Relative Acceleration Equation

Relative acceleration equation can be derived from the the relative velocity equation,

     v_B = v_A + v_B/A

Differentiate with respect to time to give

Just like the relative velocity equation, the relative acceleration equation can be separated into linear motion and angular motion. However, it is important to note that the angular motion has two components, tangential and normal acceleration.

Each rotation term can be written as cross products, giving

     a_B = a_A + ω_AB × (ω_AB × r_AB) + α_AB × r_AB

This form shows that the relative acceleration is composed of the translating motion of base point A and the rotating motion of point B about A.

For plane motion, the normal rotation terms can be simplified as -ω²r giving

     a_B = a_A - ω²r_AB + α × r_AB

Another way to write the relative acceleration equation is

     a_B = a_A - ω²re_n + αre_t