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Homework Statement
A uniform rod (mass 'm', length 'l') held horizontally above the ground. It is released from its supports and struck vertically upwards at one end. With what impulse should the rod be struck if it is to return to exactly its starting position and orientation?
Homework Equations
I know the moment of inertia of a rod about its centre is ml^2/12,
Torque = Moment of Inertia x Angular acceleration
and the rod moves in the vertical plane around the CM in spirals, but apart from that I'm really stuck.
I can't seem to get the concept of how the rod returns to its starting position.
The Attempt at a Solution
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I tried to conserve energy, mgh=0.5 Iω^2 + KE but I'm not sure where that gets me.
Thanks for any help or pointers :)