Solving for Max Height and Angular Velocity of a Thin Rod

AI Thread Summary
The discussion focuses on calculating the maximum height and angular velocity of a thin rod released from rest after receiving an upward impulse. Participants note that the problem lacks sufficient information, specifically the magnitude of the impulse, which is crucial for determining the initial velocity of the center of mass and angular velocity. The relationship between linear and angular momentum is explored, but without the impulse value, the calculations remain incomplete. It is suggested that the solution may need to express maximum height as a function of the impulse rather than a specific numerical answer. Overall, the consensus is that essential data is missing from the problem statement.
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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 :)
 
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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.
 
Tanya Sharma said:
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.
 
Well to me it looks as thought OP isn't supposed to solve for a number, but max height as a function of I.
 
albega said:

Homework Statement


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

Length L, mass M, impulse, I...
 
BiGyElLoWhAt said:
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.
 
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