Engr Help

Linear Impulse and Momentum for a Particle in a Plane Click here to skip to Impact.

Key Concept: The principle of linear impulse and momentum for a particle is just an integrated

form of Euler's First Law by integrating F and ma with respect to time instead of just starting

from F = ma.

In a Nut Shell: The principle of linear impulse and momentum for a particle is that the linear

impulse acting on the particle equals its change in linear momentum during the time of the

impulse, say from t₁ to t₂.

t₂

∫ Σ F dt = m v₂ - m v₁

t₁

Principle of Linear Impulse and Momentum for a Particle

NOTE: The principle of linear impulse and momentum is a vector equation.

i.e. It has x and y components.

Meaning of terms:

t₂

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

t₁

Σ F = ΣF_xi + ΣF_y j = sum of all external forces acting on the particle

m v₂ = linear momentum of the particle at time t₂

m v₁ = linear momentum of the particle at time t₁

Strategy:

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

not all forces acting on the particle 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

particle