Momentum is a measure of an object's resistance to a change in motion. It is a vector quantity, meaning it has both magnitude (size) and direction. The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity. The exam weight of this unit is 12-18%, and it tends to span over ~14-17 45-minute class periods.

There are a few key concepts and formulas related to momentum that are important to understand:

• The law of conservation of momentum: This states that in an isolated system (one that is not affected by external forces), the total momentum of the system remains constant. This means that if two objects collide and stick together, their combined momentum after the collision will be equal to their combined momentum before the collision.
• Impulse: This is the change in momentum of an object over a given time period. The formula for impulse is J = Δp = FΔt, where J is impulse, Δp is change in momentum, F is force, and Δt is time.
• Elastic and inelastic collisions: Elastic collisions are those in which the kinetic energy of the objects is conserved before and after the collision. Inelastic collisions are those in which kinetic energy is not conserved. Inelastic collisions often result in objects sticking together after the collision.
• Work-energy theorem: This states that the work done on an object is equal to the change in kinetic energy of the object. The formula for the work-energy theorem is W = ΔK = Fd, where W is work, ΔK is change in kinetic energy, F is force, and d is distance.

5.1 Momentum and Impulse

Momentum is a measure of an object's resistance to a change in motion, which is defined as the product of an object's mass and velocity. In other words, momentum is the "amount of motion" an object has. It is a vector quantity, meaning it has both magnitude (size) and direction. The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity.

The law of conservation of momentum states that in an isolated system, the total momentum of the system remains constant. This means that if two objects collide and stick together, their combined momentum after the collision will be equal to their combined momentum before the collision. This law is a fundamental concept in physics, and it has many important applications, including in collisions, rocket propulsion, and the behavior of subatomic particles.

Impulse, on the other hand, is the change in momentum of an object over a given time period. It is the product of the force applied to an object and the time over which the force is applied. The formula for impulse is J = Δp = FΔt, where J is impulse, Δp is change in momentum, F is force, and Δt is time. When an object experiences an impulse, its momentum changes. Impulse can be thought of as the "amount of force" applied to an object over time.

5.2 Representations of Changes in Momentum

In physics, momentum can be represented in several different ways, depending on the context of the problem. Some of the most common representations of momentum at an AP Physics 1 level are:

• Vector notation: Momentum is a vector quantity, meaning it has both magnitude (size) and direction. It is often represented as a vector with the symbol "p" and an arrow pointing in the direction of the momentum. The magnitude of the vector represents the size of the momentum, and the direction of the vector represents the direction of the momentum.
• Scalar notation: Momentum can also be represented as a scalar (a number with no direction) by only considering its magnitude. In this case, the formula for momentum is still p = mv, where p is momentum, m is mass, and v is velocity. However, in this representation, the direction of the momentum is not considered.
• Graphical representation: Momentum can also be represented graphically, typically as a point on a coordinate plane. The x-coordinate of the point represents the momentum in the x-direction, and the y-coordinate of the point represents the momentum in the y-direction. This representation allows for the visualization of the direction and magnitude of the momentum.
• Component notation: Momentum can be broken down into its x and y components. For example, if an object has a velocity of (vx,vy) and a mass of m, the momentum can be represented as (mxvx, myvy) where mx and my are the mass in the x and y direction respectively.
• Momentum diagrams: Momentum diagrams are used to represent the momentum of an object before and after a collision, usually in the form of arrows pointing in the direction of the momentum. The length of the arrow represents the magnitude of the momentum, and the direction of the arrow represents the direction of the momentum. Momentum diagrams are often used to visualize the conservation of momentum in collisions.

5.3 Open and Closed Systems: Momentum

In physics, systems can be classified as either open or closed systems depending on whether they exchange matter or energy with their surroundings. This distinction is important when considering the conservation of momentum.

A closed system is one in which no matter or energy is exchanged with the surroundings. In a closed system, the total momentum of the system remains constant, according to the law of conservation of momentum. This means that if two objects collide and stick together, their combined momentum after the collision will be equal to their combined momentum before the collision. This is known as an "isolated" system, where the total momentum is conserved.

An open system, on the other hand, is one in which matter or energy is exchanged with the surroundings. In an open system, the total momentum of the system may not remain constant. For example, if an object collides with a wall and bounces back, the total momentum of the system (object + wall) will not be conserved because the wall exerts a force on the object, and as a result, the momentum of the system changes.

5.4 Conservation of Linear Momentum

The conservation of linear momentum is a fundamental principle in physics that states that the total linear momentum of a closed system (a system in which no matter or energy is exchanged with the surroundings) remains constant over time. This principle is often referred to as the law of conservation of momentum. Linear momentum is the product of an object's mass and velocity, and it is a vector quantity, meaning it has both magnitude (size) and direction.

The conservation of linear momentum can be observed in many physical situations, such as in collisions between objects. When two objects collide and stick together, the total linear momentum of the system (the two objects) before the collision is equal to the total linear momentum of the system after the collision. This is known as the law of conservation of momentum.

The conservation of linear momentum can also be observed in situations where an object is acted upon by an external force, such as a rocket propulsion system. In this case, the momentum of the rocket and the momentum of the exhaust gases must be considered. The total momentum of the system (rocket + exhaust gases) remains constant, even though the rocket is accelerating.

The conservation of linear momentum can be mathematically represented by the following equation:

∑p1 = ∑p2

where ∑p1 is the initial total linear momentum of the system and ∑p2 is the final total linear momentum of the system.