 # Unit of Torque

## What Is Torque?

The force which is applied to any object to make it rotate is the moment of force or torque.

When the motion of an object over distances is greater than its own size, these bodies are considered as point objects, we use kinematics to describe the motion of these point-sized objects in one, two, and three-dimension,  and some work is required to make changes in the configuration and motion of these objects.

• Unit of torque

• S.I. unit of torque

•  CGS unit of torque

• Other units of torque

• S.I. base unit of torque

You come across these objects daily but are they point-sized in actual?

Well, the objects we see in a real-life aren’t point-sized in an absolute sense. These objects have a bounded size, made up of very large particles.

Here, we would extend the application of Newton’s laws of motion to describe the rotational motion of these finite-sized objects.

Since there are many particles inside the object interacting with each other, these interacting particles together form a system.

Thus, any object of finite size forms a system.

A large body that is made of many particles has the center of mass which states that the mass of the system of the body is supposed to be concentrated at the center. If an external force is applied then the center of mass remains the same or unaffected.

What is an External Force?

We studied in the chapter laws of motion that when a force (H) is applied to any object of mass(k), the object starts accelerating. The statement can be represented by the equation:

 H = k x b

Where b is the acceleration

H is the force

k is the mass

Similarly, When you switch on a fan, the center of the fan remains unmoved, while the fan rotates with angular acceleration. Now this center which remains unmoved is the center of mass of the fan that remains at rest.

You might be wondering that the force we studied in the above relation H=k x b was for applying a force to the bodies in the linear motion, then which kind of force is responsible for producing angular acceleration?

You might be contemplating what does angular acceleration means?

Torque is a measure of the ability of a force to bring the body in rotation. Just as a net force causes acceleration, a net torque causes angular acceleration, where angular acceleration is the rate of change of angular velocity (the velocity at which the body sweeps an angle Ө per unit time). Given by :

 Angular acceleration (s) = change in angular velocity (df) w.r.t time (g) =  $\frac{{df }}{dg}$

Torque or Moment of Force

The object starts rotating about the fixed point or the axis of rotation when an external force is applied. The force applied is called the torque.

In figure.2, we can see that as soon as the external force or torque or moment of force is applied. The twisting of this object is about the axis of rotation which is measured by the product of the magnitude of the force H and the perpendicular distance (k) of the action of a force from the axis of rotation. The torque is represented by the Greek letter N. The statement is represented by the equation given below:

 →   →        →                     ៱N =  H    x    k  =  kN SinӨ n

→         →    ៱                                        →

Where Ө is the angle between k  and  H.    n     is the vector along  N.

→                                                                         →        →

Here, the direction of  N  is perpendicular to the plane containing k  and  H.

So you can consider torque as the angular equivalent of force. Torque brings forces into the kinematics of the rotational world.

Why is Torque So Important?

Torque is a fundamental concept of physics (as an attribute of force or the moment of force applied in the concepts of rotational motion of rigid bodies) that helps us apprehend how things happen around us. With the help of torque, it can be dictated what the direction and magnitude of a rotational force applied on an object are, allowing you to evaluate the results it may generate.

Basically, torque can help you determine whether the force applied will result in a counterclockwise or clockwise motion.

Torque also helps you to predict the angular acceleration from which the object is being rotated. Since torque can be large or small, it is measured in different units as described below in the table

## Units of Torque: MKS and CGS Unit

 The MKS unit of torque is Newton-meter or N-m or Kg m^2 sec ^ - 2.In the cgs system, the unit is dyne centimeter  (dyne-cm).The dimensional formula for torque is [M ^ 1 L ^ 2 T ^ - 2]  which is equivalent to Joule.

Real-life Applications of Torque

• Old Telephone

We used to rotate the numbers on the dial ina clockwise or counterclockwise direction. Torque is making that rotational push which is exerted by our fingers on the dial.

• Ferris Wheel

The wheel of the Ferris wheel is rotating about its axis, the torque is pushing this wheel to make a rotation.

• Lock-Key

When you twist the key inside the lock, the lock opens. The torque is creating the twisting motion that is put on the key.

### Summary

The torque is required only for creating angular acceleration in the body, but for uniform rotation, no torque is needed.

Torque is just a force that is applied to the axis of rotation with the center of mass of an object, a force applied a distance 'k' away from the center of mass, which causes an object to rotate. Torque is responsible for producing angular acceleration in the body. A bigger force means a bigger torque, and a larger distance from the fixed point also means a bigger torque.

1. What is a static torque?

A static torque is one that does not produce an angular acceleration.

For example, Someone pushing on a closed-door is applying a static torque to the door because the door is not rotating about its hinges, despite the force applied.

A boy who is pedaling a bicycle at a constant speed is applying a static torque because the bicycle is not accelerating.

2. Why is the handle of a screw made wide?

Since the Torque is a turning moment of force which is equal to the force (H) x distance (k)  from the axis of rotation.

Therefore, in order to create a turning effect or a moment of force, the force required will be smaller because the distance k from the axis of rotation is large. Due to this reason, the handle of a screw is made wide.