In Physics, Momentum is the 'quantity of motion' in a body, and Impulse is the effect of a large force acting for a very short time. Interestingly, both share the exact same dimensional formula.
Momentum Formula: p = mv.
Impulse Formula: J = F × t.
Shared Dimensional Formula: [M L T⁻¹].
SI Unit: kg·m/s or N·s.
Theorem: Impulse = Change in Momentum.
Formula: Linear Momentum = Mass × Velocity (p = mv)
Calculation: Momentum = [M] × [L T⁻¹] Dimension of Momentum = [M L T⁻¹]
Formula: Impulse = Force × Time (J = F × t)
Calculation: Impulse = [M L T⁻²] × [T] Impulse = [M L T⁻²⁺¹] Dimension of Impulse = [M L T⁻¹]
The calculations above prove the Impulse-Momentum Theorem, which states that Impulse is equal to the change in Momentum (J = Δp). Because they represent the same physical change, they must have the same units (kg·m/s or N·s) and dimensions.
The dimensional formula of impulse is [M L T⁻¹].
The dimensional formula of linear momentum is also [M L T⁻¹]. Both impulse and momentum share the same dimensions.
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