Question

The dimensions of angular velocity is-
1. [M⁰ L⁰ T⁰]
2. [M⁰ L⁰ T^-1]
3. [M0 L1 T1]
4. [M0 L-1 T1]

Answer 1

Correct Answer - Option 2 : [M⁰ L⁰ T^-1]

The correct answer is option 2) i.e. [M0 L0 T-1]

CONCEPT:

• Angular velocity is the velocity associated with objects moving on a curved path.
  • While on a curved path, the displacement is the change in angle about the point of rotation or curved motion.

Angular velocity, \(ω =\frac{angle}{time} =\frac{d\theta}{dt}\)

For circular motion, \(ω =\frac{d\theta}{dt} = \frac{360^∘}{t} = \frac{2π}{t} \:rad/s\)

EXPLANATION:

• Angular displacement is defined as the ratio of arc length and radius.
• Thus, angular displacement is the ratio of two like quantities and is dimensionless.
• Angular velocity is the rate of change of angular displacement with time.
• Hence, the SI base unit for angular velocity is s^-1.
• Therefore, the dimension of the angular velocity is [M0 L0 T-1].