A counterclockwise (ccw) rotation carries a positive sign. (A) True B) False
The correct answer and explanation is:
Correct Answer: A) True
Explanation:
In mathematics and physics, rotation direction is conventionally assigned a sign to distinguish between clockwise (CW) and counterclockwise (CCW) rotations. According to the standard convention used in coordinate geometry and vector mathematics:
- A counterclockwise (CCW) rotation is considered positive.
- A clockwise (CW) rotation is considered negative.
This convention aligns with the right-hand rule, a fundamental principle in physics and vector calculus. According to the right-hand rule, if you curl the fingers of your right hand in the direction of rotation, your thumb points in the direction of the positive axis perpendicular to the plane of rotation. This is especially relevant in three-dimensional vector systems and in calculating cross products.
For example, in the two-dimensional Cartesian coordinate system, when a point or figure is rotated around the origin:
- A positive angle of rotation moves the point in a counterclockwise direction.
- A negative angle of rotation moves it clockwise.
Let’s say you rotate a point (1, 0) by 90° around the origin:
- A +90° rotation moves it to (0, 1), which is CCW.
- A –90° rotation moves it to (0, –1), which is CW.
This positive-CCW and negative-CW convention is widely used in:
- Trigonometry (e.g., unit circle)
- Physics (e.g., angular momentum and torque)
- Engineering (e.g., rotational mechanics)
- Computer graphics and animation (e.g., object transformations)
Understanding this convention is crucial when interpreting angular values, solving rotational problems, or programming graphics and simulations. Mistaking the sign of rotation can result in mirrored or unintended behavior in practical applications. Therefore, it’s important to remember: counterclockwise rotation is positive.