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Question

A homogeneous bar OA of length l and weight G located in a vertical plane and articulated in the O plane is at rest in a vertical position. What angular velocity should this barrel be printed to reach a horizontal position if friction is neglected?

Answer 1

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Work it in reverse -- what angular velocity would it have at the vertical position if it fell from horizontal?

initial PE = mgℓ/2

final KE = ½Iω² = ½*(mℓ²/3)ω²

equate the two:

mgℓ/2 = mℓ²ω²/6 → → →divide through by mℓ/6

3g = ℓω² → → → → → ω = √(3g / ℓ)

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