Navigating the world of physics requires a solid understanding of fundamental equations. This comprehensive equation sheet serves as your go-to resource, covering key concepts across various branches of physics. While specific curriculum requirements may vary, this sheet provides a robust foundation applicable to many educational levels and beyond. We've organized it for clarity and ease of use, ensuring you're well-equipped to tackle your physics challenges.
Note: This sheet provides a summary; it's crucial to understand the underlying principles and limitations of each equation. Always consult your textbook and lecture notes for a complete understanding.
Mechanics
Kinematics (Motion in one dimension)
- Displacement: Δx = xf - xi
- Average Velocity: vavg = Δx/Δt
- Instantaneous Velocity: v = dx/dt
- Average Acceleration: aavg = Δv/Δt
- Instantaneous Acceleration: a = dv/dt
- Equations of Motion (constant acceleration):
- v = v0 + at
- Δx = v0t + (1/2)at²
- v² = v0² + 2aΔx
- Δx = (v + v0)t/2
Kinematics (Motion in two dimensions - Projectile Motion)
- Horizontal velocity (constant): vx = v0cosθ
- Vertical velocity (under gravity): vy = v0sinθ - gt
- Horizontal displacement: Δx = vxt
- Vertical displacement: Δy = v0sinθt - (1/2)gt²
Dynamics (Forces and Newton's Laws)
- Newton's Second Law: ΣF = ma
- Weight: W = mg
- Friction (kinetic): fk = μkN
- Friction (static): fs ≤ μsN
- Hooke's Law: F = -kx
Work, Energy, and Power
- Work: W = Fdcosθ
- Kinetic Energy: KE = (1/2)mv²
- Potential Energy (gravitational): PEg = mgh
- Potential Energy (elastic): PEe = (1/2)kx²
- Work-Energy Theorem: Wnet = ΔKE
- Power: P = W/t = Fv
Momentum and Impulse
- Momentum: p = mv
- Impulse: J = Δp = FΔt
- Conservation of Momentum: m1v1i + m2v2i = m1v1f + m2v2f
Circular Motion
- Centripetal Acceleration: ac = v²/r = ω²r
- Centripetal Force: Fc = mv²/r = mω²r
Thermodynamics
- Temperature Conversions:
- K = °C + 273.15
- °F = (9/5)°C + 32
- Heat: Q = mcΔT
- Specific Heat Capacity: c = Q/mΔT
- Latent Heat: Q = mL
- Ideal Gas Law: PV = nRT
Waves and Optics
- Wave Speed: v = fλ
- Doppler Effect: fo = fs(v ± vo)/(v ± vs)
- Index of Refraction: n = c/v
- Snell's Law: n1sinθ1 = n2sinθ2
- Thin Lens Equation: 1/f = 1/do + 1/di
- Magnification: M = -di/do
Electricity and Magnetism
- Coulomb's Law: F = k|q1q2|/r²
- Electric Field: E = F/q
- Electric Potential: V = kq/r
- Ohm's Law: V = IR
- Power (electrical): P = IV = I²R = V²/R
- Magnetic Force (on a moving charge): F = qvBsinθ
- Magnetic Force (on a current-carrying wire): F = ILBsinθ
This equation sheet provides a starting point for your physics journey. Remember to supplement this with detailed study and practice problems to fully grasp the concepts. Good luck!
