The angular momentum of a system of particles is conserved

Options

A. when no external force acts upon the system
B. when no external torque acts upon the system
C. when no external impulse acts upon the system
D. when axis of rotation remains same

Explanation

To determine when the angular momentum of a system of particles is conserved, we can analyze the conditions under which this conservation occurs. Here’s a step-by-step solution:

### Step 1: Understand Angular Momentum
Angular momentum (L) is a vector quantity that represents the rotational inertia and rotational velocity of a system. It is defined as:
\[ L = I \omega \]
where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

### Step 2: Identify Conditions for Conservation
For angular momentum to be conserved, we need to identify the conditions that must be met. The key condition is that there should be no external influences affecting the system.

### Step 3: Analyze External Forces and Torques
1. **External Force**: While external forces can affect the linear momentum of a system, they do not directly determine the conservation of angular momentum.
2. **External Torque**: The crucial factor for the conservation of angular momentum is the absence of external torque. Torque (\( \tau \)) is related to angular momentum by the equation:
\[ \tau = \frac{dL}{dt} \]
If there is no external torque acting on the system, then:
\[ \tau = 0 \Rightarrow \frac{dL}{dt} = 0 \]
This implies that the angular momentum \( L \) remains constant.

### Step 4: Conclusion
Thus, the angular momentum of a system of particles is conserved when there is no external torque acting on the system.

### Final Answer
The correct condition for the conservation of angular momentum is:
- **When no external torque acts on the system.**