The angular momentum of body remains conserve if :

Options

A. applied force on body is zero.
B. applied torque on body is zero.
C. applied force on body is constant.
D. applied torque on body is constant.

Answer

To determine when the angular momentum of a body remains conserved, we need to analyze the conditions under which angular momentum is conserved in rotational motion. Here’s a step-by-step solution:

### Step 1: Understand Angular Momentum
Angular momentum (L) of a body is defined as the product of its moment of inertia (I) and its angular velocity (ω):
\[ L = I \cdot \omega \]

### Step 2: Identify the Conditions for Conservation
Angular momentum is conserved in a system when there are no external torques acting on it. This is analogous to linear momentum, which is conserved when there are no external forces acting on a body.

### Step 3: Analyze the Given Options
- **A. Applied force on the body is zero**: This condition relates to linear momentum, not angular momentum.
- **B. Applied torque on the body is zero**: This is the correct condition for the conservation of angular momentum. If the net external torque acting on a body is zero, its angular momentum remains constant.
- **C. Applied force on the body is constant**: This does not guarantee conservation of angular momentum, as it may still result in a net torque.
- **D. Applied torque on the body is constant**: If the torque is constant, it implies that angular momentum is changing at a constant rate, thus not conserved.

### Step 4: Conclusion
The correct answer is **B. Applied torque on the body is zero**. This means that if there are no external torques acting on the system, the angular momentum of the body will remain conserved.

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