Question

A particle of mass m is moving with constant velocity v parallel to the x axis as shown in the figure. It's angular momentum about origin is

Answer 1

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A body of mass M is moving with a constant velocity v parallel to the x-axis. Let the perpendicular distance between the X-axis and the path of the particle be r. Then the angular momentum of the body about X-axis is given,

L = r × p, where r is the perpendicular distance between the path of the particle and X-axis, and p is the linear momentum of the particle. Since r and p are perpendicular to each other we have ,

| L | = M | v | |r|= M v r

Since M, v, and r are all constant L is constant.
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Answer 2

Given:

Particle of mass = m

Velocity = v

Velocity is parallel to = x-axis

To find:

Angular momentum about origin

Solution:

The position vector is specified as -

= ai + bj

Angular momentum = m ( ai + b) x vi

Calculating the cross product -

The angular momentum of the particle  will be - mvb  

This also represents in the direction of z-axis

Thus, in the scalar form  

= mvb

Answer: Angular momentum about origin is mvb.