What is the correct angular description of a vector given at 49.0 degrees counterclockwise from the x-axis?
The correct angular description of the vector given at 49.0 degrees counterclockwise from the x-axis is 49.0° and 231.0°.
Understanding Vector Angles in Physics
Vector Representation:
In Physics, vectors are quantities that have both magnitude and direction. When representing vectors in two dimensions, the magnitude is typically given along with the angle the vector makes with respect to a reference axis, often the x-axis.
Angle Measurement in Physics:
Counterclockwise vs. Clockwise:
In Physics, angles are commonly measured counterclockwise from the x-axis as the positive direction, with clockwise being the negative direction. It is important to consider this convention when working with vector angles.
Interpreting the Given Vector:
Options Analysis:
- Option (a) 5.2 cm at 49.0° correctly represents the vector as 49.0° counterclockwise from the x-axis.
- Option (b) 5.2 cm at -49.0° is incorrect because a negative angle would point the vector below the x-axis.
- Option (c) 5.2 cm at 231.0° represents the vector pointing in the same direction but measured clockwise from the negative x-axis.
- Option (d) 5.2 cm at -231.0° is incorrect as it represents an angle in the opposite quadrant.
Conclusion:
When analyzing vector angles in Physics, it is crucial to understand the conventions of measuring angles counterclockwise from the positive x-axis. In the given scenario, options (a) 49.0° and (c) 231.0° correctly represent the same vector but from different starting points. It is essential to accurately interpret and convert vector angles to ensure precise calculations and representations in Physics.