Ap Physics One Equation Sheet

AP Physics 1 Equation Sheet

Below is a comprehensive list of essential equations for AP Physics 1, organized by topic. These formulas are critical for solving problems and understanding key concepts in the course.

1. Kinematics

• Displacement (Δx):
  [ \Delta x = x_f - x_i ]
  
• Average Velocity (v_avg):
  [ v_{avg} = \frac{\Delta x}{\Delta t} ]
  
• Average Speed:
  [ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} ]
  
• Constant Acceleration Equations:
  [ v_f = v_i + a \Delta t ]
  [ \Delta x = v_i \Delta t + \frac{1}{2} a (\Delta t)^2 ]
  [ v_f^2 = v_i^2 + 2a \Delta x ]
  

2. Dynamics

• Newton’s Second Law:
  [ F = ma ]
  
• Weight (Gravitational Force):
  [ F_g = mg ]
  
• Normal Force (N):
  [ N = mg \cos(\theta) \quad \text{(on an incline)} ]
  
• Frictional Force (f):
  [ f = \mu N ]
  
  • (\mu_s): Coefficient of static friction
    
  • (\mu_k): Coefficient of kinetic friction
    
• Tension (T):
  Depends on the system; often resolved into components.
  

3. Work, Energy, and Power

• Work (W):
  [ W = F \cdot d \cdot \cos(\theta) ]
  
• Kinetic Energy (KE):
  [ KE = \frac{1}{2} mv^2 ]
  
• Work-Energy Theorem:
  [ W_{net} = \Delta KE ]
  
• Potential Energy (PE):
  [ PE_g = mgh ]
  
• Power (P):
  [ P = \frac{W}{t} = F \cdot v ]
  

4. Linear Momentum

• Momentum (p):
  [ p = mv ]
  
• Impulse (J):
  [ J = F \Delta t = \Delta p ]
  
• Conservation of Momentum:
  [ m1 v{1i} + m2 v{2i} = m1 v{1f} + m2 v{2f} ]
  

5. Simple Harmonic Motion (SHM)

• Period (T):
  [ T = 2\pi \sqrt{\frac{m}{k}} ]
  
  • (k): Spring constant
    
• Frequency (f):
  [ f = \frac{1}{T} ]
  
• Displacement in SHM:
  [ x(t) = A \cos\left(\frac{2\pi t}{T}\right) ]
  

6. Circular Motion

• Centripetal Force (F_c):
  [ F_c = \frac{mv^2}{r} = mr\omega^2 ]
  
  • (\omega): Angular velocity
    
• Centripetal Acceleration (a_c):
  [ a_c = \frac{v^2}{r} = r\omega^2 ]
  

7. Rotational Motion

• Rotational Kinematics:
  [ \theta = \omega t + \frac{1}{2} \alpha t^2 ]
  [ \omega_f^2 = \omega_i^2 + 2\alpha \theta ]
  
  • (\alpha): Angular acceleration
    
• Moment of Inertia (I):
  [ I = \sum m_i r_i^2 ]
  
• Torque ((\tau)):
  [ \tau = r \times F = I\alpha ]
  

8. Gravitation

• Universal Gravitation (F_g):
  [ F_g = G \frac{m_1 m_2}{r^2} ]
  
  • (G = 6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2)
    
• Gravitational Potential Energy (PE_g):
  [ PE_g = -\frac{GmM}{r} ]
  

9. Fluid Mechanics

• Density ((\rho)):
  [ \rho = \frac{m}{V} ]
  
• Pressure (P):
  [ P = \frac{F}{A} ]
  
• Buoyant Force (F_B):
  [ FB = \rho{fluid} V_{submerged} g ]
  
• Continuity Equation (A1v1 = A2v2):
  [ A_1 v_1 = A_2 v_2 ]
  

10. Thermodynamics

• Thermal Energy (Q):
  [ Q = mc\Delta T ]
  
  • (c): Specific heat capacity
    
• Ideal Gas Law:
  [ PV = nRT ]
  
  • (R = 8.314 \, \text{J/(mol} \cdot \text{K)})
    
• First Law of Thermodynamics:
  [ \Delta U = Q - W ]
  

Key Constants

• Gravitational Acceleration ((g)): (9.8 \, \text{m/s}^2)
  
• Planck’s Constant ((h)): (6.626 \times 10^{-34} \, \text{J} \cdot \text{s})
  
• Boltzmann Constant ((k_B)): (1.38 \times 10^{-23} \, \text{J/K})