Torque Formula and Equation

The idea of torque arose from the study of  Archimedes of the utilisation of machines or levers. Torque can be reckoned as a twist for any physical object around its definite axis or regarded as a linear force of a pull or push. The point at which the object is set to rotate is the axis of rotation. Torque is denoted by tau(τ), and M. denotes the moment of force. In this article, we’ll see the torque formula, the equations, and the torque meaning.

Define Torque

The moment of force or simply movement is also known as torque. It refers to the force that helps an object rotate about its axis, fulcrum, and pivot. The thought of force is similar to the force of pulling or pushing an object, while on the other hand, torque is an idea in which it forces the object to rotate, and it also adverts to the turning effect. The angle at which point the object rotates is called the axis of rotation. Acceleration and mass are the main factors to find a linear force, which involves rotation.

Torque Formula 

When we use a wrench for fixing a bolt, its force varies the rotational movement along its axis. This process is known as torque. Torque is defined as the changing effect of force on the rotation line.

The formula of torque can be calculated as;

τ = F × d 

Where F = force which is applied to the object, or linear force

d = The normal  distance covered from the axis of rotation 

τ = tau 

The magnitude of torque can be described as ;

τ = Fd siny

Where y is the angle between the axis of rotation and the force applied. The unit of torque is measured in a Newton metre (Nm).

Derivation of Torque Formula 

The SI unit of torque is measured in a Newton metre (Nm).

The amount of rate of change in angular momentum concerning time = ΔL/ΔT

Now, ΔL/ΔT = Δ(I ω)/ΔT = I . Δω/ΔT ……….eq (1)

Where (I) is constant because the shape and mass of the object are the same or unchanged.

Δω/ΔT adverts to the amount of rate of change in angular velocity concerning time known as angular acceleration which is denoted as alpha (α).

With the help of equation (1), we can write;

ΔL/ΔT = I α………eq(2)

Where I = Moment of inertia, which cites the rotational equivalent of inertia of a linear motion. And the same is the angular acceleration which also cites rotational motion, equal to linear acceleration.

So from the above equation, we can conclude that,

ΔL/ΔT = τ, Which refers to the amount of change in angular momentum concerning the time, also called torque.

Now, Torque = moment of a force.

T = F x r = Fr siny……….eq(3)

Where F =  the vector of forcer = position vector 

y = Angle present between the Lever’s arm and the force vector.

“x” = Cross-Product 

So now,

Τ = r F sin y = r ma siny = r m αr siny = mr2. α siny = I α siny = I X α…….…eq(4)

T = I α {from the above eq(4)}

or  T = I (ω2-ω1)/t 

Where α = Angular acceleration for that rate of changing time from the initial value to the final value or from the initial angular velocity to the final angular velocity.

Use of Torque in a Car 

Torque meaning is an aspect of twisting for rotational force. The engine present in a motorcar rotates about its axis, creating torque. The strength of a vehicle can be determined by its torque. The acceleration induced in a car to accelerate from its initial position to the final position on the track is due to the torque which makes the engine shaft accelerate in seconds. 

Let’s take another look at torque by solving a question. 

• Suppose a Car mechanic uses a force of 600 Newton to wrench for losing a bolt. The force applied by the car mechanic is perpendicular to the wrench’s arm. The distance covered from the mechanic hand to the bolt is about 0.20 m. Find out the magnitude applied to the torque?

The angle between the force and the wrench in the moment of the arm is 90 degrees.

We know  that, sin 90y = 1

The magnitude of torque is given by;

T = F × r × siny 

Therefore, the torque’s magnitude is given by 

(600N) (0.2m) = 120 N m

Therefore, the torque magnitude is 120 Newton-metres (N m).

Conclusion

Torque refers to the force which causes a body or an object to rotate about its axis or cause motion. It is also known as the turning effect. The point at which the object rotates about its axis is also called the axis of rotation. Torque helps to tell us about how powerful an object can be, such as cars, heavy trucks, etc. The torque formula can be represented as  T = F × r × siny. The SI unit of torque is measured in a Newton metre (Nm).