Question

Find the dimensions of (a) angular speed w, (b) angular acceleration and (c) torque τ and (d) moment of interia I.
Concept of Physics - 1 , HC VERMA , Chapter "Introduction to Physics".

Answer 1

Hello Dear.

(a) We know that the formula of Angular speed is :-

Angular speed , ω = θ / t  
Now , changing into dimensions .
ω = M⁰L⁰ / T 
ω = M⁰L⁰T⁻¹
ω = T⁻¹ 
Hence the dimensional formula of angular speed is T⁻¹ .


(b) We know that the formula of Angular acceleration is :-
 α = ω /t 
Now changing into dimensions,
α = M⁰L⁰T⁻¹ / T
α = M⁰L⁰T⁻²
α = T⁻²
Hence the dimensional formula of angular Acceleration is is T⁻² .


(c) We know the formula of Torque is :-
 τ = F.r
Now, changing into dimensions,
τ = [MLT⁻²] . L
τ = ML²T⁻²
Hence Dimensional formula of Torque is ML²T⁻² .


(d) We know the formula of Moment of Inertia is :- 
I = mr²
Now changing into dimensions.
I = M. L²
I = ML²T°
Hence the dimensional formula of Moment of Inertia is ML² .


Hope it Helps.