Solving Angular Momentum & Energy Conservation for Velocity at Point A

[asi123]

Homework Statement

Hey guys.
So I got this disk connected to a spring which is connected to a wall.
A mass m hits the disk with a velocity v and sticks to it.
The question is to find the velocity of m at point A.
As you can see I used the conservation of the angular momentum to find $$\omega$$ at the beginning.
The thing I'm not sure about is the energy conservation equation I wrote there, I'm not sure about the gravitational potential energy, I mean, is this right?

10x.

Homework Equations

The Attempt at a Solution

 

[asi123]

Any idea guys?

 

[OmCheeto]

Any idea guys?

I'm not sure I fully understand the diagram, but shouldn't v*cos(squiggle)=0?

 

[asi123]

I'm not sure I fully understand the diagram, but shouldn't v*cos(squiggle)=0?

Why?

 

[OmCheeto]

Why?

That's why I posted that I didn't understand the diagram.
Is the disk resting on the floor at y=0?
Is the disk pivoted frictionlessly at it's center?

I assumed that since you mentioned gravity, that the disk is in a vertical plane.

My assumption was that the disc was fixed on some axis or point and therefore the v*cos(squiggle) component had to be zero. Also, none of the momentum of the mass m would be imparted to the disc as there was no mention of it's mass. So the magnitude of of the velocity of mass m would have to be the same in the direction of sin(squiggle).

Hope that helps.