Dynamics & Forces
Understanding how forces cause motion and change in velocity
First Law (Law of Inertia)
An object at rest stays at rest, and an object in motion stays in motion with constant velocity, unless acted upon by a net external force.
Key Concept: Inertia is the tendency of an object to resist changes in its state of motion. Mass is a measure of inertia.
Second Law (F = ma)
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Net force equals mass times acceleration
This is the most important equation in dynamics. It tells us that forces cause acceleration, not velocity.
Third Law (Action-Reaction)
For every action, there is an equal and opposite reaction. Forces always occur in pairs.
Force on object 1 by object 2 equals negative force on object 2 by object 1
Gravitational Force (Weight)
Weight equals mass times gravitational acceleration
Always acts downward toward the center of the Earth. On Earth's surface, g = 9.8 m/s².
Normal Force
The perpendicular contact force exerted by a surface on an object. It prevents objects from passing through surfaces.
Friction Force
Friction equals coefficient of friction times normal force
- Static friction (μₛ): Prevents motion from starting, f ≤ μₛN
- Kinetic friction (μₖ): Opposes motion when sliding, f = μₖN
- Usually μₛ > μₖ (harder to start moving than to keep moving)
Tension Force
The pulling force transmitted through a string, rope, cable, or wire when pulled from opposite ends. Always pulls along the direction of the rope.
A free body diagram (FBD) is a simplified representation showing all forces acting on a single object. It's the most important tool for solving dynamics problems.
Steps to Draw an FBD:
- Isolate the object of interest
- Draw a dot or simple shape to represent the object
- Draw arrows representing all forces acting ON the object
- Label each force with its type and magnitude
- Choose a coordinate system
Important: Only include forces acting ON the object, not forces the object exerts on other things. Action-reaction pairs act on different objects!
When an object moves in a circular path at constant speed, it experiences centripetal acceleration directed toward the center of the circle.
Centripetal acceleration
Centripetal force (net force toward center)
Important: Centripetal force is not a new type of force. It's the net force (from tension, gravity, friction, etc.) that causes circular motion.
Period and Frequency
Speed in terms of period T
Frequency is inverse of period