Principle of Linear Impulse/Momentum in a Plane Click here for a discussion of Impact

Key Concept: The principle of linear impulse and momentum is just an integrated form of

Euler's First Law by integrating with respect to time. Any analysis can start directly with

Euler's First Law or with the application of the principle of linear impulse and momentum.

In a Nut Shell: The principle of impulse and momentum in a plane is that the linear impulse acting

on a body equals its change in linear momentum during the time of the impulse, say from t₁ to t₂. Integration of Euler’s First Law yields the Principle of Linear Impulse and Momentum.

Σ F = m a_C

Euler’s First Law

Integration with respect to time yields

t₂

∫ Σ F dt = m v_c2 - m v_c1

t₁

Principle of Linear Impulse and Momentum

where

t₂

∫ Σ F dt = the linear impulse acting on the body from t₁ to t₂

t₁

Σ F = F_x i + F_y j = sum of all external forces acting on the body in the x-y plane

m v_c2 = linear momentum of body at time t₂ and v_c2 = v_c2x i + v_c2y j

m v_c1 = linear momentum of body at time t₁ and v_c1 = v_c1x i + v_c1y j

note: C refers to the center of mass of the body

Strategy:

Step 1: Draw a free body diagram showing all external forces acting on the body.

Note that not all forces on the body may result in a change in its linear momentum.

Step 2: Calculate the linear impulse and set it equal to the change in linear momentum

of the center of mass, C

Click here for an example.

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Copyright © 2019 Richard C. Coddington
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