Essential Physics Formulas: Kinematics and Dynamics

Posted on Oct 29, 2025 in Mathematics

Cristián Arriagada: Essential Physics Formulas

This compilation provides fundamental equations covering kinematics, dynamics, work, energy, and rotational motion in classical mechanics. These formulas are crucial for solving problems involving motion and forces.

1. Kinematics (Equations of Motion)

1.1. Uniformly Accelerated Motion (MUA)

  • Velocity: V = V0 + a(t – t0)
  • Position: X = X0 + V0t + 1/2 at2
  • Velocity-Position: V2 = V02 + 2a(X – X0)
  • Time: t = (V – V0) / a

1.2. Uniform Rectilinear Motion (MRU)

  • Velocity: V = (X – X0) / t
  • Position: X = X0 + Vt

1.3. Projectile Motion

Assuming initial position (x0, y0) and initial velocity V0 at angle θ.

  • Horizontal Position: x(t) = x0 + (V0 cosθ) t
  • Vertical Position: Y(t) = Y0 + (V0 sinθ) t – 1/2 gt2
  • Vertical Velocity: Vy(t) = V0 sinθ – gt
  • Time to Max Height: tmax = (V0 sinθ) / g
  • Maximum Height: Ymax = Y0 + (V0 sinθ)2 / (2g)
  • Maximum Range: Xmax = X0 + (V02 sin(2θ)) / g

1.4. Free Fall

Assuming initial vertical position Y0 and initial vertical velocity V0y.

  • Vertical Position: Y(t) = Y0 + V0yt – 1/2 gt2
  • Vertical Velocity: Vy(t) = V0y – gt

2. Circular Motion

2.1. Uniformly Accelerated Circular Motion (MCA)

  • Angular Velocity: ω(t) = ω0 + αt
  • Tangential Acceleration: at = αr

2.2. Uniform Circular Motion (MCU)

  • Tangential Velocity: v = rω
  • Centripetal Acceleration: ac = v2 / r

3. Work, Energy, and Rotational Dynamics

3.1. Work and Energy Principles

  • Work (W): W = F cosθ Δx
  • Work-Energy Theorem: Wnet = Kf – Ki
  • Work by Conservative Forces: Wcons = – ΔU
  • Potential Energy Notation: Ep = U

3.2. Rotational Dynamics and Angular Momentum

  • Center of Mass (RCM): RCM = Σ (miri) / M
  • Torque (τ): τ = R F sinθ
  • Rotational Second Law: τ = I α
  • Angular Momentum (L): L = Iω
  • Conservation of Angular Momentum: Li = Lf