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.

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