Angular Momentum Of A Particle

Angular momentum (L) can be defined as moment of Linear Momentum about a point.

The angular momentum of a particle of mass m moving with velocity v (having a linear momentum p=mv) about a point is defined as

Let a particle P of mass m rotating about an Axis through O in the x-y plane. Let the particle has linear momentum p which makes θ with its position vector OP=r, now the angular momentum

The direction of angular momentum vector L is perpendicular to the plane of vector r and vector p in the sense given by right hand rule. Thus in the present case, Vector L points in Z-direction.

Special Case

(I) If θ= 0 or 180, then sinθ= 0, Therefore L= rpsinθ = 0 (minimum)

Hence, the angular momentum is zero, if the line of action of Linear Momentum pass through the point of rotation.

(II) If θ= 90, then sin90= 1, Therefore L= rpsin90= rp (Maximum)

Hence, the angular momentum is maximum.

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Special Case

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