Momentum and its direction

What you will learn

p = mv; signed momentum and changes in transportation contexts.

Specification mapping: B2.4

Prerequisites: B1.3, B2.2

Physical principles

Linear momentum p is mass multiplied by velocity: p = mv. Its SI unit is kg m s⁻¹, equivalent to N s. Momentum is a vector and has the direction of velocity. A heavy slow object and a light fast object can have the same momentum, but this does not make all their other physical properties equivalent.

For one-dimensional problems, choose a positive direction and use signed velocities. A reversal can produce a momentum change larger in magnitude than the final momentum alone. The change is Δp = pfinal − pinitial, not the sum of unsigned speeds unless the directions make that appropriate.

For a system, total momentum is the vector sum of component momenta. Oppositely directed momenta can cancel even though both objects are moving. Momentum is conserved for an isolated system with negligible net external impulse; this supporting principle does not mean each object keeps its own momentum during a collision. The central required relation here is p = mv.

Scientific diagram and interpretation

The object travels 60 m east then 30 m west. Total path length is 90 m; resultant displacement is 30 m east. Separated paths are shown for legibility.

Equations and relationships

p = mv

Worked examples and applications

Vehicle momentum

A 1.20 × 10³ kg car travels east at 15.0 m s⁻¹. p = 1200 × 15.0 = 18000 kg m s⁻¹ east = 1.80 × 10⁴ kg m s⁻¹ east.

Rebound

A 0.20 kg ball initially has v = +10 m s⁻¹ and rebounds at −6.0 m s⁻¹. Δp = 0.20(−6.0−10) = −3.2 kg m s⁻¹. Its momentum change points in the negative direction.

Common misconceptions

Momentum is not kinetic energy; equal momentum does not prove equal energy or equal collision damage.

Examination technique

Include direction and use final minus initial when calculating a change.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.