Question

The motor of an engine is rotating about its axis with an angular velocity of `100`rpm. It comes to rest in `15s`, after being switched off. If angular deceleration is constant, what is the number to revolutions made by it before coming to rest ?

Answer 1

Here, `n_(1) = 100"rpm" = (100)/(60) rps`,
`n_(2) = 0, t = 15 s, alpha = ?, n = ?`
`alpha = (omega_(2) - omega_(1))/(t) = (2pi(n_(2) - n_(1)))/(t)`
`= (2pi(0-(100)/(60)))/(15) = - (2pi)/(9) rad s^(-2)`
`theta = omega_(1)t + (1)/(2) alpha t^(2)`
`= 2pi xx (100)/(60) xx 15 + (1)/(2) (-(2pi)/(9)) (15)^(2)`
`= 50pi - 25 pi = 25 pi`
Number of rotations made,
`n = (theta)/(2pi) = (25pi)/(2pi) = 12.5`