Find the dimensions of

A. angular speed ω,

B. angular acceleration α,

C. torque Γ and

D. moment of inertia I.

Some of the equations involving these quantities are

and

The symbols have standard meanings.

A. Angular speed is the rate of change of angular position of an object w.r.t. time.

Dimensions of dθ =[M⁰L⁰T⁰]

Dimensions of dt = [T]

Dimensions of ω = .

B. Angular acceleration is the rate of change of angular speed w.r.t time.

Dimensions of dω =

Dimensions of dt = [T]

Dimensions of =

C. Torque is the rotational effect of a linear force. It is the turning effect when a force is applied on a body that can rotate.

Torque(T) = Force(F) × distance from axis (r)

Dimensions of F = [MLT^-2]

Dimensions of r = [L¹]

Dimensions of T = [MLT^-2] × [L¹] = [ML²T^-2]

D. Moment of inertia is defined as the inertia of a rotating body w.r.t. its axis of rotation.

Moment of inertia (I) = mass of body (m) × square of ⊥ distance from axis(r²)

Dimensions of m = [M]

Dimensions of r² = [L²]

Dimensions of I = [M] × [L²] = [ML²]