Darwinbots3/Physics

Basic concepts

Forces' linear affects

Any force acting on a body, at any point on a body, applies the same change in acceleration to the body's center of mass. Consider the diagram below:

__________
|        |
|        |  
|   X    |  <--- $\vec{Force_1}$
|        |
|________|  <--- $\vec{Force_2}$
 Diagram 1 

Where X is the center of mass for the body. $\vec{Force_1}$ is exactly centered, so it produces no torque. The change in acceleration of the body's center of mass is given by $\Delta \vec{a} = \frac{\vec{Force_1}}{Mass}$.

Let $\vec{Force_2}$ have the same magnitude and direction as $\vec{Force_1}$. However it's applying its force at a different point on the body, and will produce torque. Even though it's off center, the change in acceleration for the body's center of mass is still $\Delta \vec{a} = \frac{\vec{Force_1}}{Mass}$.

Forces' angular affects

Consider Diagram 1 again. $\vec{Force_1}$ will not produce any change in angular acceleration for the body, because it is centered. $\vec{Force_2}$ will produce change in angular acceleration, because it is off center. In general, the torque ($\tau$) produced by a force is given by:

$\tau = \vec{F} \cdot \vec{r_{\perp}^{P}}$

And the change in angular acceleration is given by:

$\Delta \alpha = \frac{\tau}{I}$

Where:

• $\tau$ is the scalar torque term.
• $\vec{F}$ is the vector Force term.
• $\vec{r_{\perp}^{P}}$ is the vector perpendicular to the vector from the body's origin to the place $\vec{F}$ is acting on the body.
• $\alpha$ is the scalar angular acceleration
• $I$ is the body's scalar moment of inertertia.

Collision

Consider a collision between two bodies: body A and body B. It is possible to show that the impulse from the collision is given by the solution to:

<math>