Question

The dimensions of angular acceleration of a body is given as-
1. M⁰L⁰T^-2
2. M⁰LT^-2
3. M⁰LT^-1
4. M⁰L⁰T^-1

Answer 1

Correct Answer - Option 1 : M⁰L⁰T^-2

The correct answer is option 1) i.e. T^-2.

CONCEPT:

• Angular acceleration: It is the rate of change angular velocity of an object with respect to time i.e.​

α=ωf−ωit

\(ω = \frac{ω_f -ω_i}{t}\)

where, α = angular acceleration, ωf = final angular velocity, ωi = initial angular velocity, and t = time

EXPLANATION:

Linear velocity (v) = Angular velocity (ω) × radius (r)

• The dimension of angular velocity is:

Angular velocity = Linear velocity/radius = LT^-1/L = T^-1 

• The dimension of angular velocity is:

Angular acceleration = angular velocity/time = T^-1/T = T^-2.

• LT^-2 is the dimensional formula of linear acceleration.
• LT^-1 is the dimensional formula of linear velocity.