The dimensional formula of Torque is
[ M1 L2 T-2 ]
where [M], [L], and [T] are the fundamental quantities: Mass, Length, and Time.
From the above formula, we can derive the dimensions of torque as (1, 2, -1).
Derivation of Dimensional Formula of Torque
We can derive this formula using the definition of torque.
In physics, we can define torque as the tendency of a force to rotate a body about some axis. So, mathematically, torque is given as:
Torque = Force * lever arm
Here, lever arm is the perpendicular distance from the axis of rotation to the line drawn along the direction of the force applied. Hence, we can also say
Torque = Force * distance
We know that Force = mass * acceleration. Substituting the value of Force in the above formula, we get
Torque = mass * acceleration * distance
- acceleration = speed / time
- speed = distance / time
- acceleration = distance / time2
Torque = ( mass * distance / time2 ) * distance Torque = ( mass * distance2 ) / time2 Torque = mass1 * distance2 * time-2
Dimensionally, we use
- [M] for mass
- [L] for distance and displacement
- [T] for time
Now the formula becomes
Torque = [M1] * [L2] * [T-2]
Hence, the dimensional equation of torque is τ = [ M1 L2 T-2 ].