When a loop rotating in a uniform magnetic field.
The magnetic flux is changing which will induce electric field along the loop (produce voltage).
If the loop is rotating with constant angular velocity \omega . (The angle is \omega t)
The magnetic flux in the loop will be \Psi =\int \vec{B}\cdot d\vec{A}= B A cos(\omega t)
So the induced emf = -\frac {d\Psi}{dt}=B A \omega sin(\omega t)

The following simulation show how it works dynamically.