Angular velocity is a measure of how quickly an object rotates around a fixed axis. It is a fundamental concept in physics and engineering, particularly in the study of rotational motion.
What is the Formula for Angular Velocity?
The basic formula for angular velocity is:
\[ \omega = \frac{\Delta \alpha}{t} \]
Where:
\(\omega\) is the angular velocity in radians per second (rad/s)
\(\Delta \alpha\) is the angle change in radians (rad)
\(t\) is the time interval in seconds (s)
Alternatively, angular velocity can be calculated using linear velocity and radius:
\[ \omega = \frac{v}{r} \]
Where:
\(v\) is the linear velocity in meters per second (m/s)
\(r\) is the radius in meters (m)
What are the calculation steps?
Determine the angle change (\(\Delta \alpha\)) or the linear velocity (\(v\)) and radius (\(r\)).
Measure the time interval (\(t\)) over which the rotation occurs (if using angle change).
Apply the appropriate formula:
If using angle change: \(\omega = \frac{\Delta \alpha}{t}\)
If using linear velocity and radius: \(\omega = \frac{v}{r}\)
Perform the calculation to find the angular velocity.
Example of Angular Velocity Calculation
Let's calculate the angular velocity of a wheel that rotates through an angle of 4π radians in 2 seconds:
Therefore, the wheel's angular velocity is 2π rad/s or approximately 6.28 rad/s.
Diagram of Angular Velocity
The following diagram illustrates the concept of angular velocity:
This diagram shows a circular path with radius r. The angle Δα represents the angle through which an object rotates in a given time. The angular velocity ω is the rate at which this angle changes over time.