# Torque and angular acceleration in rotating frames

If we are using the equation $$\tau=I\cdot \alpha$$ (where $$\tau$$ is the torque, $$I$$ is the moment of inertia, $$\alpha$$ is the angular acceleration) in a rotating frame of reference, we have to account for the fictitious forces, so, my question is, do these forces 'act' on the center of mass of the extended object?

As far as I know, the force $$-ma_{frame}$$ can be thought of as acting at the center of mass effectively, it gives the correct force and torque as we would get if we were to apply the force on each infinitesimal part of the body.

What about the coreolis term, the euler term and the centripetal term of fictitious force?

The fictitious forces are called inertial forces because their magnitude depends on the inertial mass. The fictitious force on a particle due to linear acceleration is $$-m \vec a_{frame}$$ and can be easily shown can be considered to act at the center of mass of a system of particles. The Coriolis force on a particle is $$-2m \vec \omega \times {d^* \vec r \over dt}$$ and cannot be considered to act at the center of mass of a system of particles due to the dependence on $$\vec \omega \times{d^* \vec r \over dt}$$, (the derivative is in the non-inertial frame). The centrifugal force on a particle $$-m {d \vec \omega \over dt} \times \vec r$$ cannot be be considered to act at the center of mass of a system of particles due to the dependence on $${d \vec \omega \over dt} \times \vec r$$.