Physics & Engineering 12 · Week 14 · Monday

Momentum Is a Vector

Learning objective: Calculate one-dimensional momentum with signed velocity, define the system, and distinguish momentum from energy.

45–60 minutes · Digital-only investigations · Student work stays locally

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What makes a moving object hard to stop?

Momentum depends on mass and velocity: p=mv. In a chosen one-dimensional reference frame, velocity can be positive or negative and so can momentum. Momentum is not merely speed: a 2 kg object at +3 m/s has +6 kg·m/s, while the same object at −3 m/s has −6 kg·m/s. The same speed can represent different directions.

Direction, units and sign conventions

Choose right as positive before entering values. Momentum is a vector with SI units kg·m/s, equivalent to N·s for an impulse. A larger mass at equal velocity has larger momentum magnitude. Negative momentum never indicates negative mass; it indicates motion in the negative coordinate direction.

Momentum and kinetic energy differ

Momentum is p=mv; kinetic energy is K=½mv². They are different physical quantities with different units. Reversing velocity reverses momentum but leaves kinetic energy magnitude unchanged. A 2 kg object reversing from +3 to −3 m/s keeps K=9 J if the speed is unchanged, but its momentum changes from +6 to −6 kg·m/s.

System and forces

The momentum of one object can change when a net external impulse acts on it. When multiple bodies form a system, the total momentum and what counts as external depends on the chosen boundary. Week 15 develops multi-object conservation in detail; Week 14 begins with the momentum of a selected body.

Vocabulary and definitions

momentum
Vector p=mv, with direction determined by velocity.
velocity
Signed or vector rate of change of position.
reference frame
Chosen coordinate system for measuring movement.
kinetic energy
Nonnegative energy K=½mv², distinct from momentum.
system boundary
The body or interacting group included in the analysis.

Worked example

A 2 kg model cart starts at +3 m/s: p=+6 kg·m/s. At −3 m/s: p=−6 kg·m/s. Δp=−12 kg·m/s despite equal initial and final kinetic energy of 9 J.

Show the chosen body, coordinate sign convention, equation, units and interval.

Student evidence portfolio

Create a signed-momentum table using +3, 0 and −3 m/s. Use the Momentum Change Calculator to record before/after values and explain the distinction from kinetic energy.

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Daily Retrieval · 4 Questions

Public open-book formative practice. Correct missed work toward the 80% learning target; formal exams must remain separately supervised.