37. What is the dimension of angular velocity? - Sindh Board (stb)

                      

EXPLANATION

Question: What is the dimension of angular velocity?

• a) M⁻¹LT⁻²
• b) M⁻¹L⁰T⁻¹
• c) M⁰L⁰T⁻¹
• d) M⁻²L⁻²T⁻²

 ANSWER: c) M⁰L⁰T⁻¹

EXPLANATION:

Angular velocity is a measure of how fast an object rotates or revolves around an axis. It is typically represented by the symbol "ω" (omega) and is defined as the rate of change of angular displacement over time.

The formula for angular velocity is:

Angular velocity (ω) = Δθ/Δt

where Δθ represents the change in angular displacement and Δt represents the change in time.

The dimensions of angular displacement (θ) are dimensionless (M⁰L⁰T⁰), as it is a ratio of arc length to the radius.

The dimensions of time (t) are [T].

Therefore, the dimensions of angular velocity can be calculated by dividing the dimensions of angular displacement by the dimensions of time:

[M⁰L⁰T⁰]/[T] = M⁰L⁰T⁰T⁻¹ = M⁰L⁰T⁻¹

Among the given options, the correct answer is:

c) M⁰L⁰T⁻¹