Derivation of Dimensional Formula of Torque
We derive dimensional formula of torque. Since we have seen that torque of an object at a distance r and having angle θ with lever arm is
Torque= Force × distance × sin(θ)
Dimensional formula of τ = dimensional formula of F × r × sin(θ) …..(1)
Now we calculate the dimensional formula of each quantity individually
Dimensional formula of F = [MLT-2]
Dimensional formula of r = [M0L1T0]
Dimensional formula of sin(θ) = [M0L0T0]
Putting all the above three dimensional formulas in Equation (1) we get
Dimensional Formula of Torque = [MLT-2] × [M0L1T0] × [M0L0T0]
Dimensional Formula of Torque = [ML2T-2]
Hence the dimensional formula of Torque is [ML2T-2]
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