Inertia

An item in motion tends to stay in motion. An item at rest tends to stay at rest.

We can distill the above two statements to the one below:

“An item tends to maintain a constant velocity.”

Not moving at all is moving at a velocity of zero. The study of Inertia makes more sense if we are on a spaceship traveling to the nearest star, Alpha Centauri. A velocity will be constant unless a Force acts on the object (to slow it down or speed it up). Driving a car on a road on a planet, you constantly lose to the friction of your contact with the road and that is why your acceleration isn’t increasing your velocity.

Appendix A

On a Starship traveling at a constant velocity, you will be weightless. With this in mind, we can consider that if we are constantly accelerating on our Starship, he will produce the force that pushes us against the floor, now we just like having gravity on Earth. We can check this thinking a step further and said if we use the acceleration of 9.8 meters per second squared, we will have what we call on Earth 1G. To grab you if you’ll decide what we are accustomed to having. Now we might tell people we’re going to go a little bit faster 10.0 meters per second squared so take your shoes off and maybe put on shorts to compensate for the higher value for g.

Our reason for using 10.0 is to make calculations easier.

Appendix B

[]I \omega = H[/]

\begin{bmatrix} I_{xx} & I_{xy} & I_{xz} \\ I_{yx} & I_{yy} & I_{yz} \\ I_{zx} & I_{zy} & I_{zz} \end{bmatrix} \begin{bmatrix} \tau_x \\ \tau_y \\ \tau_z \end{bmatrix} = \begin{bmatrix} \alpha_x \\ \alpha_y \\ \alpha_z \end{bmatrix}

Below we show the nine components of the Inertia matrix I:

\begin{bmatrix} \sum m_i(y_i^2 + z_i^2) & - \sum m_ix_iy_i & - \sum m_ix_iz_i \\ \\ - \sum m_iy_ix_i & \sum m_i(x_i^2 + z_i^2) & - \sum m_iy_iz_i \\ \\ - \sum m_iz_ix_i & - \sum m_iz_iy_i & \sum m_i(x_i^2 + y_i^2) \end{bmatrix}