1. Units and Dimensional Analysis

• Base SI Units Length (meter, m), Mass (kilogram, kg), Time (second, s).
• Dimensional Analysis Using dimensions (like L, M, T) to check if an equation is consistent.

2. Vectors

• Scalar (Dot) Product A • B = |A| |B| cos(theta). Result is a scalar.
• Vector (Cross) Product |A x B| = |A| |B| sin(theta). Result is a vector perpendicular to both A and B.

3 & 4. Motion (Kinematics)

• Equations for Constant Acceleration v = u + at
s = ut + 0.5at²
v² = u² + 2as
• Projectile Motion Horizontal motion is constant velocity (x = v_x * t). Vertical motion is constant acceleration (using kinematics with a = -g).

5. Newton’s Laws of Motion

• Newton's Second Law F_net = ma (Net Force = mass * acceleration)
• Linear Momentum (p) p = mv (momentum = mass * velocity).
• Conservation of Momentum In a closed system, total initial momentum equals total final momentum. m1u1 + m2u2 = m1v1 + m2v2.

6. Circular Motion

• Centripetal Acceleration (a_c) a_c = v² / r
• Centripetal Force (F_c) F_c = ma_c = mv² / r (This is a net force directed towards the center).

7 & 8. Work, Energy, and Power

• Work Done (W) W = F * d * cos(theta)
• Kinetic Energy (KE) KE = 0.5 * mv²
• Gravitational Potential Energy (PE) PE = mgh
• Spring Potential Energy PE_spring = 0.5 * kx² (where k is the spring constant).
• Conservation of Energy Total Initial Energy = Total Final Energy. KE_i + PE_i = KE_f + PE_f.
• Power (P) P = Work / time = F * v

9 & 10. Rotational Motion & Statics

• Torque (tau) tau = r * F * sin(theta)
• Equilibrium Conditions 1. Net Force = 0 (Translational Equilibrium).
  2. Net Torque = 0 (Rotational Equilibrium).
• Elasticity (Hooke's Law) F = -kx (Force exerted by a spring).

11. Oscillations

• Period of a Mass-Spring System (T) T = 2 * pi * sqrt(m/k)
• Period of a Simple Pendulum (T) T = 2 * pi * sqrt(L/g)

12. Gravity

• Newton's Law of Universal Gravitation F_g = G * (m1 * m2) / r² (where G is the gravitational constant).