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Newton's second law:

A point mass moving in the plane with an applied force. You can try to made the mass move in a circle and then see what happens when the force is suddenly removed, which will demonstrate Newton's first law (no net force implies motion at constant speed in a constant direction). Also observe which force directions cause the speed to increase or decrease.

- The mass of the particle is not 0.
- The radius of the mass is 0.

We call these bodies "rigid" because we assume that they do not deform under applied forces or moments.

A *rigid body* is an extended area of material that
includes all the points inside it, and which moves so that
the distances and angles between all its points remain
constant. The location of a rigid body can be described by
the position of one point \(P\) inside it, together with the
rotation angle of the body (one angle in 2D, three angles in
3D).

Neither point masses nor rigid bodies can physically exist, as no body can really be a single point with no extent, and no extended body can be exactly rigid. Despite this, these are very useful models for mechanics and dynamics.

location description | velocity description | |
---|---|---|

point mass | position vector \( \vec{r}_P \) | velocity vector \( \vec{ v}_P \) |

rigid body in 2D | position vector \( \vec{r}_P \) angle \( \theta \) | velocity vector \( \vec{v}_P \) angular velocity \( \omega \) |

rigid body in 3D | position vector \( \vec{r}_P \) angles \( \theta,\phi,\psi \) | velocity vector \( \vec{v}_P \) angular velocity vector \( \vec{\omega} \) |