Question

A particle of mass m moves in the XY plane with a
velocity V along the straight line AB.

If the angular momentum of the particle with respect to origin is La, when it is at A and Lb when it is at B, then why is La = Lb?

Explain. ​

Answer 1

The angular momentum of particle at A(La) = The angular momentum of particle at B(Lb)

• Angular momentum defines L = r × p = rmvsin∅(-k)

• The magnitude of L from the above formula can be L = mvrsin∅ = mvd

• d is the closest distance of the particle from the origin

• The distance of points A and B from the otigin is same which results in the same angular momentum.So La = Lb

Answer 2

Hi friend here is your answer

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Consider in vector form

L = r X p

&

L = r X mv

Where V is the velocity vector

The velocity vector will be same at both points A and B

r is perpendicular vector to the velocity vector from origin and that is perpendicular to AB so r is same in both case

Hence LA = LB

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Hope it helps you...................!!