Question

The flywheel of a steam engine has a radius of gyration 2 m and mass 2000 kg. The starting torque of the steam engine is 4000 N-m and is constant. Determine the angular acceleration of the flywheel:
1. 0.5 rad/s²
2. 0.4 rad/s²
3. 0.2 rad/s²
4. 0.8 rad/s²

Answer 1

Correct Answer - Option 1 : 0.5 rad/s²

Concept:

Mass moment of inertia of the flywheel is given by:

I = mk2 

Starting torque of the engine is given by:

T = I.α

where I = moment of inertia, α = angular acceleration

Calculation:

Given:

m = 2000 kg, k = 2 m, T = 4000 N-m

Now, I = mk2 = 2000 × 22 = 8000 kg-m2

Angular acceleration of the flywheel:

\(\alpha=\frac{T}{I}=\frac{4000}{8000}=0.5\) rad/s2

∴ The angular acceleration of the flywheel is 0.5 rad/s².