How to Calculate Angular Deceleration for a Flywheel

What is the angular deceleration of a flywheel that slows down while rotating through 48 revolutions?

Given data: Initial angular velocity = 583 rev/min, Final angular velocity = 377 rev/min, Number of revolutions = 48

Angular Deceleration Calculation

The angular deceleration of the flywheel is approximately -3.347 rad/s².

To calculate the angular deceleration of a flywheel that slows down while rotating through 48 revolutions, follow these steps:

1. Convert the initial and final angular velocities to rad/s:
• Initial angular velocity (ωi) = 583 rev/min = 61.052 rad/s
• Final angular velocity (ωf) = 377 rev/min = 39.442 rad/s
2. Calculate the angular displacement (θ) from the number of revolutions:
• Number of revolutions = 48
• Angular displacement (θ) = 48 rev × 2π rad/rev = 96π rad
3. Use the angular motion equations:
• ωf² = ωi² + 2αθ
• Solve for angular acceleration (α): α = ((39.442 rad/s)² - (61.052 rad/s)²) / (2 × 96π rad)
4. Calculate the angular deceleration:
• Angular deceleration ≈ -3.347 rad/s²

By following these steps, you can determine the angular deceleration of the flywheel when it slows down while rotating through a certain number of revolutions.