New cartesian sign convention

The Cartesian sign convention!

In physics and engineering, the Cartesian sign convention is a widely used convention for assigning signs to quantities in Cartesian coordinates. It's essential for correctly interpreting and analyzing problems involving motion, forces, and energies.

Here's the convention:

Positive directions:

1. X-axis: To the right (positive)
2. Y-axis: Up (positive)
3. Z-axis: Out of the page (positive, for 2D projections)

Negative directions:

1. X-axis: To the left (negative)
2. Y-axis: Down (negative)
3. Z-axis: Into the page (negative, for 2D projections)

Sign conventions for common quantities:

1. Displacement (s): Positive if the object moves in the positive direction, negative if it moves in the negative direction.
2. Velocity (v): Positive if the object moves in the positive direction, negative if it moves in the negative direction.
3. Acceleration (a): Positive if the object accelerates in the positive direction, negative if it accelerates in the negative direction.
4. Force (F): Positive if the force acts in the positive direction, negative if it acts in the negative direction.
5. Work (W): Positive if the force moves the object in the positive direction, negative if it moves the object in the negative direction.
6. Energy (E): Positive if the energy is stored or transferred in the positive direction, negative if it's stored or transferred in the negative direction.

Important notes:

• When dealing with 3D problems, the sign convention applies to each axis separately.
• When using vectors, the direction of the vector is important, not just its magnitude.
• The sign convention is not absolute and may vary depending on the specific problem or context.

By following this Cartesian sign convention, you'll be able to accurately analyze and solve problems involving motion, forces, and energies in physics and engineering.