Login |  Password

The Fundamental Equation of Dynamics

  • The fundamental equation of dynamics of a mass point (Newton's second law):
    $$ m \frac{d\vec{v}}{d t} = \vec{F}.$$
  • The same equation expressed in projections on the tangent and the normal of the point's trajectory:
    $$ m \frac{d v_{\parallel}}{d t} = F_\parallel, m \frac{v^2}{R} = F_\perp.$$
  • The equation of dynamics of a point in the non-inertial reference frame $ K^\prime $ which rotates with a constant angular velocity $ \vec{\omega} $ about an axis translating with an acceleration $ \vec{a_0} $:
    $$m\vec{a^\prime} = \vec{F} - m \vec{a_0} + m \omega^2 \vec{R} + 2 m \vec{v^\prime} \times \vec{\omega},$$

    where $ \vec{R} $ is the radius vector of the point relative to the axis of rotation of the $ K^\prime $ frame.

Keywords: 
dynamics, second law, Newton
‹ KinematicsupLaws of Conservation of Energy, Momentum, and Angular Momentum ›