A Flywheel with a mass of 320 Kg and radius of gyration of 26 cm accelerates from rest to 750 rpm in
10 seconds.
Calculate: torque required for this acceleration
To calculate the torque required for this acceleration, we can use the formula:
Torque = I * α
Where:
I = moment of inertia of the flywheel
α = angular acceleration
First, we need to calculate the moment of inertia of the flywheel using the formula:
I = m * r^2
Where:
m = mass of the flywheel
r = radius of gyration
I = 320 kg * (0.26 m)^2
I = 320 kg * 0.0676 m^2
I = 21.632 kg m^2
Next, we need to calculate the angular acceleration using the formula:
ω = ω_0 + α*t
Where:
ω = final angular velocity (in rad/s) = 750 rpm * 2π/60
ω = 78.54 rad/s
ω_0 = initial angular velocity = 0 rad/s
t = time taken = 10 s
α = (ω - ω_0) / t
α = (78.54 rad/s - 0 rad/s) / 10 s
α = 7.854 rad/s^2
Now, we can calculate the torque:
Torque = 21.632 kg m^2 * 7.854 rad/s^2
Torque = 169.85 Nm
Therefore, the torque required for this acceleration is 169.85 Nm.