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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 in N.
  • 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 ΣF is 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 N is NOT equal to mg. It balances only the perpendicular component of the weight.
  • Action-Reaction Pairs: Identify them by remembering they act on two different objects. N and W on a stationary block are NOT an action-reaction pair.