itsme24
Nov15-06, 12:38 AM
Ok the problem is:
Energy is to be stored in a flywheel in the shape of a uniform solid disk with a radius of 1.30 m and a mass of 72.0 kg. To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3600 m/s^2.
What I did was solve for the angular velocity through the radial acceleration:
3600m/s^2 = rw^2
w = 52.6 rad/s
Then I solved for the moment of inertia:
I = mr^2 = 72.0kg(1.30m)^2 = 122 kg*m^2
Finally I plugged it all into the rotational kinetic energy equation:
K = (1/2)(122m*m^2)(52.6rad/s)^2 = 1.68*10^5 J
The actual answer is 8.42*10^4, exactly half of what I got. I don't suppose someone could explain where the *(1/2) is coming from?
Energy is to be stored in a flywheel in the shape of a uniform solid disk with a radius of 1.30 m and a mass of 72.0 kg. To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3600 m/s^2.
What I did was solve for the angular velocity through the radial acceleration:
3600m/s^2 = rw^2
w = 52.6 rad/s
Then I solved for the moment of inertia:
I = mr^2 = 72.0kg(1.30m)^2 = 122 kg*m^2
Finally I plugged it all into the rotational kinetic energy equation:
K = (1/2)(122m*m^2)(52.6rad/s)^2 = 1.68*10^5 J
The actual answer is 8.42*10^4, exactly half of what I got. I don't suppose someone could explain where the *(1/2) is coming from?