Moment of inertia of a body depends upon

Options

A. axis of rotation
B. torque
C. angular momentum
D. angular velocity

Explanation

To determine what the moment of inertia of a body depends upon, we can analyze the factors involved in its calculation. Here’s a step-by-step solution:

### Step 1: Understand the Definition of Moment of Inertia
The moment of inertia (I) is a measure of an object's resistance to changes in its rotational motion. It depends on how the mass of the object is distributed relative to the axis of rotation.

**Hint:** Recall that moment of inertia is analogous to mass in linear motion.

### Step 2: Recall the Formula for Moment of Inertia
The moment of inertia for a point mass is given by the formula:
\[ I = m r^2 \]
where:
- \( I \) is the moment of inertia,
- \( m \) is the mass of the object,
- \( r \) is the distance from the axis of rotation.

**Hint:** Identify the variables in the formula and their significance.

### Step 3: Analyze the Variables
From the formula, we can see that the moment of inertia depends on:
- The mass of the body (m)
- The distance (r) from the axis of rotation

**Hint:** Think about how changing the position of the mass or the axis of rotation affects the moment of inertia.

### Step 4: Consider the Options Given
The options provided are:
1. Axis of rotation
2. Torque
3. Angular momentum
4. Angular velocity

Among these, the axis of rotation is directly related to the distance \( r \) in the formula for moment of inertia.

**Hint:** Eliminate options that do not directly relate to the distribution of mass or its distance from the axis.

### Step 5: Conclusion
Since the moment of inertia is influenced by how far the mass is from the axis of rotation, we conclude that the moment of inertia of a body depends upon the axis of rotation.

**Final Answer:** The correct option is **1. Axis of rotation**.