1Which of these has the same dimensions as torque?
Torque and internal energy both have the dimensions [M L² T⁻²].
MechanicsClass 11, System of Particles and Rotational Motion
Dimensional formula of Torque
[M L2 T-2]
Force times perpendicular distance. Torque has the same dimension as work but they are different quantities, and torque is not measured in joules.
How to get the dimensional formula of torque
- Start from the definition: torque = force × length.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- Put in the dimension of each part: [M L T-2] × [L].
- Add the powers of each base quantity: [M L2 T-2].
Quantities with the dimensions [M L² T⁻²]
- Work
- Energy
- Kinetic energy
- Potential energy
- Torsional constant
- Gravitational potential energy
- Strain energy
- Heat
- Internal energy
- Electric potential energy
- Work function
- Photon energy
- Binding energy
Equal dimensions do not make them the same quantity. Compare torque with the others in the full grid.
Three questions on torque
2What is the SI unit of torque?
The SI unit of torque is the newton metre (N m).
3Which one has different dimensions from the others?
Moment of inertia is [M L²]. The other three are all [M L² T⁻²].
An equation that uses torque
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
τ = r F sin(θ)tau[M L2 T-2]=r F sin(theta)[M L2 T-2]Dimensionally consistentEvery term is [M L2 T-2]
r = lengthθ = angle
Torque: quick answers
What is the dimensional formula of torque?
The dimensional formula of torque is [M L² T⁻²]. It comes from torque = force × length.
What is the SI unit of torque?
The SI unit of torque is the newton metre (N m).
Which quantities have the same dimensions as torque?
Torque shares [M L² T⁻²] with work, energy, kinetic energy, potential energy, torsional constant, gravitational potential energy, strain energy, heat. Equal dimensions do not make them the same quantity.