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Hello! The angular velocity in the non-inertial frame of a rotating body of mass m is ##\Omega## and I need to find the force acting on the body (in the non-inertial frame associated with the body). In the book they say (without any derivation, they just state it) that the force is: $$\bar{F}=m\bar{g}+2m\bar{v}\times\bar{\Omega}+m(\bar{r}\times\bar{\dot{\Omega}})+\frac{\partial}{\partial \bar{r}} \frac{m( \bar{\Omega}\times \bar{r} )^2}{2}$$ So we have gravity, Coriolis force and centrifugal force. But what is the second to last term and how do you derive it? Thank you!