4 min readβ’january 13, 2023

Daniella Garcia-Loos

In this unit, we'll only be talking about **linear momentum**, but look forward to angular momentum in the next unit! Conceptually, its quite hard to describe without using quantities, but essentially, it is a measurement of mass in motion. The most basic equation for **linear momentum** is:

p = mv

- It's a vector
- Units are kg*m/s
- It is NOT the same as kinetic energy
- Kinetic energy is a scalar and describes a different relationship

Let's try to derive Newton's Second Law using momentum!

Now that looks pretty familiar, doesn't it?

Let's take a closer look at one part of this derivation.

This change in momentum actually has a special name, **Impulse**! (Or as some like to call, Jimpulse)

Or the calculus version:

We tend to use calculus when the force or the mass is variable, like with a rocket!

Here are some **key things to know about impulse**:

- Impulse is the product of force and time, represented mathematically as J = F*Ξt.

Additionally, AP loves to ask questions about impulse in relation to graphs!

Impulse is the area under the curve (check out the integral!) of a Force vs. Time graph.

The curves won't always look as pretty as they did in AP Physics 1 because we have the power of calculus now!

β οΈ *So..what does impulse really mean?*

Have you ever tried an egg drop experiment? One where you tried to shield a poor egg from cracking as soon as it hit the ground?

Think back to which experiments worked best...theoretically the ones that work best should be the ones that increase the amount of time of impact!

The center of mass of a system of objects is a point that represents the average position of all the objects in the system. The velocity of the center of mass of a system of objects is the rate of change of the position of the center of mass with respect to time.

Here are some key things to remember when solving a problem asking for the **velocity of the center of mass:**

During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier womenβs match, reaching a speed of 58 m/s (209 km/h). What is the average force exerted on the 0.057-kg tennis ball by Venus Williamsβ racquet, assuming that the ballβs speed just after impact is 58 m/s, that the initial horizontal component of the velocity before impact is negligible, and that the ball remained in contact with the racquet for 5.0 ms (milliseconds)?(Taken from Lumen Learning)

**Answer:**
To determine the change in momentum, substitute the values for the initial and final velocities into the equation above.

Now the magnitude of the net external force can determined by usingΒ

Use the Impulse formula on your formula chart, and don't forget to include your bounds/limits of integration!

Again, use the formula on your chart and integrate with bounds. Take note that there is an alternate form of resolving this with another impulse formula

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