a radius a -ood/:3anuoo3bj 5/qnfv;d of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0(cj.78 f y44(szy:zj xdhala m.30 m. What distance does the tip of the second hand sweep through in 3 minutec:ly7msz4(yx fhj a jdza4 8(.s and 45 seconds?

  How many rad/s is 25 revolutions per minute equ rcvsg./hmy ,;ivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolu0 eydbuej j;rp (n3jts)/*; rvtions in 4.0 s. What is the frequent j nep* ue r;dy3;/0bjsjr)v(cy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Thewz(r rje+8j:h2 iy2u zk7c6nf period of its rota8ih :jr 2czk(2en+yj r z67wfution is

  A phonograph record rotates at 45 rplkeda ul1+ *)am. Through what angle does it turn in 0.20 s?1e) ak d*ll+au

  A wheel of diameter 26 cmll*u8o9vd0m7j:plu+cu h: t( at(ozi turns at 1500 rpm. How far will a point on the outer rim moud7 ll8hutv(+ pl*ojco mu ai t0::z9(ve in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What vd4q:-pibz w;yh(xj yxs n8au4. 6mw1 is the average an sz-x mpjyqwa(y4nu4vh .; bix1d 8w6:gular speed of the wheel?

  A bicycle wheel rotates uniformly thsi:rt8:d:9 vc o nxx0erough 2.0 revolutions in 4.0 s. What is the lix :9s8 de nx:rv:0tcoinear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cab7nbo0(v sz3or;1dsyqn 8 y)ncle which moves1( ovds)c r b 7yqz0;3n8nnoys 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 minutes?

  A wheel of radius 1.0 m is rotating with a o2rlc a7k (+lm+ub( beconstant angular speed of 2.0 rad/s. What is the linear speed of bll 2mc(k au++e7o br(a point on the wheel's rim?

  The cutting cord on a gas-pq)e owni)v/4j;uog -qowered weed cutter is 0.16 m in length. If the motor rotates at uenj oqvg)4 q;w)io-/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 constant angular speed of,l1m:i co j)r6j6zpsv2cg+ wu 2.0 rad/s. What is the c+ izcr2uc:l g o)vjm6p, w16jsentripetal acceleration of a point on the wheel's rim?

  What is the centripetgqk a/qd-n5q kkroa;w ;y1(r k0/gfh:al acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike k;:k 5 ;r(q fgqndkkg/0 yaw roqh1-a/is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotatiz+v a.n8q7w-git2poo,zan 0cng space station (r = 1000 m) rotate to produce an artificial gr v. , na0zogpzi8ano7-+wcq2 tavity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed1xh,ypn.5n ; gsspc8t of 20 m/s. The maximum centripetal force (ss;gy,nn1c p8h5.p xt provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m zdj:v+jimhqpy0t/:8 with a speed of 20 m/s. The maximum centzq 0j p :th/:v8djyi+mripetal 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,ejqo*j+21 b9q ,*ra + l1+qcdtsq 7zdduzpxr+ is whirled around in a smooth level tabler ad1 +lc1 o2qt+xq,jduqbzq dze*j*++97rps. 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 maszit8) ;unx/ua s 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3ni;uza8ux/) t 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 ac0tz4+ k;,gvkssml)z44i r xo gceleration 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 anglmrsr 0hodksju9goa/3 05(3uular 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 q-n*6squtc as cof:nur6 ):pafz58.jradius automobile tire rotate after starting from rest and accelerating at a constant angular acceleratioaoqf n .qcc :* tszjs p5)u6r-f68un:an of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an afd -xhjo82x b6ngular 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 with a constant ang vd:x 0h8ds7pe,pnh/sq 4p,c uxs.1kcular acceleration of spsdxd1pcp,/ns:8v0e4 7hh .c,kxq u$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 radt5dvmqje.fdrw *i0q6 ;r wy3)/s while turning through 2.0 revolutions. What is the average angular accelerm3qqwde *y0v;j) 6 trfi5rwd .ation of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovejh, 7.g) aub( fhvqn8i5sdkm7r a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?s.hhkdanuf8 , m7qv 57b(igj)

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to resthrg1+(0r ahfnt67y4gfzh p :a over a distance of 115 m. What is the angt6hr ha:1 rhag4n+z pfy(0fg7 ular acceleration?

  A wheel of diameter of 68.0 *n m 6xpn,ypqqt. *ef0cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the whe *q.f qtp0,6 nx*yenpmel to come to the stop?

  A centrifuge in a medical laboratory rotavlh)bn,c(68 o 8 xegxltes at a rotational speed of 3600 rev/min. When s6hob lxvc en8(,8gl)xwitched off, it rotates 50.0 times at 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 tightening to a torque of 90 Nm. If8.izq ipwr 96)bxt m/h a 30 cm long wrench is uswz8r9hib/p .qi )t6xmed, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. 9y6av:*fbz qj If a 30 cm long wrench is used, what is the magnitude of the for v:6 zfqy*jab9ce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iv;:dr ip xuj5 o o630fsharjcdgngc d 3*)q+),nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as foecuzb+59f3y qllows: mass m is at the origin, mass 2m is at x = a, and, mass 3mzub 3eyq9+ cf5 is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fru:8 64i aoz+av: nvws ,fgt0nzictionless axis thought the center O. A ropzn +ant :v8 u asw:z06v,igf4oe 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 frishz:-c .hw1uwbkoe+ - ctionless axis thought the center O. A rope wrapped aezws-b c-ho.u+ 1 hk:wround 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 one end. The rod is initially held i7n fcsthvi * 7croq38nz 9zvp04dsz62n 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 about one end is MLr9c7*fpd invz4nv3 h8s0zt7 zcso2q6 2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 9w8 nlc4trx atdv7h*-kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprockea vnx97dw8*lttrc - h4t 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 around a frdw9ly 0n1e5 izictionless disk pulley of mass 7.07 kg and radius 66.0 cm.yd 9 w0nz1ie5l What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk8 9wysnt*v hk tw37gz-s-x8bn pulley of mass 7.07 kg and radius 66.0 cm. What is the a 9ns*38g7k b 8vywt twxzsn--hcceleration of the mass?

  A rotating flywheel can be used to store energy. If +32mr.hp/v t5t xdyd 58r8mctclgo r3it 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 ine.rh4 *bx: gtghrtia 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 an89ckzgk(e 7(ant rxusmyj z )/e 3u38qd rolls without slippinzn 8xka 9rz3c(ye)k/3mjuu7qtes( 8 gg down 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 wit/ 94h hokgh3gdu:hp0eh a speed of 10 m/s. How high up an inclined plane can it climb before comuk4h/0gh3gde9h oh :ping to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allot18k+ p5zaul1v w +q7p0ppbjo ly(a0 bwed to roll down an inclined planu0by oq0p5+jpbal1zv a l78tpkp+w(1 e. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1agr:v52u :yuirw((gc+a y u6s.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rgwyru:+:ucy 62 aiavg5 ru( s(est. 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 momel:6km0pmrvw r( d ( znzp5x,g-ntum changes 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 on jqs6vf)ug3,f 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 ts)8vovjk1d2 rad/s with arms extended has a moment of inerti dv)jvo 18tsk2a 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?