Unit of 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.

Torque is the moment of force that enables a body to rotate on its own axis and gain angular acceleration. The SI unit of Torque is N.m. It is a vector quantity and can be both static and dynamic. In the following sections, we will learn about the units of torque in detail. Torque is also known as turning effect, rotational effect, a moment of force, or moment.

If the magnitude of a body is lower than the movement of an object over a specific distance then it is known as a point object. The motion of the point objects is described in one, two, and three dimensions with the help of kinematics. The point objects are made up of usually very large particles. The rotational behavior of these boundless particles is described by Newton's Law of Motion.

Contents of the Article

This article explains to you the meaning of torque, its importance, and its units. If you incur any doubts while reading this, then you can simply refer to the frequently asked questions at the end of this article.

On this Page, We will Learn

• 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 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 a 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 that 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 linear motion, then which kind of force is responsible for producing angular acceleration?

Angular Acceleration

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) = df/dg

The Formula of Torque

Torque = force x distance

Torque = rF sin θ

Where, r= radius, F = force,  θ= angle between lever arm.

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:

\[\vec{N}=\vec{H}\times \vec{k}=kN sin\theta \hat{n}\]

Where Ө is the angle between \[\vec{k}\]  and  \[\vec{H}\].  n is the unit vector along  \[\vec{N}\].

Here, the direction of  \[\vec{N}\]  is perpendicular to the plane containing \[\vec{k}\]  and  \[\vec{H}\].

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

Importance of Torque

• Torque explains the concept of the rotational motion of rigid bodies. 

• The direction and intention of the force applied to a body can be detected by the concept of torque. 

• It also determines the clockwise and anti-clockwise motions on a body. 

• Torque also determines the angular acceleration when a body rotates.

Units of Torque in MKS and Dimension

• The MKS unit of Torque is Newton-meter or N-m or kgm²sec^-2.

• The dimensional formula of Torque is ML²T^-2 which is equivalent to Joule.

Different Units of Torque

• The SI unit of torque is a newton-meter. 

• The SI base unit of torque is kgm²sec^-2.

• The non-SI unit of torque is meter-kilogram-force

• In the CGS system, the unit of Torque is dyne-centimeter (dyne-cm)

Other units of Torque

• inch-pound-force 

• foot-pounds-force 

• ounce-force-inches(ozf.in)

• pounce-force-feet (lb.ft)

Real-life Applications of Torque

Old Telephone

We used to rotate the numbers on the dial in a clockwise or counterclockwise direction. Torque is making that rotational push that 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.