Definition: This calculator determines the angular velocity (\( \omega \)) at a given time (\( t \)) based on the initial angular velocity (\( \omega_0 \)) and angular acceleration (\( \alpha \)).
Purpose: It assists physicists and engineers in analyzing the rotational motion of objects under constant angular acceleration.
The calculator uses the relationship:
Where:
Explanation: Enter the time, initial angular velocity, and angular acceleration in the chosen units, and the calculator computes angular velocity in radians per second and degrees per second. Note: The image output (137.3389 rad/s for \( t = 25.33 \, \text{s} \), \( \omega_0 = 2.33 \, \text{rad/s} \), \( \alpha = 5.33 \, \text{rad/s}^2 \)) matches the calculation \( 2.33 + 5.33 \cdot 25.33 \approx 137.3389 \, \text{rad/s} \).
Details: Angular velocity is essential for understanding rotational motion, used in designing systems like motors, gyroscopes, and rotating machinery.
Tips: Enter positive values for time, initial angular velocity, and angular acceleration, then click "Calculate." Results show angular velocity in radians per second and degrees per second (to 5 decimal places, or scientific notation if less than 0.0001).