Answer:
θ = 12.5 rotations
Explanation:
The number of rotations can be found by using the second equation of motion:
[tex]\theta = \omega_i t + \frac{1}{2}\alpha t^2\\\\[/tex]
where,
[tex]\theta[/tex] = angular displacement = ?
ωi = initial angular speed = 0 rad/s
t = time = 5 s
α = angular acceleration = 2π rad/s²
Therefore,
[tex]\theta = (0\ rad/s)(5\ s)+\frac{1}{2}(2\pi\ rad/s^2)(5\ s)^2\\\\\theta = 78.54\ rad[/tex]
converting it to no. or rotations:
[tex]\theta = (78.54\ rad)(\frac{1\ rotation}{2\pi\ rad})[/tex]
θ = 12.5 rotations
