1Which of these has the same dimensions as angular momentum?
Angular momentum 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 momentum
[M L2 T-1]
Moment of inertia times angular velocity, also r times p. It has the dimension of Planck's constant.
How to get the dimensional formula of angular momentum
- Start from the definition: angular momentum = moment of inertia × angular velocity.
- moment of inertia = mass × length2, so moment of inertia is [M] × [L]2 = [M L2].
- angle = length / length, so angle is [L] / [L] = [M0 L0 T0].
- angular velocity = angle / time, so angular velocity is [M0 L0 T0] / [T] = [T-1].
- Put in the dimension of each part: [M L2] × [T-1].
- 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 momentum with the others in the full grid.
Three questions on angular momentum
2What is the SI unit of angular momentum?
The SI unit of angular momentum is the kilogram metre squared per second (kg m²/s).
3Which one has different dimensions from the others?
Thrust is [M L T⁻²]. The other three are all [M L² T⁻¹].
Angular momentum: quick answers
What is the dimensional formula of angular momentum?
The dimensional formula of angular momentum is [M L² T⁻¹]. It comes from angular momentum = moment of inertia × angular velocity.
What is the SI unit of angular momentum?
The SI unit of angular momentum is the kilogram metre squared per second (kg m²/s).
Which quantities have the same dimensions as angular momentum?
Angular momentum shares [M L² T⁻¹] with angular impulse, Planck's constant, reduced Planck's constant (h-bar). Equal dimensions do not make them the same quantity.