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Show that the angular momentum about any point of a single particle moving with constant velocity remains constant throughout the motion. |
Answer» Solution :Let the particle with velocity vbe at point Pat some instant t. We want to calculate the angular momentum of the particle about an arbitrary point O.  The angular momentum is `L = r × mv`. Its magnitude is `mvr sin θ` , where `θ` is the angle between r and v as shown in Fig. 7.19. Although the particle changes position with time, the line of DIRECTION of v remains the same and hence `OM = r sin θ` . is a constant. Further, the direction of l is perpendicular to the PLANE of r and v. It is into the page of the figure.This direction does not change with time. Thus, l remains the same in magnitude and direction and is therefore CONSERVED. Is there any external torque on the particle? |
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