A dental drill accelerates from rest to 900 rpm in 2 sec . What is the angular acceleration ? How many revolutions does it makes in coming to full speed ?

Explanation

Given `omega_(i) = 0 , omega_(f) = 900 rpm = (900)/(60)` rps
i.e. `omega_(f) = 15 rps , t = 2s , alpha = ? , theta = ? `
We know that `omega_(f) = omega_(i) + alpha t`
i.e. `15 = 0 + alpha (20)`
`therefore alpha = (15)/(2) = 7.5 rps^(2)`
We know that `theta = omega_(i) t + (1)/(2) alpha t^(2)`
i.e. `theta = 0 + (1)/(2) xx 7.5 xx (2)^(2) i.e. theta = 15` revolutions
Hence angular acceleration is `7.5 r ps^(2)` and number of revolution made will be 15.