# Moment Arm [GATE Notes]

By Deepak Yadav|Updated : September 30th, 2022

Let's define the moment before delving into moment arm's specifics. Moment of a force, or simply moment, is a term used in physics to describe a force's tendency to cause a body to spin around a given point or axis. This differs from a body's tendency to translate or move in the force's direction.

The moment arm, or the distance from the axis of rotation, is significant in this concept. By altering the moment arm, simple machines like a lever, pulley, gear, and most others produce mechanical advantage. The newton meter (kgm²/s²) is the SI unit for the moment. Let's dive further into the moment arm and torque concepts.

## What is a Moment Arm?

The moment arm of a joint is the distance between its axis and the line of force acting on it. A moment arm for each joint is utilized in an activity. The greater the length of the moment arm, the more load will be delivered to the joint axis via leverage.

### Moment Arm Definition

"An object's ability to rotate about an axis is determined by the effect of a force, which is defined by a moment arm."

### Moment Arm Formula

Consider attempting to separate a nut and bolt as an example. Suppose the small moment arm prevents you from completing the task by hand. In that case, you can use a crescent, which gives you a considerably larger moment arm and enables you to apply much less force to produce much greater torque (rotational force) at the nut. For the following reasons, torque at an axis:

Torque = Force x Moment arm

Hence, the moment arm formula will be:

Moment Arm = Torque / Force

### What is Torque?

Torque is the rotational equivalent of force in physics and mechanics. It is also known as the moment, moment of force, rotating force, or turning effect, depending on the field of study. It is an example of how a force can alter a body's rotational motion. The idea was developed due to Archimedes' study on levers, as his well-known quotation has shown: "Give me a lever and a place to stand, and I will move the Earth".

## How do Force Vectors Relate to Moments?

A force vector represents a force's direction. In terms of Engineering mechanics, we are aware of the fundamentals of the line of force of gravity. When we lift an object, several force vectors are at work. We have forces like gravity, friction on an object, ground reaction, muscle forces (created along the line between a muscle's origin and insertion), momentum forces, and much more. The total of all vectors and their corresponding forces determines how a movement will turn out.

## Example of Moment Arm

For example, if I were to punch a punching bag, the following forces and vectors would be at work.

• I'd generate power from my legs to start the punch with ground reaction forces.
• Internal forces from each muscle engaged, including those in the foot, legs, trunk, and arm.
• The force behind my arm.
• The bag's momentum.

## Problems on moment Arm

Question  - A 16 N force produce a moment of 64 Nm. The moment arm is_____.

Answer - 4 m

Question  - A 1 m long uniform beam of 2 kg mass is being lifted vertically up by a force F at the 100 cm mark. What is the minimum force required to do so?

Answer - 10 N

 Important GATE Topics BJT Bipolar Junction Transistor Difference Between Printer And Plotter Breakdown Diode Types Of Op Amp Integrated Circuits Tellegens Theorem JFET Amplifier What Is Gear Maximum Power Transfer Theorem Degree Of Static Indeterminacy

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## FAQs on Moment Arm

• The distance measured perpendicularly between the force's line of action and the center of moments is known as the moment arm or lever arm.

• The rotating outcome of a linear force is torque, also known as a moment or moment of force. Torque is calculated as the product of the force and the moment arm, which is the angle between the force's line of action and its axis of rotation.

• The influence of a force to cause (or prevent) the rotation of an item along an axis is determined by a moment arm. It is the shortest possible perpendicular distance between the joint's axis and the line of force being applied to resist it.

• The moment is a phrase used to describe an object's tendency to rotate along an axis when one or more forces are applied, but not necessarily when the object's angular momentum is changed (the concept is called torque in physics).

• The separation between a muscle's line of action and a joint axis is referred to as a muscle moment arm. This distance is crucial for determining how well a muscle can produce torque around a joint axis.

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