The fan rotates at 100 rpm. Determine the moment of inertia of the fan if, after switching off the engine

| January 10, 2021 | education

The fan rotates at 100 rpm. Determine the moment of inertia of the fan if, after switching off the engine, the braking moment applied to it 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 Newton’s 2 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 speed of the fan.
Since the fan has stopped, w = 0 rev / s.
w0 = 2 * P * 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.



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