In a projectile motion, where is the angular momentum is minimum ?

Options

A. At the starting point
B. On the landing point
C. Highest point of projectile
D. As no such posting.

Explanation

To determine where the angular momentum is minimum in a projectile motion, we can follow these steps:

### Step 1: Understand the Definition of Angular Momentum
Angular momentum (L) is defined as the cross product of the position vector (r) and the linear momentum (mv). The formula is given by:
\[ L = r \times mv \]
Where:
- \( r \) is the position vector from the origin to the projectile.
- \( m \) is the mass of the projectile.
- \( v \) is the velocity of the projectile.

### Step 2: Analyze the Components of Angular Momentum
The angular momentum depends on:
- The magnitude of the position vector \( r \).
- The mass \( m \) and velocity \( v \) of the projectile.
- The angle \( \theta \) between the position vector \( r \) and the velocity vector \( v \).

### Step 3: Identify Conditions for Minimum Angular Momentum
To find the minimum angular momentum:
- The angular momentum will be minimum when the value of \( r \) is zero because \( L = r \times mv \) implies that if \( r = 0 \), then \( L = 0 \).
- Since \( m \) and \( v \) cannot be zero (the projectile has mass and is in motion), the only way to minimize \( L \) is to have \( r = 0 \).

### Step 4: Determine the Position of the Projectile
In the context of projectile motion:
- At the starting point (when the projectile is launched), the position vector \( r \) is zero because it is at the origin.
- At the landing point and at the highest point, the position vector \( r \) will have a non-zero value, leading to a non-zero angular momentum.

### Conclusion
The angular momentum is minimum at the starting point of the projectile motion, where \( r = 0 \).

### Final Answer
The angular momentum is minimum at the starting point of the projectile.

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