Torque formula | Torque Equation

1)
Torque formula can be framed considering Torque as the Moment of Force. It is the cross product of Lever Arm Length (r) and the Force applied (F).

  T = r x F = r F Sin θ  ………….(1)
 
Lever arm length r is the shortest distance between the rotation axis and the point of application of the force.

and

θ = angle made between Lever arm and the line of action of the force being applied.

and

F Sin θ is the perpendicular component of the force which is the effective component of the applied force responsible for the rotation.

2) The formula of Torque can also be obtained as the time rate of change of angular momentum.

 T = ΔL/ΔT …………(2)


3) Formula for torque is available as the cross product of Moment of Inertia(I) and Angular Acceleration(α)

T= I X α   ……………(3)
(Tao = I cross Alpha)

Torque Formula | Torque equation

Torque formula
Torque Formula – details below

Formula of torque

r X F

Torque formula
The force is perpendicular to the radius of rotation.Max Torque = Fr
torque derivation
The force is not perpendicular here. See the diagram below for resolved components of force F

equation of moment of force
The effective force that generates torque = Vertically resolved component (in green) of F = F sinθ

Torque is the rotational equivalent of force. As force gives a push and pull for the translational motion domain, torque provides a twist in rotational motion.

In other words, as force causes translational motion, the Torque causes rotational motion.

We can’t separate a torque from a force as it is not possible to apply a torque without applying a force.

The SI unit for torque is the newton metre (N⋅m).

Formula for torque

I x Alpha

From equation 3 in the above paragraph we can notice couple of interesting things.

I (moment of inertia) is the rotational equivalent of mass(inertia) of Translational motion.

Similarly angular acceleration α (alpha) is the rotational motion equivalent of linear acceleration.

Product of mass m and linear acceleration a represents Force in Translational motion.

Similarly I and α in product form represent Torque (τ), which in turn is the rotational equivalent of Force.

Related Post:
Derivation of Torque



Torque formula | Torque Equation
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