Torque and angular speed data over one cycle for a shaft

Torque and angular speed data over one cycle for a shaft carrying a flywheel are shown in the figures. The moment of inertia (in kgm²) of the flywheel is _______ is.

I =?

E = 3000 ×		π -	π		- 1500[2π - π] = 0
			2

T_mean × 2π = E
T_mean = 0
ω_min = 10 rad/s at θ = π/2
ω_max = 20 rad/s at θ = π

=	10 × 2	= 0.67
	30

ΔE = 3000 ×	π	= 1500π = Iω²C_S
	2

1500π = I × ω²_mean × 0.67
= 1500 Δ = I × 15² × 0.67
I = 31.26 kg-m²