For a certain engine having an average speed of 1200 rpm,

For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within 2% about the average speed. The fluctuation of kinetic energy per cycle is found to be 2 kJ. What is the least possible mass of the flywheel if its diameter is not to exceed 1 m?

Average speed, N = 1200 rpm
Co-efficient of fluctuation of speed

= C_s =	ω₁ - ω₂	= 2% = 0.02
	ω

Fluctuation of kinetic energy = ΔE = 2 × 10³J

Now, ΔE =	1	Iω²₁ -	1	Iω²₂ =	1	I(ω²₁ - ω²₂)
	2		2		2

Since	ω₁ + ω₂	= ω
	2

= I		ω₁ + ω₂		(ω₁ - ω₂)
		ω

Iω	(ω₁ + ω₂)	.ω
	ω

= Iω²c_s.

⇒ 2 × 10² =	1	MR².ω².C²_s
	2

where R = Radius of disc

=	1	M ×		1		²	×		2176200		× 0.02
	2			2					60

∴ M =	2 × 10³ × 60 × 60 × 8
	0.02 × (2 × π × 1200)²

= 50.65 ≈ 51 kg.