Question

A particle of mass m is moving with velocity V along a line y= x + 5. find the angular momentum of the particle about a perpendicular axis passing through origin O​

Answer 1

Answer:

Angular Momentum of a particle of mass m moving with velocity V along a line y=x+5 about a perpendicular axis passing through origin O is zero.

Explanation:

The angular momentum of a particle of mass m, moving with velocity V along a line y = x + 5, about a perpendicular axis passing through origin O can be calculated by using the following formula:

• L = r x mv

• Where,
• r is the position vector of the particle with respect to the origin O.
• m is the mass of the particle.
• v is the velocity of the particle.

• In this case, we need to find the position vector of the particle with respect to the origin. The equation for the line y = x + 5 can be re-written in vector form as r = xi + (x + 5)j, where i and j are the unit vectors in x and y direction respectively.

• Substituting the values in the formula, we get

• L = (xi + (x + 5)j) x mv = m(xi x vj - (x + 5)j x vi)

• Since the particle is moving along the line y = x + 5, we have vi = i and vj = 1. Hence,

• L = m(-i x vj) = - mvi

• The magnitude of the angular momentum is given by |L| = mv, and its direction is perpendicular to the plane of the particle's motion.

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