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Chapter 11: Problem 8

Does a particle moving at constant speed in a straight line have angular momentum about a point on the line? About a point not on the line? In either case, is its angular momentum constant?

Short Answer

Expert verified
A particle moving at constant speed in a straight line has zero angular momentum about a point on the line but it does have constant angular momentum about a point not on the line.

Step by step solution

01

Understand the problem and the conditions

Angular momentum is given by the cross product of the position vector and momentum. A particle can have angular momentum about a certain point if there is a perpendicular component of the position vector and momentum. Here, the particle is under two conditions - moving at constant speed and in a straight line.
02

Angular momentum about a point on the line

In this case, the position vector is always parallel to the velocity vector (or momentum), as both are aligned on the same straight line. The cross product of two parallel vectors is zero. Therefore, the angular momentum about a point on the line is zero.
03

Angular momentum about a point not on the line

A point not on the line would have a position vector not parallel to the velocity vector. Hence, a nonzero perpendicular component exists. Thus, the particle will have angular momentum about this point. Because particle velocity (speed and direction) and position relative to the off-axis point are constant, the angular momentum is constant.

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