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Summary -Important Principles (Impulse and Momentum)

Note: The starting point for all problems in Kinetics is to draw a free body diagram to

identify all external forces and moments acting on the body and apply Euler’s First and

Second Laws.

Both of Euler’s laws can be integrated with respect to time to yield forms applicable when

the forces and/or moments are given in terms of time or for impact problems.

Integration of Euler’s first law

Σ F = m a_C

Euler’s First Law

with respect to time yields the principle of linear impulse and momentum –

t₂

∫ Σ F dt = m v_c2 - m v_c1

t₁

Principle of Linear Impulse and Momentum

The linear impulse acting on a body equals its change in linear momentum during the time of the impulse. Here

t₂

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

t₁

Σ F = F_xi + 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_c2yj

m v_c1 = linear momentum of body at time t₁and v_c1 = v_c1x i + v_c1yj

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