🌪️ Angular Displacement Calculator
Calculate angular change
How to Use This Calculator
Enter Initial Angle
Input the starting angular position (θ₀) in degrees. This is the angle where the object begins. For example, if a wheel starts at the 0° position, enter 0.
Enter Final Angle
Input the ending angular position (θ_f) in degrees. This is the angle where the object ends up. The calculator will automatically handle values greater than 360° or negative values.
Calculate and Review Results
Click the "Calculate" button to compute the angular displacement. The result will be displayed in degrees and also converted to radians for your convenience. A positive value indicates counterclockwise rotation, while negative indicates clockwise rotation.
Formula
Δθ = θ_f - θ₀
Where:
• Δθ = Angular displacement (degrees or radians)
• θ_f = Final angular position (degrees)
• θ₀ = Initial angular position (degrees)
Example 1: Simple Rotation
A wheel rotates from 30° to 150°. Calculate the angular displacement.
Given:
• Initial angle (θ₀) = 30°
• Final angle (θ_f) = 150°
Solution:
Δθ = θ_f - θ₀
Δθ = 150° - 30°
Δθ = 120°
Converting to radians: 120° × (π/180) = 2.094 rad
Example 2: Complete Rotation
A record player rotates from 45° to 405°. Calculate the angular displacement.
Given:
• Initial angle (θ₀) = 45°
• Final angle (θ_f) = 405°
Solution:
Δθ = θ_f - θ₀
Δθ = 405° - 45°
Δθ = 360° (one complete rotation)
Converting to radians: 360° × (π/180) = 2π rad = 6.283 rad
Frequently Asked Questions
What is angular displacement?
Angular displacement is the change in angular position of a rotating object. It measures how far an object has rotated from its initial position to its final position, regardless of the path taken. It's a vector quantity measured in degrees or radians.
How is angular displacement different from angular distance?
Angular displacement is a vector quantity that represents the shortest angular change between two positions. Angular distance is a scalar quantity that represents the total angular path traveled. For example, if an object rotates 450°, the angular displacement is 90° (450° - 360° = 90°), but the angular distance is 450°.
Can angular displacement be greater than 360°?
Yes, angular displacement can be any value. However, for many purposes, it's useful to reduce values greater than 360° to their equivalent value between 0° and 360°. For example, 450° is equivalent to 90° (450° - 360° = 90°). This calculator shows the actual displacement without reduction.
What does a negative angular displacement mean?
A negative angular displacement indicates clockwise rotation, while positive indicates counterclockwise rotation. The sign convention depends on the coordinate system, but typically positive is counterclockwise when viewed from above.
How do I convert degrees to radians?
To convert degrees to radians, multiply by π/180. For example, 180° = π radians, 90° = π/2 radians, and 360° = 2π radians. This calculator automatically shows both values for your convenience.
Where is angular displacement used in real life?
Angular displacement is used in many applications: calculating the rotation of wheels in vehicles, analyzing the motion of pendulums and gears, understanding satellite positioning, designing robotic arms, studying planetary motion, and analyzing the performance of rotating machinery in engineering applications.
About Angular Displacement Calculator
The angular displacement calculator computes the change in angular position from initial to final angle. Angular displacement is a fundamental concept in rotational kinematics, describing how far an object has rotated from its starting position.
Unlike linear displacement, which measures distance in a straight line, angular displacement measures rotation around a fixed axis. This calculator is essential for students learning rotational motion, engineers designing rotating systems, and anyone analyzing circular or rotational movements.