Which one of the following statements concerning the moment of inertia I is false?

Options

A. Moment of inertia I may be expressed in units of `kg*m^(2)`.
B. Moment of inertia I depends on the angular acceleration of the object as it rotates.
C. Moment of inertia I depends on the location of the rotation axis relative to the particles that make up the object.
D. Moment of inertia I depends on the orientation of the rotation axis relative to the particles that make up the object

Answer

To determine which statement concerning the moment of inertia \( I \) is false, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Understanding Moment of Inertia**:
The moment of inertia \( I \) is defined as the sum of the products of the mass of each particle in a body and the square of its distance from the axis of rotation. The formula is given by:
\[ I = \sum m_i r_i^2 \]
where \( m_i \) is the mass of the \( i^{th} \) particle and \( r_i \) is its distance from the axis of rotation.

2. **Analyzing the Statements**:
We have four statements to evaluate:

- **Statement 1**: The moment of inertia \( I \) may be expressed in units of \( \text{kg m}^2 \).
- **Evaluation**: This statement is true. The units of moment of inertia are indeed \( \text{kg m}^2 \).

- **Statement 2**: The moment of inertia \( I \) depends on the angular acceleration of the object as it rotates.
- **Evaluation**: This statement is false. The moment of inertia is a property of the mass distribution relative to the axis of rotation and does not depend on angular acceleration.

- **Statement 3**: The moment of inertia depends on the location of the rotation axis relative to the particles that make up the object.
- **Evaluation**: This statement is true. The moment of inertia changes if the axis of rotation is moved because the distances \( r_i \) change.

- **Statement 4**: The moment of inertia depends on the orientation of the rotation axis relative to the particles that make up the object.
- **Evaluation**: This statement is true. The orientation of the axis affects the distances from the particles to the axis, thus changing the moment of inertia.

3. **Conclusion**:
After evaluating all the statements, we find that the false statement is:
- **Statement 2**: The moment of inertia \( I \) depends on the angular acceleration of the object as it rotates.

### Final Answer:
The false statement concerning the moment of inertia \( I \) is **Statement 2**.

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