In rotational mechanics, what is the perpendicular distance between the line of action of a force and the axis of rotation called?

Introduction / Context:
Rotational motion and turning effects of forces are central topics in mechanics. When a force is applied at some distance from an axis of rotation, it produces a turning effect known as a moment or torque. The size of this turning effect depends not only on the magnitude of the force but also on how far the line of action of the force is from the axis. The special name for this perpendicular distance is an important term that often appears in theory and numerical questions.

Given Data / Assumptions:
• We have a rigid body that can rotate about an axis.
• A force acts on the body at some point, and its line of action does not pass through the axis.
• The perpendicular distance from the axis to the line of action of the force is considered.
• We seek the correct technical term used in physics for that perpendicular distance.

Concept / Approach:
The turning effect or moment of a force about an axis is given by the expression
Moment = Force * perpendicular distance from the axis.
This perpendicular distance from the axis of rotation to the line of action of the force is known as the moment arm or lever arm. It is crucial that the distance measured is the shortest distance, hence perpendicular. This is different from the straight line distance from the axis to the point of application when the force is not perpendicular. Other terms like moment of inertia and torque refer to different concepts and should not be confused with the distance itself.

Step-by-Step Solution:
Step 1: Recall the formula for the moment or torque of a force about an axis, which is torque = F * r_perp. Step 2: Identify r_perp as the perpendicular distance from the axis of rotation to the line of action of the force. Step 3: Recall the terminology used for this distance, which is called the moment arm or lever arm. Step 4: Examine the given options and search for the term that matches this definition. Step 5: Recognise that moment arm is the correct name for this perpendicular distance.

Verification / Alternative check:
You can verify this understanding from practical examples such as using a spanner to turn a nut. The longer the handle, the larger the moment arm for the same applied force and the easier it becomes to turn the nut. This everyday experience is often explained in textbooks with the phrase longer lever arm or larger moment arm. The same idea is applied in levers, doors and see saws. In all these cases, it is the perpendicular distance from the pivot or hinge that determines the turning effect.

Why Other Options Are Wrong:
Moment of inertia: This is a measure of how much a body resists angular acceleration and depends on mass distribution, not a simple distance by itself.
Altitude: This word is used mainly in geometry for the height of a triangle or in geography for height above sea level, not for torque calculations.
Base: Base is also a geometric term for one side of a figure and does not denote the perpendicular distance from an axis to a force line in mechanics.
Torque: Torque or moment is the product of the force and the moment arm. It is the turning effect, not the distance that enters the formula.

Common Pitfalls:
Students sometimes confuse moment arm with moment of inertia because both appear in rotational motion formulas. Another mistake is to think the distance used in torque calculations is just the straight line distance from the axis to the point of application, even when the line of action of the force is not perpendicular. The correct procedure is always to take the perpendicular distance from the axis to the force line. Drawing a clear diagram and marking the right angle distance helps to avoid these errors.

Final Answer:
The perpendicular distance from the axis of rotation to the line of action of a force is called the moment arm or lever arm.