## Torque Formula

## What is Torque Formula?

Torque is a fundamental concept in physics that describes the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force causes an object to move in a straight line, torque causes an object to rotate. This formula calculates the torque produced by a force applied at a given angle to a rotational point. The torque formula, given below, is essential for analyzing situations involving rotational motion:

**Torque (𝜏) = Force (𝐹) × Lever Arm (𝑟) × sin(𝜃)**

- 𝐹 is the magnitude of the force applied.
- 𝑟 is the distance from the pivot point to the point where the force is exerted.
- 𝜃 is the angle between the force vector and the lever arm.

The concept of torque was first brought into clear scientific light by Sir Isaac Newton in his foundational works on classical mechanics. Although he did not specifically coin the term “torque,” his laws of motion and revolutionary ideas laid the groundwork for this vital physical quantity. Torque plays a critical role in every rotational motion from the simplest door hinges to the most complex engineering systems like car engines and space stations.

## Applications of Torque Formula

**Vehicle Dynamics**: Engineers use the torque formula to design engines and transmission systems that control how vehicles accelerate and handle.**Sports Equipment**: The design of golf clubs and baseball bats heavily relies on torque calculations to maximize performance and enhance the player’s control.**Construction Machinery**: Torque determines the effectiveness of equipment such as cranes and wrecking balls, influencing how they lift and move heavy loads.**Electric Motors**: Manufacturers apply the torque formula to optimize the performance of electric motors used in appliances, power tools, and vehicles.**Robotics**: Robots employ torque to control the precise movement of their joints and limbs, essential for tasks ranging from assembly line work to complex surgeries.**Wind Turbines**: In wind turbines, torque plays a critical role in converting wind energy into mechanical power efficiently.

## Example Problems on Torque Formula

### Example 1: Calculating Torque in a Wrench

**Problem**: Suppose you apply a force of 30 Newtons to a wrench at an angle of 90 degrees, and the distance from the pivot point (nut) to where the force is applied is 0.15 meters. Calculate the torque.

**Solution**: The torque can be calculated using the formula: 𝜏 = 𝐹 × 𝑟 × sin(𝜃) Where:

- 𝐹=30 N (force applied)
- 𝑟=0.15 m (distance from pivot)
- 𝜃=90∘ (angle of force)

Since sin(90∘)=1

𝜏 = 30 × 0.15 × 1 = 4.5 Nm

**Torque** = 4.5 Nm

### Example 2: Determining Force Required

**Problem**: How much force must be applied perpendicular to a lever arm of 0.5 meters to produce a torque of 20 Nm?

**Solution**: Rearrange the torque formula to solve for force: 𝐹=𝜏 / ( 𝑟×sin(𝜃) ) Given:

- 𝜏=20 Nm (torque required)
- 𝑟=0.5 m (lever arm length)
- 𝜃=90∘ (angle of force)

Since sin(90∘)=1

𝐹 = 20 / ( 0.5 × 1) = 40 N

**Force required** = 40 N

### Example 3: Torque from an Angled Force

**Problem**: A person applies a force of 50 Newtons at an angle of 30 degrees to the horizontal on a spanner. The spanner’s length from the nut to the point of force application is 0.2 meters. Calculate the torque generated.

**Solution**: Using the torque formula: 𝜏 = 𝐹 × 𝑟 × sin(𝜃)

Where:

- 𝐹 = 50 N
- 𝑟 = 0.2 m
- 𝜃 = 30∘

Using sin(30∘) = 0.5

𝜏 = 50 × 0.2 × 0.5 = 5 Nm

**Torque** = 5 Nm

## FAQs

## How to Calculate Torque from RPM

To find torque from RPM, use: 𝜏 = ( 𝑃 × 5252 ) / 𝑅𝑃𝑀, where 𝑃 is power in horsepower.

## How Do You Calculate Torque from Force?

Calculate torque using 𝜏 = 𝐹 × 𝑟 × sin(𝜃), where 𝐹 is force, 𝑟 is arm length, 𝜃 is angle.

## What Is the Unit of Torque?

Torque unit: Newton-meter (Nm).