Understanding Angular Momentum in Projectile Motion
In projectile motion, angular momentum is an essential concept that relates to the motion of the object concerning a point, usually the origin or a reference point. The angular momentum of a projectile is influenced by its velocity and the distance from the reference point.
Angular Momentum at Different Points
- Starting Point: At the moment the projectile is launched, it has a certain velocity and is at a defined distance from the reference point. The angular momentum is calculated using the formula L = r × p, where r is the distance from the reference point and p is the linear momentum (mass × velocity).
- Highest Point: At the peak of its trajectory, the vertical component of the projectile's velocity is zero. However, it still has horizontal velocity. While the angular momentum here is not minimum, it is essential to note that it is still influenced by the horizontal distance from the reference point.
- Return to the Ground: When the projectile returns to the ground, it has a similar distance from the reference point as it had at launch, therefore the angular momentum is nearly similar to that at the starting point.
Why Minimum at Starting Point?
- When the projectile is launched, it has the most significant distance from the reference point given the initial height. As it travels upwards and then downwards, the distance decreases and then increases again, but it is always zero at the starting point regarding the vertical component.
- The minimum angular momentum occurs when the reference point is at the launch point, as any deviation from this point in terms of height or horizontal distance will yield a greater angular momentum due to the nature of the r × p relationship.
In conclusion, the correct answer is option 'B', as the angular momentum is minimum at the starting point.