1. What is Angular Displacement?

Angular displacement is the angle through which an object rotates about a fixed axis. It's measured in radians and represents the change in angular position of a rotating object.

2. How Does the Calculator Work?

The calculator uses the angular displacement formula:

Where:

• \( \Delta\theta \) — Angular displacement (radians)
• \( \omega \) — Angular velocity (radians per second)
• \( t \) — Time (seconds)

Explanation: The formula calculates how much an object has rotated given its constant angular velocity over a certain time period.

3. Importance of Angular Displacement

Details: Angular displacement is fundamental in rotational kinematics, used in engineering, physics, and mechanical systems to analyze rotating objects.

4. Using the Calculator

Tips: Enter angular velocity in rad/s and time in seconds. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: How to convert between radians and degrees?
A: 1 radian = 180/π degrees (≈57.3°). Multiply radians by 180/π to get degrees.

Q3: Does this formula work for non-constant angular velocity?
A: No, this simple formula only works when angular velocity is constant. For variable velocity, integration is needed.

Q4: What are practical applications of this calculation?
A: Used in designing gears, motors, turbines, and analyzing planetary motion or rotating machinery.

Q5: What if my angular velocity is in RPM?
A: Convert RPM to rad/s first: multiply RPM by 2π/60 (since 1 RPM = 2π radians per minute = 2π/60 rad/s).