Mechanical Motion#
Motion is a change in position of an object over time.
Newton's Laws of Motion#
- If the vector sum of all forces acting on an object is zero, then the velocity of the object is constant. \(\(\sum \vec F = 0 \; \Leftrightarrow \; \frac{\diff \vec{v} }{ \diff t } = 0\)\)
- If an object is accelerating, then there is a force on it. \(\(\vec F = m \cdot \vec a\)\)
- If one object \(A\) exerts a force \(F_A\) on a second object \(B\), then \(B\) simultaneously exerts a force \(F_B = - F_A\) on \(A\), and the two forces are equal in magnitude and opposite in direction.
Classical Mechanics#
| Motion | Translation | { Rotation} (Radius \(r\)) |
|---|---|---|
| Strecke/Winkel | \(\vec x\) | \(\vec \varphi = \frac{\vec x}{r}\) |
| Geschwindigkeit | \(\vec v = \dot{\vec x}\) | \(\vec \omega = \dot{\vec \varphi} = \frac{\vec v}{r}\) |
| Beschleunigung | \(\vec a = \dot{\vec v} = \ddot{\vec x}\) | \(\vec \alpha = \dot{\vec \omega} = \ddot{\vec \varphi} = \frac{\vec a}{r}\) |
| Masse/Trägh. | \(m\) | \(\Theta = \int_V \vec r^2_\perp \diff m\) |
| Impuls/Drall | \(\vec p =m \vec v\) | \(\vec L = \ma \Theta \vec \omega = \vec r \times \vec p\) |
| Kraft/Moment | \(\vec F = \dot{\vec p} = m \vec a\) | \(\vec M = \dot{\vec L} = \ma \Theta \vec \alpha = \vec r \times \vec F\) |
| Energie | \(E_{\ir kin}=\frac12mv^2\) | \(E_{\ir rot}=\frac12 \Theta \omega ^2\) |
| Leistung | \(P = \vec F \bdot \vec v\) | \(P = \vec M \bdot \vec \omega\) |