A rod of length $l$ rotating about one end with angular velocity $\omega$ in field $B$ (perpendicular to rotation plane): EMF $= B\omega l^2/2$. Derivation: a small element at distance $r$ from the pivot has velocity $v = \omega r$, so $d\varepsilon = Bv\,dr = B\omega r\,dr$. Integrating from 0 to $l$: $\varepsilon = B\omega l^2/2$. Alternatively: the rod sweeps area $dA/dt = l^2\omega/2$ (sector area per unit time). For a disc of radius $R$ rotating: EMF between center and rim $= B\omega R^2/2$ — this is the Faraday disc dynamo.