1Which of these has the same dimensions as angular impulse?
Angular impulse and reduced Planck's constant (h-bar) both have the dimensions [M L² T⁻¹].
MechanicsClass 11, System of Particles and Rotational Motion
Dimensional formula of Angular impulse
[M L2 T-1]
Torque times the time it acts. It has the same dimension as angular momentum, which is why it equals the change in angular momentum.
How to get the dimensional formula of angular impulse
- Start from the definition: angular impulse = torque × time.
- 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].
- torque = force × length, so torque is [M L T-2] × [L] = [M L2 T-2].
- Put in the dimension of each part: [M L2 T-2] × [T].
- Add the powers of each base quantity: [M L2 T-1].
Quantities with the dimensions [M L² T⁻¹]
Equal dimensions do not make them the same quantity. Compare angular impulse with the others in the full grid.
Three questions on angular impulse
2What is the SI unit of angular impulse?
The SI unit of angular impulse is the newton metre second (N m s).
3Which one has different dimensions from the others?
Force is [M L T⁻²]. The other three are all [M L² T⁻¹].
Angular impulse: quick answers
What is the dimensional formula of angular impulse?
The dimensional formula of angular impulse is [M L² T⁻¹]. It comes from angular impulse = torque × time.
What is the SI unit of angular impulse?
The SI unit of angular impulse is the newton metre second (N m s).
Which quantities have the same dimensions as angular impulse?
Angular impulse shares [M L² T⁻¹] with angular momentum, Planck's constant, reduced Planck's constant (h-bar). Equal dimensions do not make them the same quantity.