First slide
Rotational motion
Question

A particle of mass m is projected with velocity v at an angle q with the horizontal. Find its angular momentum about the point of projection when it is at
the highest point of its trajectory.

Moderate
Solution

At the highest point of its trajectory velocity of projectile is v θcos in the horizontal direction and value of maximum height is
 

hmax=v2sin2θ2g
Angular momentum about the point of projection is
L=phmax=(mvcosθ)v2sin2θ2g 
L=mv2cosθsin2θ2g
L=mv3sinθsin2θ4g

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