When a fan is switched on, it makes `10` rotations in the first `2 s`. How many rotations will it make in the next `2 s`, assuming uniform angular acceleration?

Explanation

`theta=omega_(0) t+(1)/(2)alpha t^(2)`
`20pi= 0+(1)/(2)alpha (2)^(2)` (`i`)
`20pi+theta'= 0+(1)/(2)alpha(2+2)^(2)` (`ii`)
Dividing (`ii`) by (`i`), we get
`(20pi+theta')/(20pi)=((4)/(2))^(2)= 4`
`theta'=60pi`
where `theta'` is the angle rotated in the next `2 s`.
Number of rotations `= (60pi)/(2pi)=30`