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:
- 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
- Calculate the angular displacement (θ) from the number of revolutions:
- Number of revolutions = 48
- Angular displacement (θ) = 48 rev × 2π rad/rev = 96π rad
- 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)
- 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.