1. What is Angular Displacement?

Angular displacement is the angle through which an object moves on a circular path. It is measured in radians and represents the difference between the final and initial angular positions of the object.

2. How Does the Calculator Work?

The calculator uses the angular displacement formula:

Where:

• \( \Delta\theta \) — Angular displacement (radians)
• \( \theta_f \) — Final angular position (radians)
• \( \theta_i \) — Initial angular position (radians)

Explanation: The formula calculates the difference between the final and initial angles to determine how much the object has rotated.

3. Importance of Angular Displacement

Details: Angular displacement is fundamental in rotational kinematics, used to calculate angular velocity, angular acceleration, and in designing rotating machinery.

4. Using the Calculator

Tips: Enter both angles in radians (1 radian ≈ 57.3 degrees). Positive values indicate counter-clockwise rotation, negative values indicate clockwise rotation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between angular displacement and distance?
A: Angular displacement measures rotation (in radians/degrees), while distance measures linear movement (in meters).

Q2: Can angular displacement be greater than 2π radians?
A: Yes, but it's often expressed modulo 2π to give the equivalent angle between 0 and 2π.

Q3: How do I convert degrees to radians?
A: Multiply degrees by π/180 (1° ≈ 0.01745 rad).

Q4: Is angular displacement a vector quantity?
A: Yes, it has both magnitude and direction (following the right-hand rule).

Q5: What's the difference between angular displacement and angular distance?
A: Displacement is the shortest angle between positions, while distance is the total angle traveled (may be larger for multiple rotations).