Angular displacement is usually express ini ntsv: rsh8-5 units of

  Angular velocity is expressed in 4eoa9am05hg3*upv wf4c- w3fi oxeb ,units of

  Angular acceleration is expressed ingzzrtlg6 + l); units of

  A boy and a girl are riding on a merry-go-round which is turning-)x z(m4jmaicke v(7a at a constant rate. The boy is near the ou z-vkiea(xjc7 m(4 a)mter edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turjajo-)so* 4uyrif1- d ning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular spj4fsyo jiod1-r)u a-*eed?

  A boy and a girl are riding on a merry-go-round which is turning at a constantv ve6j,ogw6v; rate. The boy is near the outer edge, and the girl is closer to the center. Who has the g,ogvve 6w6; vjreater linear speed?

  A boy and a girl are riding a merry-go-round which is nokr- ;ixcn /1turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceockn rx;n-1/i leration?

  A boy and a girl are riding a merry-go-round which is turning at aa:jk /xmw5/ :efrr t.a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential:mawe/t5 f/ ak:r x.rj acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate hnm r(7 ;wppg sq)an:(statepnwsgp ()7h n;( amrq:ment?

  Rolling without slipping depends on, 3u0igss:kmf,u* r1 xt+jyti

  Two equal forces are applied to*1jf +i :nnuw7gzr7ur a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are apprin+wrg ju:uf1 7z*n7lied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door zljh, vsa-2kchm 56j-at the doorknob. The first force is applied perpendicular to the dzmj-h5l6a,c kj 2 sh-voor; 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,24,33 pk ;ywsbeekeht perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the23t hskwp4,ee ;kyb3e first to the torque of the second is

  What is the quantity used to measure an objecca60l k0poih0t's resistance to changes in rotation?i0a lco60p0 kh

  Consider two uniform solid spheres where both have the same diameter, but oneac- 4 sa7kc2 +bfltnc; has twice the mass of tcnf sa7t+; ba24 cck-lhe other. 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 one has twice the radius of ldz3/lpn a7)sq)r9ng the other. The ratio of the larger sphere's moment of in9sal)3 p)dq/rgzl nn7ertia to that of the smaller sphere is

  Consider two uniform solid spheres where one h-awz 9*n*auuca *-dhtas twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the*wu *n h*9c-a -dazuta smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M and,u9pwkkl 7t eg/o+2d d 3R, what happens to t ekk owtl2 d/7pu,g9d+he sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that objecd l:bigu e5tvt,y -up-kqh1b +*sdm 0(t will

  The moment of inertia of a solid cylinder about its ax n( dt/s;v hk 0.pce-wu:(vzke c/j)dzis 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 has k r *rn;vzydraa55*8z q0mqn3 a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kr8n3z05 armzk q*; vr5ydan q*inetic 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 h**/6syrol ivM and radius R rolls without slipping down an inclined plane h**6/lryi vos 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 withoutqxw597ud rqr 7 slipping down an inc7qquw r 97drx5lined 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 particles changes when a net externald 89nun63jfk f fjfnn u68 k3df9orce acts on the system." This statement is

  In what circumstances can the angular velocity ofll32;i g(vbux system of particles change without any change in the system's 2v(l ;xuil3 bgangular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any v(8k ceggnk0.iw47 d3vwfw0 rfriction which may be present. What happens over time to the Earth's angular momentum about the Sukw wce gfkv30n4 ird7(w. 0g8vn?

  The Earth moves about the Sun in an elliptical orbit. As the Earth w 6s(9bvsnb,e moves close to the Sun, then which of the following best desbe,s b6w(n v9scribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pullf u5)l6l1q qwjing in his outstretched arms close to his bodyq5ljfw1 6ul )q. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette m fl sosa15u*7pyfh d2bj5:zgq 7,e7u (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of 7u:1d 7hs5*s 5j a2,foygqb m lzfpe7urotation?

  An ice skater performs a pirouette (a fast spin) by pulli4b k /;) iyvkf;bim-vpm o.j7rng in his outstretched arms close to his body. m.v)7yiip/kbmo f 4-krb; v ;jWhat happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momenfy* bmkvs2.:t;*rovp;eq m - 7lsr fz0tum.

  What arc length does the Earth travel in a three month period in its nz0imj, ;mao(h early circular orbit about the Sun witojm0m(i;z , hah a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the -9q m nvkbt1)ok* qa4ctip of the second * kbakqqt4nmo -1)v9chand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions pe5 k x csr.tmk+wx7fxam0:6mk*r minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutilx.c:h4 m;fgd + 3bcuhons in 4.0 s. What is the :4bfclxhd m+;3hugc . frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of s:,+crs,4:h4tjuknf tpfxe1 0.40 kHz. The period of its rotationte: s+,t pc,:h4fjx 4sfrk u1n is

  A phonograph record rota5bz/pdedzz.. r72lw i8vwxd/m4wt:i tes at 45 rpm. Through what angle does it turn in 0.20 ti/w: 8.z 7id /wm4 2dvpr d5.zezbxwls?

  A wheel of diameter 26 cm turnsnz(z tq eg 1l/f)qij)/ at 1500 rpm. How far will a point on the outer rim move in)(1lezi/jq/ g )zqnf t 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions its1mui+( h8 yksc 3j8b5vd5idn 4.0 s. What is the average angular speed of the wheel?ikhs msic(y db+1j58 vudt853

  A bicycle wheel rotates uniformly through 2.0 revolutio:9 e)snz / m3ensepna0ns in 4.0 s. What is the linear speed of a point 0.10 m from ez9 asn/sem p:03)nenthe center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 kmxgmms3l7 6z3f . The cable which moves the car is driven mgm 3ls7 63zfxby 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 rotaizr7 (x*thof; ting with a constant angular speed of 2.0 rad/s. What is the linear speed ftz; (*ri xo7hof a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motorux 8rcjjip* 2: rotates at the rate of 20 rev/s, what is thpj 8u c:x2r*jie 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 rad/sa:0 u,w:ux xex. What is the centripetal acceler0uxu xw e,:ax:ation of a point on the wheel's rim?

  What is the centripetal acceleration ohbr 0d;dbo9;l f a point on the perimeter of a bicycle wheel of diameter 70;0b dhl9obr;d .0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, roqx0 ni2ixtolitx6+5 .tating space station (r = 1000 m) rotate to produce an artificiat02 x56.iioxiqlt +nxl gravity of $9.80 \; m/s^2$?

  A car is negotiating av27 cn6i ww29zpzmbp/ flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (prob /z 2z9vi76m2wcwpn pvided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circury h;47ivulu* lar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal forceu uy7l*4vhr;i (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 8g8gsf* xln(h a 0.750-m string, is whirled around in a smooth level table. If t8xh (l sgf8n*ghe 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 anvv9y)pchiv7+p*e2d c,( v n ftd radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s7 v,(i9f d+vpy)h vcce2*nvtp.
(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 conw97fw xanu7 t llp4e gx)./yy.stant 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 wi.t3 cg/jnh y+j 77y )t9dtm(qh/hngiith 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 0.300-m radius automq3frro7i s9+dobile tire rotate after starting from rest and accelerating at a constant angular ad+o rq 9if7sr3cceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratbe5d 1d t-mabd8 xm3r2)ja+ rxsgh,y5 ion 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 a6epvysu+on60ia omurea6 h 0 d/; we0.ngular acceleration of ms+ 6eeru0ev uaio0;po066 y /.wdhan $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while turninzwbjr0u6l7:p g through 2.0 revolutions. What is the average angular accel06: b 7jpurzwleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformlyigpow* * )w;baqwyj+6 from 8.40 m/s to rest over a distance of 115 m. What is the tot6 b* aoy jqww);p*igw+al number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cmbef:i/k bbyxb+) 7 3um slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is37) bubkibbxy f e+m:/ the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 mv np n y5((bih,qqz8)p/s to rest over a distance of 115pi 5,)pv (bq8y (nznhq m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rota ;te/*s 6w1.9odndakto bbu4vtional speed of 3600 rev/min. When switched off, it rotates 50.0 time tdvb9.1odt/wn s4o;eb*6ak us 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 torqk yhi*ud61s5+g ) jmq; vooawh.zi*i,ue of 90 Nm. If a 30 cm long wrench is used, what is thvaho;uy+os wh*dmjg.)z5 i16*i, iq k e magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a tmqp,9a35co geu p*5dvorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude pg9u,dq* ec3opa5 v 5mof the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia3bzo9( )zyei 5rc7ivc $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as-rdn x/nel/ 4t follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of tn//e xrld-n4inertia about the origin?

  A solid cylinder of mass 10 kg is pi8nv8/e1x i gghvoted about a frictionless axis thought the center O. A rope wrapped around the ohe/8 nvx8 gi1guter 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 frictionless axisfx, aodfgf2(1 thought the center O. A rope wgf(of1 d,a 2fxrapped 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 hinged at one end. The rod is initially held in the md19jf ncmdbs;((i* fhorizonta n (fm9dmji;1bcfs *d(l 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 ML2/3.)

  Consider a bicycle wheel to bbwr2u xb/a fu)mc3- p)e 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 achieve, assumingf - /xuwmcbbr23a)u)p it rolls without slipping?

  A 1.53-kg mass hangs on ah55 xcqv b1ea(a m:4xs rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is thsxaaqe xhv :mb4(5c 51e angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley ;6d vwkf xj 1yi6hl1d5of mass 7.07 kg and radius 66.0 cm. What is hldy6k6;dxfw jv1 1i5the acceleration of the mass?

  A rotating flywheel can be used to ba)1 *v8mmgo4 y .gnkmyu 95austore 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 inertiar2.q dh; neywds8xa :c; g(qf9 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 sp3xzf- egrzke9m) 9xdf a(8 s:tarts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of sxa9 -3mk :8)zfedrzpx9gef (the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls+kp rd x2cvu) :z-cvlq)tu+ h- with a speed of 10 m/s. How high up an inclined plane can it climb l+pdv) v)utc:- ukh2q z-+rxcbefore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and ob746r:vp lpwvwa mvv6l /.o1allowed to roll down an inclined plane. How fast is it moving after dropping w1p6l6m/ b vorvvw4v7pao:l. a vertical distance of 3.0 m?

A solid sphere of mass 1+q2hz/yo boz( .5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it q2(zyoz ohb/ +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 ch3zfzqotxf*o2 0 *zv9 danges 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 i4xvf(5skqh- 9etob5fqq r :whj 2 +p9cnertia 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 extended has a moment of in1 wwcx cdu+d ynev,4t9d*9kb2ertia ofdeyc4vt19w,bxd du wnck2 *9+
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?