f1\' fignre skater goes into n spin. havrang her arms up \"nd else to lim body,
ID: 1786778 • Letter: F
Question
f1' fignre skater goes into n spin. havrang her arms up "nd else to lim body, illustrating romservation of angular moneam. In u ehesesroom desotustrstion of the above effect, a studeut is stamding n n rotating platform, which s spinniag with 2 rev/s The student is holding twu beavy dumbbells & kg each, veiginally tigbely pressed to his/her b t ody at a negligible distanee from the acis of totation. The student then extends the urrs horeontally, bringing ench durbbell 80 e froen the uxis of rutation. Assume the student (wsthout dumbbelbs) and the Platform hrve (ombinod rolntinnl inertia of / 8kg, mi anrl (inlilen the case of the ligure skuater) negloct che rotational inertin of extended arms. (a) find the original (b) fined the angulsr momentom c (e) find the Bnal !' (note: there are tao arries) (d) find the final (e) find the change in kinetic energy 5. A nietry-go-round on a playground haantational inertia50kg . ma and la spinning at w-2rad/s. Ai m-30kg kid hops on the platform. Im anay from the axis of rotation, with no initial velocity. (a) find the new rotational inertia f (b) Find the new angular velocity w An M = 2kg disk with R lin is freely spinning with w " 4 rad/a A ring with m = 0.5 kg, r = 80 cm is dropped onto the center of the dsk and sticks to it. Find the new (in rad/s).Explanation / Answer
2. given student standing on a rotating platform
angular speed, wi = 2 rev/s
mass of each dumbell, m = 5kg
final distance of dumbells from axis of rotation, d = 0.8 cm
moment of inertia without dumbell, I = 8 kg m^2
a. original angular speed = w = 2 rev/s = 2*2*pi rad/s = 12.566 rad/s
b. initial angular momentum = Iw = 100.53096 kg m^2 rad/s
c. final moment of inertia, I' = I + 2*m*d^2 = 14.4 kg m^2
d. final angular speed = Iw/I' = 6.9811 rad/s
e. change in KE = initial KE - final KE = 0.5(Iw^2 - I'w'^2) = 280.719972088 J
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