[quote author=Fu-Kwun Hwang link=topic=1281.msg4947#msg4947 date=1257256703]
I think the magnetic field is assumed to be uniform B=B[sub]0[/sub].
The magnetic flux pass through the coil depends on the angle \theta=\omega t,
assume the coil rotate at constant angular velocity \omega.
i.e. \Psi=\int \vec{B}\cdot d\vec{s}= B A cos(\theta)=B A cos(\omega t)
From Faraday's law, induced voltage V= -\frac{d\Psi}{dt}= BA\omega \sin(\omega t)
So the voltage is a sine wave (without commutator).
[/quote]
i agree with the above analysis that AC generator (without commutator) the emf induced in the coil is a sine wave.

so is it that with a commutator, which flip the current in half cycle rotation,  therefore emf induced in the coil will be a |sine| wave?

if that is true, then i understand why the emf induced is |sine| wave.

By the way,
i am certain http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/motdct.html is accurate for torque vs time is a |sine| wave.
[img]http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/imgmag/dcmtorv.gif[/img]