Lecture 3.2: The Why of Motion

Momentum is the measure of an object's 'unstoppability'.

Today's Essential Questions

• What is momentum?
• What is impulse?
• How does impulse change an object's momentum?

Connecting to Our Last Investigation

Your research on impulse showed a relationship between force and time in collisions. You saw that how long a force is applied is just as important as how strong it is. Today, we'll formalize that relationship with the Impulse-Momentum Theorem, the key to all modern vehicle safety design.

What is Momentum?

Momentum (p) is a measure of an object's quantity of motion. It's often described as inertia in motion. To calculate it, we combine an object's mass and its velocity.

Momentum is a vector—its direction is the same as the velocity's direction.

The Unstoppability Question

Which is harder to stop?

• A massive truck moving very slowly?
• A small, fast-moving baseball?

{% include marp-physics-image.html concept="momentum_comparison" context="lecture" position="center" %}

The answer is, "it depends!" You need to know both the mass and the velocity to calculate the momentum. The object with more momentum is harder to stop.

How Do We Change Momentum?

To change an object's momentum (i.e., to change its velocity), you must apply an external force. But the duration of that force matters.

Impulse (J) is the term for a force applied over a period of time. It is the "thing" that causes a change in momentum.

The Impulse-Momentum Theorem

This is one of the most important relationships in all of physics. It states that the impulse applied to an object is equal to the change in that object's momentum.

This simple equation is the secret behind every modern automotive safety feature.

The Egg Toss Analogy

Imagine catching a raw egg.

• Option 1: You hold your hands rigid. The egg stops very quickly ( is small). To change its momentum to zero in such a short time, the force () on the egg must be very large. The egg breaks.
• Option 2: You move your hands backward as you catch it. This increases the time it takes for the egg to stop ( is large). Since the change in momentum is the same, a larger means the force () is much smaller. The egg is saved.

{% include marp-physics-image.html concept="impulse_egg_catch" context="lecture" position="center" %}

Safety by the Numbers

Let's apply this to a 70 kg person in a car that crashes, going from 15 m/s (34 mph) to 0 m/s. Their change in momentum () is the same no matter how they stop. But the force on them is not.

• Scenario 1: No Airbag
  The person hits the dashboard, stopping in 0.01 seconds.

  This is a crushing, deadly force.

• Scenario 2: With Airbag
  The airbag increases the stopping time to 0.1 seconds.

  This is a much smaller, survivable force.

Thinking Lens: Cause and Effect

The Impulse-Momentum theorem () is a perfect mathematical model of cause and effect.

Question: Which side of the equation represents the "cause" of a change in motion, and which side represents the "effect"? How does this relationship explain the core principle of all collision safety design?

Preparing for Our Next Task

The Impulse-Momentum Theorem is the central idea you will use to explain why crumple zones work in the upcoming vehicle safety simulation lab. You will see directly how changing the time of a collision affects the forces involved.

Summary: Answering Our Questions

• What is momentum?
  Momentum () is the quantity of motion an object has, combining its mass and velocity.

• What is impulse?
  Impulse () is a force applied over a time interval.

• How does impulse change an object's momentum?
  An impulse causes a change in momentum. By increasing the time of an impact (), we can decrease the force () for the same change in momentum.

Prompt: In 2-3 sentences, explain why a small force applied for a long time can have the same effect on an object's motion as a large force applied for a short time.