#AP Physics 1: Momentum & Impulse - The Night Before

Hey! Let's get you prepped and confident for tomorrow's exam. We're going to break down momentum and impulse, making sure everything sticks. Let's do this!

#1. Momentum: The Motion Measurer

#What is Momentum?

• Definition: Momentum ($\vec{p}$) is a measure of how much 'oomph' an object has in its motion. It's the product of an object's mass (m) and its velocity ($\vec{v}$).
  $$\vec{p} = m\vec{v}$$
• Key Point: Momentum is a vector, meaning it has both magnitude and direction. The direction of momentum is the same as the direction of the velocity.
• Units: kg⋅m/s

#Total Momentum

• To find the total momentum of a system, simply add up the individual momentums of each object. $$\vec{p}_{total} = \vec{p}_1 + \vec{p}_2 + \vec{p}_3 + ...$$

#Linear vs. Angular Momentum

• Linear Momentum: What we're focusing on here – for objects moving in a straight line.
• Angular Momentum: For rotating objects (you'll see this specified in questions if it's relevant).

#Example Problems

Example Problem 1:

A car (mass 1000 kg) is traveling at 30 m/s and then stops. What's the change in momentum?

• Initial momentum: $p_i = (1000 \text{ kg}) \times (30 \text{ m/s}) = 30000 \text{ kg m/s}$
• Final momentum: $p_f = (1000 \text{ kg}) \times (0 \text{ m/s}) = 0 \text{ kg m/s}$
• Change in momentum: $Δp = p_f - p_i = 0 - 30000 = -30000 \text{ kg m/s}$ (The negative sign indicates the direction of the change)

Example Problem 2:

A 0.2 kg ball is thrown at 20 m/s. What's its momentum?

• $p = (0.2 \text{ kg}) \times (20 \text{ m/s}) = 4 \text{ kg m/s}$

Example Problem 3:

A 2000 kg car at 10 m/s hits a stationary 3000 kg truck. They move together at 5 m/s. What's the total momentum before and after?

• Before: $p_{car} = (2000 \text{ kg}) \times (10 \text{ m/s}) = 20000 \text{ kg m/s}$, $p_{...