a unoform rod AB of length 2l & mass m is rotating in a horizontal plane about a vertical axis through A with angular velocity w . when the midpoint of the rod dtrikes the fixed nail , it is brought to rest immediately . find the impulse exerted by nail
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Answer:
4ML/3ω.
Explanation:
The impulse which will be given to the rod is given as the integration of NLdt where l is the length of the rod and N is the impulse which is given to the rod. This integration must be equal to the linear momentum L which is Iω. So, the ΔL will be L(final) - L(initial) = 0 - (-Iω) = Iω.
So, the integration of NLdt=Iω or the l is constant so the integration of Ndt is known as the linear impulse which is required. So, it will be M(L^2)/3ω where L is 2L. Hence, linear impulse is 4ML/3ω. Where one L which was constant on the right hand side gets cancelled with the L on the left hand side.
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