If a steel disk with diameter 05 m and thickness 50 mm accel

If a steel disk with diameter 0.5 m and thickness 50 mm accelerates at a constant rate from 0 rpm to 1000 rpm in 4 seconds (constant acceleration). Find the necessary moment.

Solution

Volume V = pi/4 * d² * t

= 3.14/4 * 0.5² * 0.05

= 0.0098125 m³

Mass m = Density * Volume

m = 7850 * 0.0098125

m = 77.028125 kg

Moment of Inertia of disk about rotational axis, I = mr² / 2

I = 77.028125 * 0.25² / 2

I = 2.407 kg-m²

Angular velocity w = 2*pi*N/60

= 2*3.14*1000 / 60

= 104.67 rad/s

Angular accelration = dw/dt

= (104.67 - 0) / 4

= 26.167 rad/s²

Moment = I * angular acceleration

= 2.407 * 26.167

= 62.98 N-m