Physics Concepts: Motion, Forces, and Laws

Physics Concepts

Motion, Forces, and Laws

Motion

MUA
V = V₀ + a * t
D = |ee₀| = V₀ * t + 1/2 * a * t²

Forces

Sum of Concurrent Forces
F_R = √(F₁² + F₂² - 2 * F₁ * F₂ * cos(alpha))
Decomposition of Forces
F_x = F * cos(?)
F_y = F * sin(?)
Deformation (Hooke's Law)
L = l₀
F = K * Δl

Newton's Laws of Motion

1st Law (Inertia)
∑F = 0
2nd Law (Acceleration)
∑F = m * a
3rd Law (Action-Reaction)
For every action, there is an equal and opposite reaction.

Sum of Forces (Different Directions)

Concurrent Forces
R = √(F₁² + F₂²)
Parallel Forces
R = F₁ + F₂

Centripetal Force

F_c = m * a_n = m * v² / r = m * ω² * r

Other

P = m * g
F_r = μ * N

Force Interactions and Types

A force is an interaction between two bodies: the force exerted and the recipient.

• Weight: Gravitational force on Earth, causing objects to fall.
• Normal Force: Contact force between two solid objects, acting in the upward direction.
• Tension: Force that supports weight (e.g., a cable). Its direction is along the rope and outward.
• Friction: Contact force that acts when a body slides or attempts to slide over another. It can reduce a body's velocity (dynamic friction) or prevent it from moving (static friction). Its direction is opposite to the force trying to cause motion. The formula is F_r = μ * N.

Additional Formulas and Concepts

MUA
V = V₀ + a * t
E = E₀ + V₀ * t + 1/2 * a * t²
Hooke's Law
F = K * Δl
Δl (elongation) = L (final) - L (initial)
Sum of Forces
Parallel: F_r = √(F₁² + F₂² + 2 * F₁ * F₂ * cos(alpha))
Pythagoras: For perpendicular forces.
Parallel Forces (Same Direction): Add the forces.
Parallel Forces (Opposite Directions): Subtract the smaller force from the larger force.
P₁ * X₁ = P₂ * X₂
Body in Equilibrium
∑F = 0
Weight
P = m * g
P - A = m * a
When calculating acceleration: F_r - P = m * a
At the top with constant velocity: ∑F = 0; F - P_x = 0
Circular Motion
a_n = v² / r = (ω * r)² / r
v = ω * r
F (magnitude) = m * a_n = m * v² / r

Newton's Laws of Motion (Detailed)

1st Law: When the net force acting on a body is zero, the body maintains its state of motion. If it was at rest, it continues at rest. If it was in motion, it continues in uniform rectilinear motion (MRU).
∑F = 0 implies no change in motion.
2nd Law: When a net force acts on a body, it causes an acceleration in the same direction as the force.
∑F = m * a
F (Newton) = kg * m/s²
a = m/s²
3rd Law: When a body exerts a force (action) on another body, the second body exerts an equal and opposite force (reaction) on the first body. Forces appear in pairs (interaction). These forces cannot be added because they are applied to different bodies. They have the same magnitude and direction but opposite sense.

Hooke's Law

Experimentally, applying a force to a spring causes deformation or elongation proportional to the applied force.
F = K * Δl
K: Elastic constant of the spring (N/m)
Δl: Elongation
L = l₀