General Planar Motion with a Center of Mass Reference

 

 

Under the influence of an unbalanced force and moment, an unconstrained rigid body will translate and rotate.

 

 

Newton's second law for general planar motion with a center of mass reference

 

∑F = ma_G

 

Each point on the body may experience a different acceleration, unlike the case for pure translation, we must take care to use the acceleration of the body's mass center (G) in Newton's second law. We can use the following kinematic relationship to determine the acceleration of G if the acceleration of another point P on the body is known.

 

a_G = a_P + α x r_G/P - ω²r_G/P

 

 

Moment equation for general planar motion with a center of mass reference

 

∑M_G = I_Gα

 

Note that the moments and mass moment of inertia are with respect to the body's center of mass G.