Lecture 4
Key Concepts
- Dynamics vs. Kinematics: Kinematics describes how objects move (v, a). Dynamics explains why they move (Force).
- Force (F): A push or a pull. It is a vector (has magnitude and direction). The unit is the Newton (N).
- Net Force (ΣF or F_net): The vector sum of all forces acting on a single object. The net force is what determines an object's acceleration.
- Inertia: An object's natural tendency to resist changes in its state of motion.
- Mass (m): The measure of inertia. A scalar property of matter. The unit is the kilogram (kg). Mass is constant everywhere.
- Weight (W): The force of gravity on an object. It is a vector. The unit is the Newton (N). Weight changes with location (
W = mg). - Inertial Frame of Reference: A non-accelerating frame where Newton's Laws are valid. (Assume the Earth is one).
- Equilibrium: A state where the net force on an object is zero (
ΣF = 0). The object's acceleration is zero, meaning it is either at rest or moving at a constant velocity.
Newton's Three Laws of Motion
| Law | Statement | Key Idea & Application |
|---|---|---|
| First Law | An object's velocity is constant if and only if the net force on it is zero. | Defines Equilibrium. Used for problems where objects are at rest or moving with constant velocity. If a = 0, then ΣF = 0. |
| Second Law | The acceleration of an object is directly proportional to the net force and inversely proportional to its mass. | The Core of Dynamics. The main equation for solving most problems. Links forces to the resulting motion. ΣF = ma. |
| Third Law | For every action, there is an equal and opposite reaction. F_(A on B) = - F_(B on A) |
Describes Force Pairs. Action-reaction forces are always on DIFFERENT bodies. Do not confuse with balanced forces on the same body. |
Common Forces & Their Properties
| Force Type | Symbol | Description & Direction |
|---|---|---|
| Gravitational (Weight) | W or F_g |
The pull of gravity. Always acts straight down. Magnitude W = mg. |
| Normal Force | N |
A contact push from a surface. Always acts perpendicular to the surface. |
| Tension | T |
A contact pull from a rope/string. Always acts along the rope, away from the object. |
| Friction | f or F_f |
A contact force resisting motion. Always acts parallel to the surface, opposite the direction of motion (or intended motion). |
Essential Tips for Exams
- Mass vs. Weight: Never mix them up! Mass is in
kg, Weight is inN. - Free-Body Diagrams: ALWAYS draw one! Represent the object as a dot and draw all force vectors originating from that dot. This is the first step to solving any force problem.
- Vector Sum: Remember that
ΣFis a vector sum. You will need to break forces into components (e.g., x and y components) for 2D problems. - Inclined Planes: When on a ramp, the Normal Force
Nis NOT equal tomg. It balances only the perpendicular component of the weight. - Action-Reaction Pairs: Identify them by remembering they act on two different objects.
NandWon a stationary block are NOT an action-reaction pair.