Angular Displacement - Definition, Unit, Formula, Derivation And FAQ

Angular displacement is a fundamental concept in Physics, especially in understanding rotational motion. When an object moves along a circular path, its change in position can be described using angles rather than straight-line distances. This angular measure helps analyze the rotation of objects in a precise and consistent way.

What is Angular Displacement?

Angular displacement refers to the angle through which a point, line, or body rotates about a fixed axis. It measures the difference between an object's starting and ending positions, described in terms of angles rather than linear distance.

Unlike linear displacement, which measures movement in a straight line, angular displacement looks at how much an object has turned from its original position. This is especially useful when analyzing rotating wheels, gears, or any circular motion.

Formula for Angular Displacement

The standard formula used to calculate angular displacement is given by:

Δθ = Δs / r

Here, Δθ is angular displacement (in radians), Δs is the distance along the arc (in meters), and r is the radius of the circle (in meters).

This equation lets you convert a distance moved along a circular path into the equivalent change in angle, measured in radians.

Step-by-Step Approach to Solve Angular Displacement Problems

1. Identify if the object is moving along a circular path and determine the center or axis of rotation.
2. Measure or calculate the arc length (Δs) that the object has travelled.
3. Find the radius (r) of the circle along which motion occurs.
4. Apply the formula Δθ = Δs / r to find angular displacement in radians.
5. If needed, convert radians to degrees (multiply the value in radians by 180/π).

Example Problem

Suppose a point moves 4 meters along the edge of a circle with a radius of 2 meters. To find the angular displacement:

Δθ = Δs / r = 4 / 2 = 2 radians

The point has turned through 2 radians from its initial position.

Key Formulas & Their Application

Formula	Variable	Meaning	Unit
Δθ = Δs / r	Δθ	Angular Displacement	Radian (rad)
Δs = r × Δθ	Δs	Arc Length	Meter (m)

Comparison: Angular vs Linear Displacement

Angular Displacement	Linear Displacement
Measures the angle turned by a radius or line (typically in radians).	Measures direct straight-line distance from one point to another (in meters).
Useful in circular motion and rotations.	Useful in straight-line (translational) motion.
Δθ = Δs / r	Δx = xfinal – xinitial

Applications and Practice

Understanding angular displacement is key for topics like rotational kinematics, gears, motors, and biomechanics. Practice solving problems by applying the core formula and identifying whether questions involve rotational or translational motion.

Try similar problems using different arc lengths and radii. Also, check your understanding with example cases from related topics, such as:

• Kinematics Equations
• Angular Velocity and Linear Velocity
• Rotation

Next Steps for Deeper Learning

• Review the steps in calculating angular displacement and solve practice questions.
• Explore advanced topics such as Angular Acceleration and Angular Momentum.
• Study rotational motion concepts, including Rotational Kinetic Energy, for a complete understanding.

For structured lessons and more practice, refer to relevant sections on Vedantu for guided learning and topic mastery.

Summary

Angular displacement provides a clear way to describe how much an object has rotated compared to where it started, using the formula Δθ = Δs / r. Applying this formula helps analyze many problems in rotational motion and related fields.

Use Vedantu resources for stepwise learning on all key Physics concepts. Continue to practice with a focus on using formulas accurately for success in all rotational motion topics.