Relation between torque and angular momentum is similar to the relation between

Options

A. acceleration and velocity
B. mass and moment of inertia
C. energy and displacement
D. force and linear momentum

Answer

To solve the question regarding the relation between torque and angular momentum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Torque (τ)**: Torque is the rotational equivalent of linear force. It is defined as the product of the force (F) and the distance (r) from the pivot point (τ = r × F).
- **Angular Momentum (L)**: Angular momentum is the rotational equivalent of linear momentum. It is defined as the product of the moment of inertia (I) and the angular velocity (ω) (L = I × ω).

2. **Identify the Relationship**:
- In rotational motion, torque is responsible for changing the angular momentum of an object. This is analogous to how force changes the linear momentum of an object in linear motion.
- Mathematically, the relationship can be expressed as:
- Torque (τ) = Rate of change of Angular Momentum (dL/dt)
- Force (F) = Rate of change of Linear Momentum (dp/dt)

3. **Compare with Given Options**:
- Now, we need to find a pair from the options given that has a similar relationship:
- Option 1: Acceleration and Velocity
- Option 2: Mass and Moment of Inertia
- Option 3: Energy and Displacement
- Option 4: Force and Linear Momentum

4. **Analyze Each Option**:
- **Acceleration and Velocity**: Acceleration is the rate of change of velocity, but it does not directly relate to the concept of torque and angular momentum.
- **Mass and Moment of Inertia**: Mass is a measure of an object's resistance to linear motion, while moment of inertia is a measure of resistance to rotational motion. This is not a direct analogy to torque and angular momentum.
- **Energy and Displacement**: Energy is not directly related to displacement in the same way torque relates to angular momentum.
- **Force and Linear Momentum**: Force is the rate of change of linear momentum, which is directly analogous to how torque is the rate of change of angular momentum.

5. **Conclusion**:
- Based on the analysis, the correct answer is **Option 4: Force and Linear Momentum**. This option reflects a similar relationship to that of torque and angular momentum.

### Final Answer:
The relation between torque and angular momentum is similar to the relation between **Force and Linear Momentum**.

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