How Can I Measure Kinetic Energy in a Non-Inertial Reference Frame?

[xkcda]

TL;DR Summary: I think A is an non inertial reference frame.So how can I measure kinetic energy about it?

I found a solution to the problem which states that Kinetic Energy about A= (Moment of Inertia about an axis passing through A*Angular Velocity^2)/2+(Mass*Velocity^2)/2 .Thus K=9.5.Can anyone please show me the derivation of this formula?

 

[jim mcnamara]

No attempt shown.

 

[jim mcnamara]

Please show some effort, so we can help you learn.

 

[jim mcnamara]

Moved to homework help.

 

[haruspex]

The first difficulty is that "with respect to point A" is ambiguous.
It is reasonable to assume, as you have, that it does not mean the fixed point in space where that corner happens to be at some instant; rather, it moves with that corner of the plate. But that still does not answer whether the reference frame is also rotating with the plate. Consider both cases.
In each case, think of what an observer in the frame would see the plate as doing.

Kinetic Energy about A= (Moment of Inertia about an axis passing through A*Angular Velocity^2)/2+(Mass*Velocity^2)/2

That seems very unlikely to be right. If you take the moment of inertia about the axis of rotation then you should not need to be adding a linear KE term: that would be double counting. Generally speaking, you can consider the instantaneous motion of a rigid body as the sum of the linear motion of its mass centre and its rotation about its mass centre. So if you have an $mv^2$ term for the linear component then the moment of inertia should be about the mass centre.