Determine the dimensions of angular acceleration . Some of the equations involving related quantities are = ₂ - ₁ t₂ - t₁ , = ₂ - ₁ t₂ - t₁ , = F r and I = mr^2 . The symbols have standard meanings.

Step-by-step solution

From the given equations, the angular velocity is given by = ₂ - ₁ t₂ - t₁ . Since angular displacement is a dimensionless quantity, its dimensions are [M^0 L^0 T^0] . The dimensions of time t are [T] . Thus, the dimensions of angular velocity are [M^0 L^0 T^0] [T] = [T⁻¹] . The angular acceleration is given by = ₂ - ₁ t₂ - t₁ . Substituting the dimensions of and t , the dimensions of are [T⁻¹] [T] = [T⁻²] .