Angular displacement is usually expre cm2a (xn nkmi7y-z7j-ss in units of

  Angular velocity is expressed in units l;b2k06gez5-; m krnu3rjh l yof

  Angular acceleration is expresse7(dh0a 3qoa-nvb 0rpar+ lk 0ed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant r1oj sekmg mec-70a22q q;u+p late. The boy is near the outer edge, and the girl is closer2+jkemaecqm o;7- gl1su 20qp to the center. Who has the greater angular displacement?

  A boy and a girl are rid7wlo4(h1 ucq3 oxx wl1ing on a merry-go-round which is turning at a constant rate. The qcl lo4(o113wxx7whu boy 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 merry-go-rounpoe :b308tsy hd which is turning at a constant rate. The boy is near the outer edge, aep08:sbo3 yh tnd the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-dw 7mtm4jx 2:y,+e3jty iwu0d go-round which is turning at a constant rate. The boy is near the outerm2due,tw 4w j:ti0 +yd73xjym 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 at6 /cj vwbbpo*0 a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangencp6 bov0w*jb/tial acceleration?

  Consider a rigid body that is rotating. Which of the following is an accuratzab ui;- ay ak/vhi(c;;a,cf9e statement?ivcy ,9a a(bu ;/-acizh;f; ak

  Rolling without slipping depen: o.q t;hu1jdvolh 82cds on

  Two equal forces are applied to a door. The first force is appliedkd*; (;36a frankcrtv at the midpoint of the door; the second force is applied at the doorknob. Both forces are3ka(r;*va ;t kd6 frnc applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is aeyma(h 18eu7x pplied perpendicular to thae7hx1um(y8e e 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 wb/qn2odglc1jf h);vmar( 9a ox/,l x*p: y0ydoorknob, perpendicular to the door. The first force is twice a2x)l jmwfn: a/y*vl y; h19odo(xgb,cqra0p /s 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 anfwf *c /2wn7twr-de9 p object's resistance to changes in rotationww wd 972e*cnrfp-/ tf?

  Consider two uniform solid spheres where both have the samblew 1 udlk v55;tk 2t0k5jv:pe diameter, but one has twice the mass of the other. The ratio of the larger momente05v kut llp5b2k w v:kjd;1t5 of 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.ciq0 5)wh2.yspxb2/aj;wu e dd,m w i the other. The ratio of the larger sphere's moment of inertw/);p0 dwm2eiwqa h d..xcjsu2 yib ,5ia to that of the smaller sphere is

  Consider two uniform solid spheres where l u2ic c9z6dq(one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inld(c692c quz iertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased thzf2k2 wv2. iyo 2M and 3R, what happens to the sphere's moihwz 2k2fy.v2 ment of inertia about a central axis?

  If a constant net torque is applied to an object, thatdc1 /eye5/nm1sok w9,rd pm7e object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. Iiwtt y l) 5hv9;)2d+pcixl(a mf this cylinder rolls without slipping, the ratio of i5(vpyw2a dihc9;)l )mxi+ lttts rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel y :v6ir/hy)ax of which has a mass of 10 kg and a ray: )/rh6xyva idius 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.

  Suppose a solid sphere of mass M and radius R rolls without slippfi(*8p.qvh ,ju:g p rking down an inclined plane starting from rest. The linear velocity of the spherevurj fg:k iq,p8 h(*.p at the bottom of the incline depends on

  Suppose a solid sphere of mass M and rad)rpv cf:qtt:6c/9k (qgvut n3ius R rolls without slipping down an incligf9tv:3v ut6/c):(qrcnq tkp ned plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of me(5t zj3:oqjparticles changes when a net external force 3:tz qjo(ejm5 acts on the system." This statement is

  In what circumstances can the angular vkzqjoc .:/wgqb n:j:0ljhc :j 0(cyf9elocity of system of particles change withoz/wc:: jonfg9jkjyqq.:l : 0j0 cch(b ut any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbitk pgc9rsv 7cp)4rtj,9. Ignore any friction which may be present. What happens over time to the Earth's angs v,)9j ktrpr4gp9 c7cular momentum about the Sun?

  The Earth moves about the Sun nqq ooonbb70/j:bu:,xkh 2n, 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 thxbhbjkboq, :: /0no 72on uqn,e Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchef*n-:lo9ieoi bs wnm *)w4la, d arms close to his body. What happens to his angular momentum about the axis of rotatio, i9o: bo-*swai l nfn)*m4lwen?

  An ice skater performs a pirouett:70jc-xg yim se (a fast spin) by pulling in his outstretched arms close to his body. m g7-:yc0sixjWhat happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast;qhvj);tfg tey*h0k*) ueu n ( spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the ak0q)*he tf;y*eu)tg (nhuj;v xis of rotation?

State the law of conservation of angudxqcopk.5r-x3b 6 h1t1o zxu+ lar momentum.

  What arc length does the Earth travel in a three month period in its nearl .:ciajh3crb(dsk ywry+69 -k y circular orbi+ jrad6 i wc y-sy9hrkk.c(3:bt about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 2q )d8z mww2m s5e w0+crmmw:l0.30 m. What distance does the tip of the second hand sweep through in 3 minurdw25m s+) mzqc2w l0:8mmwewtes and 45 seconds?

  How many rad/s is 25 rip qx,am/+t5ycw0fhyb.7(m :,fxhji evolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutionn1n)d+ f cpmc .:zq*tis in 4.0 s. What is the frequency of the nnqi)c*ct. d+1p:f zmwheel's rotation?

  A pulsar (a rotating neutron star) emits pulwpzkhdyc0+ h/a8++qdzs 7xu8 ses at a frequency of 0.40 kHz. The period d zp+kc7az 0s+x8qyhw/d +u8hof its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in(gp7qu uqn1(uzuy(e( c:bj r0 0.20 s? r (u(ne0bq(zq:7yuu(u cj1pg

  A wheel of diameter 26 cm tue ,aal9m.7 hwq2ib0jfrns at 1500 rpm. How far will a point on the outer rim move in 2.1 s jh27walm.0bqf ia 9e,?

  A bicycle wheel rotates uniformly -so; ihl3zh)qtok u,6through 2.0 revolutions in 4.0 s. What is the aqo ;sz6 lth)hio3 u,-kverage angular speed of the wheel?

  A bicycle wheel rotates uniformly thr2jgx0bfnmh 7u1dq/h; ough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center j gn 0/ub h;7xmfhqd21of the wheel?

  A cable car at a ski resort carries skijea,-z:jl* +asq f4qfers 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 minutes?lqa 4e+ f j:a*jz,-sfq

  A wheel of radius 1.0 m is rotam ar/bdod.lgy*/6 d 8uting with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wblyum/a r/ddg* 86 do.heel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m 8i,uht0 o3a eada)ul/.xno- min length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the /aoheu,i-l08a mnu3a. )txd o cord?

  A wheel of radius 1.0 m is rotating with a constant angular 3u.kv()uya8w6wkus dspeed of 2.0 rad/s. What is the centripetal accelerationwud 6.kay swu)(3vuk8 of a point on the wheel's rim?

  What is the centripetal acce uq n*21i*rv9bmkhh4nleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike irbqiu14 k2 nhnv9m**hs moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, roto1g8fm iiz ,y/ v(raz*c7t/ekating space station (r = 1000 m) rotate to produce an ky*7 iz grzt8f e vim,1o/a/c(artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curv f0uhl gw/k6*ie of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by s/hi6 0uklwfg* tatic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circu( 0t4hk y3twza;5ngl+ yin9mpxp0q2ej4h h 1 tlar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static hj0 etmnilp y 3+h 09tyk2t145 gpqw4xazn h;(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 around in a1e;skag 97zqc(.uia 8,x d sfg smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed ca97z,dsf8u;eqxk 1ig gcasa (.n the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slippm)e(ftn5c ; gbzlo/m) 4;eryoing 10 m down a lane at 4.3 mrgeml4n/b;( 5eo)) tozycf;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 acceleration tf2mll*a )c6b6m npz c8st(h3of $4.5 rad/s^2$. 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 angular acceleration ofn5wzk/ve ;zo + $4.5 rad/s^2$. 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 automobi(q99k1ug. jvu)sl lc5dnl q+rle tire rotate after starting from rest and accelerating at a constant a9.(udu csvq jk5 1g9lqnr )l+lngular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an az( o fqqe 9:bzy)9cjycsp *p6/ngular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at,bl6tt ; qpn *0txa;hj 20 rad/s decelerates with a constant angular acceleratinp;tbt*;,tah xj6 lq 0on 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 spn vf)kr+-y p8xeed of 6.0 rad/s while turning through 2.0 v-x)8rky+ f pnrevolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 u2+plecm: cf3m/s to rest over a distance of 115 f3p ml cecu2:+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 from 8.40 m/s 9nj+w7 zt5wld to rest over a distance of 115 m. What is the angular actw+ jlnw795z dceleration?

  A wheel of diameter of 68.0 cm slows down uni q/cl2z(ed by+s07kd4w 6ympsformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the sto47(ysd y6 kmc/sp w2qbe0+ zldp?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 a1tyl5* o0-r/ bizceufmr6- trev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before -mo b1 60 ty tu*/frleicra-5zcoming 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. If a h+kxa akpejk2o5lui8h+ 9;y8lup/ +t30 cm long tk opkeijyxk;lpu 9/a 8+a+ u5h+8 2hlwrench 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 tighr6 ko atkd85(ke1v fgulz07+ utening to a torque of 90 Nm. If a 30 cm long wrench is used, whad eukkk6o tf+7a 15ur0g8( vzlt is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i0f 87m( f;3eu3n xg/wkfbdapv3+ i vzdnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled an fs3e ;gb- t8)p gd/cfpo3ma9s follows: mass m is at the origin, mass 2m is at x = a,ac/dget8bfn 3gpo3-;)p fms9 and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted:a h fy/m eg0x(v39fwd about a frictionless axis thought the center O. A rope wrapped arm( fwxe/h 90gyv f3:adound 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 cylinder?

  A solid cylinder of mass 10 kg iskzsa u/5q6e1 x 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 = 0.5s ux/k165qez a0 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. The rod is initially held in the hmzmi e93 3w1qt9x(dl i2s 4yc(lxf8sworizontal position, and then released as the free end is al 3td3imsiwxf sw 189mc2z(xql 9yle(4lowed 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 mac9zk5,a/*z bi- +ipc, thqvzoss 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 achieve, assuming it rolls withoh,oz9t i5/cqzc -+zi,av kp*b ut slipping?

  A 1.53-kg mass hangs on a ropeb0jvv b9;vu;vq :e (vb wrapped around a frictionless disk pulley of mass 7.07 kg and rabv:vu jv(0e ;vq9bv; bdius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a 9mh:q+ox)9ehx9ut qsj p c/ qr lh4a,9frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of h9h9pq+o, :h)l9 xxre/t9 ucmqaj s4qthe mass?

  A rotating flywheel c37 redx*io:u ru(6 cz2e2zomqwvh7w3an be used 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 inw/5rs.8r1-cn m b6:-mxxhgm8 u ikulpertia 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.i 9y:p rlabg7g0,idwo 18vm m50 kg and radius 0.010 m starts from rest and rolls without slipping down og0ayw: i dmp7b g1i r5m8v,l9a 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 r/+0 jzzn99m5z w (io pmcyqxb,olls with a speed of 10 m/s. How high up an inclined plane can it clim zyz/9mmw,+ni9(pxzbc5 j0qo b before coming to rest?

  A hoop of radius 0.50 m and a v lx//ilc z6;mro,-sn mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast isci l//-ov nsxrz;6l,m it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without sljoo,k4* l:9 u ynylpp4ipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphekynjlp9upyo,4 4 l:*o re 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 momen:v vl0w o6:msrtum 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 orc6 wo1) f6t;3 u ry1jd(n c ,ll2(+kjbthbnokf 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 rotaef0 n /f+x5 ba nd()q:bahw7dating at 5.00 rad/s with arms extended has a moment of inertia oa0n:wb5xa(f7 /d efhq abdn)+ f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?