What is the point of rotation for a plank kicked on ice?

[phys_learner]

Homework Statement

A thin uniform plank of length L lies at rest on a horizontal sheet of ice. If the plank is given a kick at one end in a direction normal to the plank, show that the plank will begin to rotate about a point located L/6 from the center.

Homework Equations

The friction can be neglected.

The Attempt at a Solution

Since the plank is free to move it has both rotational and translational motion after it gets the kick. If the centre of mass of the plank moves with linear velocity 'v', then its linear momentum is 'mv' where m is mass of plank, and angular momentum is mvr where 'r' is the distance from the CM. I tried conservation of momentum but(0=mv+ mvr) that did not lead to any result. Please shed some light on the problem. Thanking you in advance

 

[Thaakisfox]

You Cant mix the two quantities together. There is angular momentum and linear momentum ;) and you have energy too ;) ;)

 

[phys_learner]

I still can't figure out the correct way to solve this question. please more help required!