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The Fundamental Equation of Dynamics

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  • 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.


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