Angular Velocity at t Calculator

Time (\( t \)):

Initial Angular Velocity (\( \omega_0 \)):

Angular Acceleration (\( \alpha \)):

(ω) Radians per Second: (rad/s) rad/sec

(ω) Degrees per Second: (°/s) degrees/second

1. What is the Angular Velocity at t Calculator?

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.

2. How Does the Calculator Work?

The calculator uses the relationship:

\[ \omega = \omega_0 + \alpha \cdot t \]

Where:

\( \omega \) — Angular velocity at time \( t \) (in radians per second or degrees per second)
\( \omega_0 \) — Initial angular velocity
\( \alpha \) — Angular acceleration
\( t \) — Time

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 \( 2.33 + 5.33 \cdot 25.33 \approx 137.3389 \, \text{rad/s} \).

3. Importance of Angular Velocity

Details: Angular velocity is essential for understanding rotational motion, used in designing systems like motors, gyroscopes, and rotating machinery.

4. Using the Calculator

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).

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