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

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SUMMARY

The discussion focuses on the mechanics of a thin uniform plank of length L that rotates after being kicked at one end on a frictionless surface. It is established that the point of rotation is located L/6 from the center of the plank. The analysis involves both translational and rotational motion, emphasizing the importance of distinguishing between linear momentum and angular momentum. The conversation highlights the necessity of applying conservation laws correctly to solve the problem effectively.

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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

 
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You Cant mix the two quantities together. There is angular momentum and linear momentum ;) and you have energy too ;) ;)
 
I still can't figure out the correct way to solve this question. please more help required!
 

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