Question

A wind turbine is rotating with an angular velocity of $180\text{rev/min}$. It comes to rest after $5\text{mins}$. Total number of revolutions made by it before it stops (Assume angular retardation is uniform)

Answer 1

Initial angular velocity ${\omega }_i=180\text{rev/min}$
After 5 mins,
Final angular velocity ${\omega }_f=0\text{rev/min}$

Since angular retardation is uniform,
Total angular displacement before it stops
$\theta =\left(\frac{{\omega }_i+{\omega }_f}{2}\right)t=\left(\frac{180+0}{2}\right)\times 5$
$=450\text{revolutions}$