Rotating mass system with a forward velocity and acceleration

[gmacmilla]

Homework Statement

I have a

solid rotating body with moment of inertia I rotating at a constant angular velocity w

body is spinning about an ideal bearing located at its CG, the system is also moving in straight line at a velocity v when it suddenly undergoes an acceleration a. I want to find an equation for the Force vector F placed on the axis of rotation by the accelerating rotating mass.
** angular velocity remains the same **

This problem has something to do with the coriolis effect and is similar to taking a spinning gyroscope and pushing it strongly in one direction. It puts a side force on your hand

Homework Equations

Not sure where to start. I have the angular velocity equations as well as the forward velocity and acceleration equations of . A good start would be helpfull please!

The Attempt at a Solution

 

[chrisk]

Consider the pivot point of the rotating body. The torque vector, N, is related to the applied force by N = r x F where r is the distance from the pivot point to the center of mass of the system. Also, the acceleration is linear so Newton's laws become F - ma = m times the second time derivative of the postion vector relative to the moving reference frame, and a is the acceleration of the system. The ma term is an inertial force and not a real force and depends on the acceleration of the moving coordinate system. F = mg in this case and points vertically downward, and ma points in a horizontal direction. The effective force acting on the pivot point is the vector addition of these two components.