There are many analogies between translational and rotational motion of bodies, which make it easier to remember certain physical relationships. For example, velocity in linear motion corresponds to angular velocity in circular motion. The table below lists the most important analogies, including their physical quantities.
| Quantity | Translation | Rotation | Description |
|---|---|---|---|
| Displacement | \( s \) | \( \varphi \) | Angle |
| Velocity | \( v = \frac{\mathrm{d}s}{\mathrm{d}t} \) | \( \omega = \frac{\mathrm{d}\varphi}{\mathrm{d}t} \) | Angular velocity |
| Acceleration | \( a = \frac{\mathrm{d}v}{\mathrm{d}t} \) | \( \alpha = \frac{\mathrm{d}\omega}{\mathrm{d}t} \) | Angular acceleration |
| Mass / Inertia | \( m \) | \( I \) | Moment of inertia |
| Momentum | \( p = mv \) | \( L = I\omega \) | Angular momentum |
| Force / Torque | \( \vec{F} = \frac{\mathrm{d}\vec{p}}{\mathrm{d}t} = m\vec{a} \) | \( \vec{D} = \frac{\mathrm{d}\vec{L}}{\mathrm{d}t} = I\vec{\alpha} \) | Torque |
| Motion equation | \( s = \frac{1}{2}a t^2 + v_0 t + s_0 \) | \( \varphi = \frac{1}{2}\alpha t^2 + \omega t + \varphi_0 \) | Angular motion equation |
| Kinetic energy | \( E_\mathrm{kin} = \frac{1}{2}mv^2 \) | \( E_\mathrm{rot} = \frac{1}{2}I\omega^2 \) | Rotational energy |
Let me know if you'd like to integrate this into a document or use another table style!