Fundamental Physics Equations

Fundamental physics equations are the backbone of AP Physics 1, connecting concepts like force, energy, and motion. Understanding these equations helps explain how objects interact and move, laying the groundwork for more complex topics in physics.

1. Newton's Second Law: F = ma

   • Describes the relationship between force, mass, and acceleration.
   • The net force acting on an object is equal to the mass of the object multiplied by its acceleration.
   • Indicates that greater force results in greater acceleration for a given mass.

2. Kinematic Equations:

   • v = v₀ + at: Relates final velocity to initial velocity, acceleration, and time.
   • x = x₀ + v₀t + ½at²: Calculates displacement based on initial position, velocity, acceleration, and time.
   • v² = v₀² + 2a(x - x₀): Connects velocities and displacement with acceleration.
   • x = ½(v + v₀)t: Averages initial and final velocity to find displacement over time.

3. Work-Energy Theorem: W = ΔKE

   • States that the work done on an object is equal to the change in its kinetic energy.
   • Highlights the relationship between force applied over a distance and energy transfer.

4. Gravitational Potential Energy: PE = mgh

   • Defines potential energy based on an object's mass, height above a reference point, and gravitational acceleration.
   • Indicates that higher positions result in greater potential energy.

5. Elastic Potential Energy: PE = ½kx²

   • Describes the potential energy stored in a spring or elastic material when compressed or stretched.
   • The energy is proportional to the square of the displacement from the equilibrium position.

6. Kinetic Energy: KE = ½mv²

   • Represents the energy of an object in motion, dependent on its mass and velocity.
   • Indicates that doubling the velocity increases kinetic energy by a factor of four.

7. Conservation of Energy: E₁ = E₂

   • States that energy cannot be created or destroyed, only transformed from one form to another.
   • Total energy in a closed system remains constant.

8. Power: P = W/t

   • Defines the rate at which work is done or energy is transferred.
   • Indicates that higher power means work is done more quickly.

9. Momentum: p = mv

   • Describes the quantity of motion an object has, dependent on its mass and velocity.
   • Momentum is a vector quantity, having both magnitude and direction.

10. Impulse-Momentum Theorem: F∆t = ∆p

    • Relates impulse (force applied over time) to the change in momentum.
    • Indicates that a larger force or longer time results in a greater change in momentum.

11. Conservation of Momentum: p₁ + p₂ = p₁' + p₂'

    • States that in a closed system, the total momentum before an interaction equals the total momentum after.
    • Applies to collisions and explosions.

12. Centripetal Acceleration: a = v²/r

    • Describes the acceleration of an object moving in a circular path, directed towards the center of the circle.
    • Indicates that greater speed or smaller radius results in greater centripetal acceleration.

13. Universal Gravitation: F = G(m₁m₂)/r²

    • Describes the gravitational force between two masses, inversely proportional to the square of the distance between them.
    • G is the gravitational constant, indicating the strength of gravity.

14. Hooke's Law: F = -kx

    • Relates the force exerted by a spring to its displacement from the equilibrium position.
    • Indicates that the force is proportional to the displacement and acts in the opposite direction.

15. Simple Harmonic Motion: ω = √(k/m)

    • Describes the motion of oscillating systems, where ω is the angular frequency.
    • Indicates that the frequency of oscillation depends on the spring constant and mass.