# What is Torque Formula? – Definition, units, and equation

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## Torque definition:

In this tutorial, we will discuss how to calculate torque using the torque formula. Torque is the rotational effect of an object around its center point. In simple words, torque is the movement that is produced when a force is applied to an object that moves around its axis of rotation or the center of rotation. To produce torque, the force applied on the object must NOT be parallel to the axis of rotation. In this article, we will discuss many things like the torque formula, how to calculate torque, the difference between positive and negative torque etc.

The term “torque” seems difficult but this effect is present almost everywhere in our daily lives. Opening of door, a wrench can produce torque, paddling the cycle, or rotation of a car tire, all are examples of torque.

Torque is a vector quantity. It is always produced in a direction, and the direction of the torque vector always depends on the direction of the force which is applied to the object.

Torque is always produced in rotational motion.

There are some terminologies you should necessarily know when using the torque formula; the Moment of force or moment is used interchangeably with torque. The radius at which force is applied is called the moment arm.

Let us take the example of door to understand it more. First, we need to understand the structure of the door. The door has a handle to open and close the door, and a center where is the door is attached. Consider handle *moment arm* and the hinge of the door as the *axis of rotation*.

Whenever you apply force on the moment arm (door handle) to open or close the door, it moves around the axis of rotation in the clockwise and anti-clockwise direction. Try to remember those terminologies when using the values in the torque formula.

## What is the axis of rotation?

The Axis of rotation is very important when you are calculating torque with the torque formula. The center point of any object around which it rotates to create an angular motion is called the axis of rotation. For example; Earth revolving around its center, the lid of the laptop also produces torque when it is opened or closed. Torque is a vector quantity; it is always produced in a direction.

Simply think of an object which you want to move somewhere, then it is understood that you would move it in a direction. If your apply force on a door to open it, it will always follow a direction.

## Positive and negative torque.

There are 2 types of torque:

- Positive Torque.
- Negative Torque.

Now the question arises is which direction is positive torque?

Positive torque is produced in an anti-clockwise direction. For example, note the movement of the clock hands. The natural direction of clock hands is clockwise which produces Negative torque. And, if the hands of the starts to rotate in the opposite direction, then the torque will become positive.

In more simple words, the positive torque direction is anti-clockwise. And, Negative torque direction is clockwise.

The positivity of the torque can be found with the right-hand rule. Simply put your right hand thumb up and fold the finger in like you are rotating your hand. The movement will be in the anti-clockwise direction which is positive torque. Do it with the left hand, the torque will become negative.

In this section, we will discuss the torque formula in detail with examples.

## Difference between Static and Dynamic Torque:

There are 2 types of torque:

Static Torque: Static torque is produced when the force is applied by hand or manually. Turning a screw with a wrench, a car door etc. the static is relatively slow.

Dynamic Torque: dynamic torque is produced when the force is applied with a power tool, for example, the torque in the tire of a car or a motorcycle etc.

## What Is Torque Formula in Physics?

There are 2 types of formulas to calculate torque:

T = F x r sin (θ)

Where T is torque, F is force, r is distance of lever arm and sin(θ) shows the angle between the force vector and the moment arm. It is also called the motor torque formula.

Also, there is a simple formula to calculate the torque:

*T = F x d *

Where *T *is Torque*, F* is force*, *and* d* is the distance of the moment arm*. *

The unit of torque is *Newton Metre, *and the unit of force is* Newton.*

Let’s take some values and calculate torque.

For example: A wrench of length 20 cm is applied force of 4 Newton to open a screw. Calculate the torque produced by the force applied.

F = 4 N

Length of the lever arm = d = 20 cm

Then,

T = 4 x 20 = 8 Nm.

2^{nd} example: the width of a door is 40cm, and the force applied to open the door is 3 Newton, calculate the torque produced when opening the door.

T =?

F = 3

d = 0.40 m

T = 3 x 0.40 = 1.20

T = 1.20 Nm.

### How to Calculate Force with Torque Formula?

Sometimes it happens when the value of torque is given and one of the remaining two values is asked to calculate. The formula for torque can be changed according to the need. For example:

When opening a door torque produced is 30 Nm, and the length of lever arm is 40cm, calculate force.

The formula will become:

T = F x d

F = T / d

F = 30 / 40 = 0.75

F = 0.75 Newton.

### How to Calculate Distance or Length of lever arm with Torque Formula?

When opening a door torque produced is 80 Nm, force applied to open the door is 4 Newton, calculate the d or the length of the lever arm.

T = F x d

d = T / F

d = 80 / 4

Distance = 20 cm