The rate of change of angular momentum is called

Options

A. angular velocity
B. angular acceleration
C. moment of inertia
D. torque

Answer

To solve the question regarding the rate of change of angular momentum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Angular Momentum**:
- Angular momentum (L) is defined as the product of the moment of inertia (I) and the angular velocity (ω). Mathematically, it can be expressed as:
\[ L = I \cdot \omega \]

2. **Rate of Change of Angular Momentum**:
- The rate of change of angular momentum is given by the formula:
\[ \frac{dL}{dt} = \text{Final Angular Momentum} - \text{Initial Angular Momentum} \div \text{Time} \]
- This can be expressed as:
\[ \frac{dL}{dt} = \frac{L_f - L_i}{t} \]

3. **Substituting Angular Momentum**:
- Substituting the expression for angular momentum into the equation gives:
\[ \frac{dL}{dt} = \frac{I \cdot \omega_f - I \cdot \omega_i}{t} \]

4. **Factoring Out Moment of Inertia**:
- We can factor out the moment of inertia (I) from the equation:
\[ \frac{dL}{dt} = I \cdot \frac{\omega_f - \omega_i}{t} \]

5. **Identifying Angular Acceleration**:
- The term \(\frac{\omega_f - \omega_i}{t}\) represents the angular acceleration (α):
\[ \alpha = \frac{\Delta \omega}{\Delta t} \]
- Thus, we can rewrite the equation as:
\[ \frac{dL}{dt} = I \cdot \alpha \]

6. **Conclusion**:
- The rate of change of angular momentum is equal to the torque (τ), which is defined as:
\[ \tau = I \cdot \alpha \]
- Therefore, the answer to the question is that the rate of change of angular momentum is called **torque**.

### Final Answer:
The rate of change of angular momentum is called **torque**.