4.1 Linear Momentum

Learning objectives

4.1A—Describe the linear momentum of an object or systemDescribe the linear momentum of an object or system.• Linear momentum is defined by the equation =pmv.-- -• Momentum is a vector quantity and has the same direction as the velocity.• Momentum can be used to analyze collisions and explosions.- i. A collision is a model for an interaction where the forces exerted between the involved objects in the system are much larger than the net external force exerted on those objects during the interaction.- ii. As only the initial and final states of a collision are analyzed, the object model may be used to analyze collisions.- iii. An explosion is a model for an interaction in which forces internal to the system move objects within that system apart. BOUNDARY STATEMENT Unless otherwise stated, the general term “momentum” will refer specifically to linear momentum. TOPIC 4.2 Change in Momentum and Impulse | AP Physics 1: Algebra-Based Course and Exam Description

Connect mass and velocity

An object's linear momentum is its mass multiplied by its velocity. Because mass is a positive scalar, momentum points in the same direction as velocity.

$\begin{gathered}\vec p=m\vec v\\ [p]=\text{kg}\,\text{m/s}\end{gathered}$

Keep direction in the result

Worked example: choose right as positive. A $2.0\,\text{kg}$ cart moves left at $3.0\,\text{m/s}$ , so $v=-3.0\,\text{m/s}$ .

$p=mv=(2.0\,\text{kg})(-3.0\,\text{m/s})=-6.0\,\text{kg}\,\text{m/s}$ .

The negative sign means the momentum is leftward. At fixed velocity, doubling mass doubles $|p|$ ; at fixed mass, doubling speed doubles $|p|$ .

Recognize interaction models

Model	Defining idea	What the model lets us focus on
Collision	Forces between the involved objects are much larger than the net external force during the brief interaction	Compare the objects' initial and final states using the object model
Explosion	Forces internal to the chosen system move its objects apart	Compare the system's states before and after the internal separation

Respect the model limits

A collision model does not mean external forces are literally zero; it means the internal interaction forces dominate during the collision interval. Unless stated otherwise in AP Physics 1, momentum means linear momentum. Impulse and momentum conservation are separate relationships developed in the following Topics.

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