Angular acceleration is a measure of how quickly an object's angular velocity changes over time. It's a crucial concept in rotational motion, describing the rate of change of angular velocity.
What is the Formula for Angular Acceleration?
The basic formula for angular acceleration is:
\[ \alpha = \frac{\omega - \omega_0}{t} \]
Where:
\(\alpha\) is the angular acceleration in radians per second squared (rad/s²)
\(\omega\) is the final angular velocity in radians per second (rad/s)
\(\omega_0\) is the initial angular velocity in radians per second (rad/s)
\(t\) is the time interval in seconds (s)
What are the calculation steps?
Determine the initial angular velocity (\(\omega_0\)) and final angular velocity (\(\omega\)) of the rotating object.
Calculate the change in angular velocity: \(\Delta \omega = \omega - \omega_0\)
Determine the time interval (\(t\)) over which this change in angular velocity occurred.
Divide the change in angular velocity by the time interval: \(\alpha = \frac{\Delta \omega}{t}\)
Example of Angular Acceleration Calculation
Let's calculate the angular acceleration of a spinning wheel that speeds up from 10 rad/s to 25 rad/s in 3 seconds:
Therefore, the wheel's angular acceleration is 5 rad/s².
Diagram of Angular Acceleration
The following diagram illustrates the concept of angular acceleration:
This graph shows angular velocity increasing linearly over time, which represents a constant angular acceleration. The slope of this line is the angular acceleration.