Overview
This lecture covers essential A Level Physics equations and formulas frequently used in exams but not typically provided on formula sheets. The session emphasizes formulas across mechanics, materials, electricity, thermal physics, uncertainty, exponentials, and waves.
Underrated and Essential Area Formula
- Circular area: ( A = \pi r^2 ), but often more useful as ( A = \frac{\pi d^2}{4} ) (using diameter directly).
Mechanics & Motion Equations
- Displacement at constant velocity: ( s = vt )
- Displacement without initial velocity: ( s = vt - \frac{1}{2}at^2 )
- Kinetic energy: ( E_k = \frac{1}{2}mv^2 )
- Gravitational potential energy: ( E_p = mgh )
- Equating energies (for vertical motion): ( \frac{1}{2}v^2 = gh ) so ( v = \sqrt{2gh} )
- Escape velocity: ( v = \sqrt{\frac{2GM}{R}} )
- Weight: ( W = mg )
- Conservation of momentum: ( m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2 )
- Perfectly inelastic collision: ( m_1u_1 + m_2u_2 = (m_1 + m_2)v )
Materials and Springs
- Elastic potential energy: ( E = \frac{1}{2}F\Delta l ) or ( E = \frac{1}{2}k(\Delta l)^2 )
- Stress: ( \text{stress} = \frac{F}{A} )
- Strain: ( \text{strain} = \frac{\Delta l}{l} )
- Young’s modulus: ( E = \frac{\text{stress}}{\text{strain}} )
- Rearranged: ( E = \frac{Fl}{A\Delta l} ) and ( \Delta l = \frac{Fl}{EA} )
Thermal Physics and Ideal Gases
- Celsius to Kelvin: ( T(\text{K}) = \theta(°\text{C}) + 273 )
- Number of moles: ( n = \frac{m}{M} )
- Number of particles: ( N = nN_A )
Uncertainty Calculations
- Percentage uncertainty (single reading): ( \frac{\text{absolute uncertainty}}{\text{measured value}} \times 100% )
- Percentage uncertainty (multiple readings): ( \frac{1}{2} \times \frac{\text{range}}{\text{mean}} \times 100% )
- Percentage uncertainty for gradients/intercepts: ( \frac{|m_\text{best}-m_\text{worst}|}{m_\text{best}} \times 100% )
- Combined uncertainty: For ( A = BC ), ( %U_A = %U_B + %U_C ); double/triple if squared/cubed._
Electricity and Circuits
- Charge: ( Q = n e )
- Parallel resistors (2): ( R_T = \frac{R_1R_2}{R_1 + R_2} )
- Potential divider: ( V_{\text{out}} = V_{\text{in}} \frac{R_2}{R_1 + R_2} )
- Ratio: ( \frac{V_1}{V_2} = \frac{R_1}{R_2} )
- Energy gained by a charge: ( eV = \frac{1}{2}mv^2 ), or ( v = \sqrt{\frac{2qV}{m}} )
- Capacitor discharge: ( Q = Q_0 e^{-t/RC} )
- Capacitor charge: ( Q = Q_0(1 - e^{-t/RC}) )
Exponentials and Log Laws
- If ( y = Ae^{-bx} ), then ( \ln y = \ln A - bx )
- For plotting: gradient = (-b), intercept = (\ln A)
- Log rules: ( \log(ab) = \log a + \log b ), ( \log(a/b) = \log a - \log b ), ( x = y^z \Rightarrow \log x = z \log y )
Waves and Optics
- Snell's law: ( n_1 \sin\theta_1 = n_2 \sin\theta_2 )
- For air to another medium: ( n = \frac{\sin i}{\sin r} )
Key Terms & Definitions
- Absolute uncertainty — The margin of error for a measured value.
- Percentage uncertainty — Absolute uncertainty divided by measured value, as a percentage.
- Young’s modulus (E) — Measure of stiffness, ( \frac{\text{stress}}{\text{strain}} ).
- Potential difference (V) — The energy per unit charge between two points in a circuit.
- Time constant (RC or τ) — The product of resistance and capacitance, characterizing capacitor charge/discharge.
Action Items / Next Steps
- Memorize non-datasheet formulas highlighted here.
- Practice applying these equations to exam questions.
- Add any useful, non-listed equations to your own formula sheet.