4.2 Representations of Changes in Momentum

Impulse-Momentum Theorem

Impulse (J) equals the change in momentum: J = Δp = FavgΔt. Impulse is a vector, measured in N·s (equivalent to kg·m/s). When a net force acts on an object over a time interval, it changes the object's momentum by exactly that impulse. This links force, time, and motion changes directly.

Force vs. Time Graphs

On a force-time graph, the area under the curve equals impulse delivered. For varying force, use the actual curve's area (integration or geometric shapes); for constant force, it's a simple rectangle (F×Δt). This graphical method lets you find Δp without knowing mass or velocity directly.

Momentum Bar Charts & Vector Diagrams

Momentum bar charts show initial momentum, impulse, and final momentum as visual bars, illustrating pinitial + J = pfinal. Since momentum and impulse are vectors, direction (sign) matters — bars can be positive or negative. These representations help track momentum changes in collisions or force interactions clearly.

Key terms

Impulse-Momentum Theorem

J = Δp = FavgΔt; the impulse on an object equals its change in momentum.

Units of Impulse

N·s, equivalent to kg·m/s (same units as momentum).

Force vs. Time Graph Area

The area under the curve represents the impulse delivered to the object.

Momentum Bar Chart

A diagram showing pinitial + J = pfinal as bars, illustrating direction and magnitude of momentum changes.

Is Impulse a Vector?

Yes — impulse has both magnitude and direction, matching the direction of the applied net force.

Try an AP-style question

What does the area under a force vs. time graph represent?

1. Work
2. Impulse
3. Acceleration
4. Power