- Let's determine the dimensions of each quantity: - Planck's constant (h): From E=hf, [h] = [Energy]/ [Frequency] = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]. - Angular momentum (L): L = Iω or L = r×p, [L] = [Moment of Inertia]×[Angular Velocity] = [ML²]×[T⁻¹] = [ML²T⁻¹]. (Alternatively, [r]×[p] = [L]×[MLT⁻¹] = [ML²T⁻¹]). Dimensions are the same. - Impulse (J): J = FΔt, [J] = [Force]×[Time] = [MLT⁻²]×[T] = [MLT⁻¹]. - Linear momentum (p): p = mv, [p] = [Mass]×[Velocity] = [M]×[LT⁻¹] = [MLT⁻¹]. Dimensions are the same. (Impulse-Momentum Theorem states J = Δp). - Moment of inertia (I): I = mr², [I] = [Mass]×[Length²] = [ML²]. - Moment of a force (Torque, τ): τ = r×F, [τ] = [Length]×[Force] = [L]×[MLT⁻²] = [ML²T⁻²]. Dimensions are different. - Energy (E): [E] = [ML²T⁻²] (e.g., Work done = Force × distance = [MLT⁻²]×[L] = [ML²T⁻²]). - Torque (τ): As calculated above, [τ] = [ML²T⁻²]. Dimensions are the same.