Welcome to Dynamics!

In this chapter, we move from simply describing how objects move (Kinematics) to understanding why they move the way they do. This is the heart of Physics: Dynamics. By the end of these notes, you’ll be able to predict exactly how an object will react when you push, pull, or drop it. Don't worry if it feels like a lot of math at first—we’ll break it down into simple, logical steps!

1. The Core Equation: Newton’s Second Law

At the center of dynamics is one of the most famous equations in science: \( F = ma \). This tells us that the net force acting on an object is directly proportional to its acceleration.

What does this actually mean?

Imagine you are pushing a shopping trolley:

  • Force (\( F \)): If you push harder (more force), the trolley speeds up faster (more acceleration).
  • Mass (\( m \)): If the trolley is full of heavy groceries (more mass), you need a much bigger force to get it to speed up at the same rate.
  • Acceleration (\( a \)): This is the change in velocity. If the forces are balanced, the acceleration is zero!

The Newton (N)

The unit of force is the Newton (N). One Newton is defined as the force required to give a mass of \( 1\,kg \) an acceleration of \( 1\,m\,s^{-2} \).

Quick Review: Always remember that \( F \) in this equation stands for the net force (or resultant force). If two people are pushing a box in opposite directions, you must subtract the smaller force from the larger one before using the formula!

Key Takeaway: \( \text{Net Force (N)} = \text{Mass (kg)} \times \text{Acceleration (m s}^{-2}) \).

2. Weight vs. Mass

In everyday life, we use these words interchangeably, but in Physics, they are very different!

  • Mass (\( m \)): Measured in \( kg \). It is a measure of how much "stuff" is in an object. It doesn't change whether you are on Earth, the Moon, or floating in space.
  • Weight (\( W \)): Measured in \( N \). It is a force caused by gravity pulling on your mass.

The Formula

\( W = mg \)

Where \( g \) is the acceleration of free fall (on Earth, this is approximately \( 9.81\,m\,s^{-2} \)).

Did you know? Your mass would be the same on the Moon, but you would weigh much less because the Moon's gravitational field strength (\( g \)) is weaker than Earth's!

3. Common Forces You Need to Know

In your exams, you will encounter these specific terms frequently. Here is a simple breakdown:

  • Tension: The pulling force exerted by a string, rope, or cable when it is pulled tight.
  • Normal Contact Force: This is the "support" force from a surface. If you are standing on the floor, the floor pushes back up on you. It is always perpendicular (at 90 degrees) to the surface.
  • Friction: The force that opposes motion between two surfaces sliding (or trying to slide) across each other.
  • Upthrust: An upward force exerted by a fluid (liquid or gas) on an object floating or submerged in it. Example: Why a boat stays afloat.

4. Free-Body Diagrams

Think of a free-body diagram as a "force map" for a single object. It helps you visualize all the forces acting on that object so you can calculate the resultant force.

How to draw one like a pro:

  1. Represent the object as a simple dot or a small box.
  2. Draw arrows pointing away from the center of the object for every force acting on it.
  3. The length of the arrow should represent the size of the force.
  4. Label every arrow (e.g., "Weight," "Friction," "Normal Contact Force").

Common Mistake to Avoid: Only include forces acting ON the object. Do not include forces that the object is exerting on other things!

5. Motion in Two Dimensions

Sometimes forces don't act in nice, straight lines. You might have a box being pulled by a rope at an angle, or a car sitting on a sloped driveway. To solve these, we resolve the forces into two perpendicular components (usually horizontal and vertical).

Resolving a Force (\( F \)) at an angle (\( \theta \)):

  • Horizontal component: \( F_x = F \cos \theta \)
  • Vertical component: \( F_y = F \sin \theta \)

Memory Aid: "Cos is Close" — The component close to the angle \( \theta \) uses \( \cos \theta \). The other one uses \( \sin \theta \).

Motion on a Slope

When an object is on a slope of angle \( \theta \):

  • The component of weight acting down the slope is \( mg \sin \theta \).
  • The component of weight acting perpendicular to the slope is \( mg \cos \theta \).

Don't worry if this seems tricky! Just remember that gravity always pulls straight down, and you are simply splitting that "downward" arrow into two parts that align with the slope.

Quick Review Box:
1. Identify all forces.
2. Resolve forces into horizontal and vertical components.
3. Find the net force in each direction.
4. Use \( F = ma \) to find the acceleration.

Key Takeaway: For equilibrium or constant velocity, the net force in any direction is zero. For acceleration, the net force equals \( mass \times acceleration \).