1Which of these has the same dimensions as angular velocity?
Angular velocity and velocity gradient both have the dimensions [T⁻¹].
MechanicsClass 11, System of Particles and Rotational Motion
Dimensional formula of Angular velocity
[T-1]
Angle turned per unit time. The radian is dimensionless, so angular velocity has the dimension of frequency.
How to get the dimensional formula of angular velocity
- Start from the definition: angular velocity = angle / time.
- angle = length / length, so angle is [L] / [L] = [M0 L0 T0].
- Put in the dimension of each part: [M0 L0 T0] / [T].
- Add the powers of each base quantity: [T-1].
Quantities with the dimensions [T⁻¹]
Equal dimensions do not make them the same quantity. Compare angular velocity with the others in the full grid.
Three questions on angular velocity
2What is the SI unit of angular velocity?
The SI unit of angular velocity is the radian per second (rad/s).
3Which one has different dimensions from the others?
Angular impulse is [M L² T⁻¹]. The other three are all [T⁻¹].
Angular velocity: quick answers
What is the dimensional formula of angular velocity?
The dimensional formula of angular velocity is [T⁻¹]. It comes from angular velocity = angle / time.
What is the SI unit of angular velocity?
The SI unit of angular velocity is the radian per second (rad/s).
Which quantities have the same dimensions as angular velocity?
Angular velocity shares [T⁻¹] with velocity gradient, frequency, angular frequency, decay constant, activity. Equal dimensions do not make them the same quantity.