The fan rotates at 100 rpm. Determine the moment of inertia of the fan if, after switching
The fan rotates at 100 rpm. Determine the moment of inertia of the fan if, after switching off the engine, the applied braking moment of 0.5 N * m (kg * m ^ 2 / s ^ 2) stops the fan after 10 s.
M = 0.5 N * m.
t = 10 s.
w = 0.
v0 = 100 r / s.
J -?
Let us write 2 Newton’s law for rotational motion: ε = M / J, where ε is the angular acceleration, M is the moment of force, J is the moment of inertia of the fan.
J = M / ε.
The angular acceleration ε is expressed by the formula: ε = (w0 – w) / t, where w0, w are the initial and final angular velocity of the fan.
Since the fan has stopped, w = 0 rev / s.
w0 = 2 * п* v0.
ε = 2 * P * v0 / t.
J = M * t / 2 * P * v0.
J = 0.5 N * m * 10 s / 2 * 3.14 * 100 rev / s = 0.008 kg * m2.
Answer: the moment of inertia of the fan is J = 0.008 kg * m2.