|May16-11, 01:52 AM||#1|
Angular Velocity, Momentum, and Kinetic Energy
1. A merry go round (1000kg) initially at rest with a diameter of 4m is pushed with a tangential force of 500N for 10s. Find the angular velocity, angular momentum, and rotational kinetic energy. After this, a little girl (mass - 1 kg) is placed on the rim of the merry go round.. Calculate the final rKE, final angular velocity, and what fraction of the initial rotational KE is lost as heat.
2. I used-
s = r x theta
F = ma
v = d/t
a = v/t
c = pi x d
angular velocity (w) = theta / t
angular momentum (L) = Inertia / w
rKE = 1/2 I w^2
3. By using the basic kinematic equations I got that d = 50m, and then calculated that to be 25 radians. I found theta to be 12.5 radians, and then using the equations found w = 1.25 radians/sec, L = 2500 Nxmxs, and KE = 1562.5 J.
For part B, it says to assume the little girl is a point mass- I am assuming she will decrease the acceleration because she increases the mass... but then I'm still missing time variables. HELP!
|May16-11, 02:29 PM||#2|
hi xobeckynoel! welcome to pf!
(have a theta: θ and an omega: ω and try using the X2 icon just above the Reply box )
the force (and the acceleration) has stopped before the girl gets on …
the merry-go-round has constant angular velocity both before and after she gets on, and you need to use conservation of angular momentum (momentum and angular momentum are always conserved if there is no relevant external force or torque )
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