Question
Show that the angular momentum about any point of a single particle moving with constant velocity remains constant throughout the motion.
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Answer
Let the particle with velocity v be at point P at 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 sinθ, where θ is the angle between r and v as shown in Fig. 6.19. 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?
The angular momentum is l = r × mv. Its magnitude is mvr sinθ, where θ is the angle between r and v as shown in Fig. 6.19. 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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