Fixed-Axis Rotation

We can express the equations of motion for a body in fixed-axis rotation as

where A is in the plane of motion and on the axis of rotation.

Now, if the body is symmetric with respect to the plane of motion (I_Azx = I_Ayz = 0) or if all forces act in the plane of motion, then these equations reduce to

When using these equations, be careful of the notation, because the moment equation is not valid if the acceleration of A is not zero.

If needed, we can also use the kinematic relationships for fixed axis rotation.

Generally, the solution of fixed-axis rotation problems involves both the equations of motion and the kinematic relationships.