Angular momentum (L) is a measure of the rotational motion of an object ā the rotational equivalent of linear momentum. Finding its dimensional formula is a common exam question.
Dimensional Formula: [M LĀ² Tā»Ā¹]
SI Unit: kgĀ·mĀ²/s (or JĀ·s).
Formula: L = IĻ = mvr.
Same Unit as Planck's Constant: h is also in JĀ·s.
Conservation: Angular momentum is conserved when no external torque acts.
Step 1: Angular Momentum = Moment of Inertia Ć Angular Velocity L = I Ć Ļ
Step 2: Moment of Inertia (I) = mass Ć radiusĀ² [I] = [M][LĀ²]
Step 3: Angular Velocity (Ļ) = angle/time [Ļ] = [Tā»Ā¹] (since angle is dimensionless)
Step 4: Therefore: [L] = [M][LĀ²][Tā»Ā¹] = [M LĀ² Tā»Ā¹]
Angular Momentum = Linear Momentum Ć Perpendicular Distance L = p Ć r = mv Ć r [L] = [M][LTā»Ā¹][L] = [M LĀ² Tā»Ā¹]
SI unit of Angular Momentum = kgĀ·mĀ²/s (kilogram metre squared per second)
This is also written as JĀ·s (Joule-second) ā the same unit as Planck's constant (h)!
The dimensional formula of angular momentum is [M LĀ² Tā»Ā¹].
The SI unit of angular momentum is kgĀ·mĀ²/s (kilogram metre squared per second), also written as JĀ·s.
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