Solving for Max Height and Angular Velocity of a Thin Rod

[albega]

Homework Statement

A thin rod of length L, mass m is suspended horizontally at rest. It is suddenly released and experiences immediately after an impulse vertically upwards at one end.

I need to find the maximum height reached by the centre of mass and the angular velocity of rotation about the centre of mass.

The Attempt at a Solution

I can't see how there is enough information given in the question. I have used the fact that J=0.5Lp here (J is angular momentum) from the relation between angular and linear impulse, and then this means 0.5Lmv=Iω, with I=mL²/12. Then 0.5Lmv=mL²ω/12. This relates v and ω by v=ωL/6. I could then probably work with constant acceleration formulae to get the answer, however both v and ω are unknowns (and I have to find ω in the next part) so I have no idea where to go.

Thanks in advance :)

 

[Tanya Sharma]

The initial velocity of CM ,angular velocity of the rod and the maximum height reached all depend upon the magnitude of impulse . So surely some data is missing from the question.

 

[albega]

The initial velocity of CM ,angular velocity of the rod and the maximum height reached all depend upon the magnitude of impulse . So surely some data is missing from the question.

Yes, as I suspected. Thanks for clarifying.

 

[BiGyElLoWhAt]

Well to me it looks as thought OP isn't supposed to solve for a number, but max height as a function of I.

 

[BiGyElLoWhAt]

Homework Statement

A thin rod of length L, mass m is suspended horizontally at rest.

Length L, mass M, impulse, I...

 

[haruspex]

Length L, mass M, impulse, I...

Except that no label is given for the impulse in the question as stated in the OP - that's what's missing.