Definition: Newton's Laws

Newton's Laws lay down the fundamentals of dynamics. We will be using these a lot throughout the course.

• 1st law: The first law asserts that an object at rest will stay at rest, and an object in motion will stay in motion. This is more of a special case of the second law.
• 2nd law: The second law relates the force acting on a mass to its acceleration: $$\vec F=m\vec a$$Remember that force and acceleration are vectors, so they have a defined direction. The net acceleration on an object is in the same direction as its net force. Force is measured in Newtons (N), where $1\, \unit N=1\, \unit{kg \cdot m/s^2}$.
• 3rd law: The third law says that every action has an equal and opposite reaction. In other words, if object A exerts a force $\vec F$ on object B, then object B exerts a force $-\vec F$ on object A.

Tip: Free body diagrams

To visualize the relationship between the forces acting on a body, it is helpful to draw a free body diagram. Label all the forces acting on an object by drawing vectors indicating the magnitude and direction of the forces. Then, use vector addition to find the net force, and that will allow you to find the net acceleration.

Definition: Types of forces

There are common types of forces worth noting:

• Gravitational force: The gravitational force on an object is the force acting on it due to gravity. If we have a mass $m$ in a gravitational field with acceleration $g$, then the gravitational force on the mass is $F_g=mg$. This value is also called the weight.
• Normal force: The normal force is the force between two objects in contact with one another. By the 3rd law, the normal force exerted by A on B is equal and opposite to the normal force exerted by B on A. The normal force is directed perpendicularly to the objects' surfaces.
• Tension force: Tension is a force intrinsic to strings. Strings tend to pull on objects toward their center, and this force we call the tension force. For now, we will always assume that the tension force in a string is constant, even when placed around a pulley.