The angular acceleration of the airplane propeller is approximately -22.38 radians per second squared. The negative sign indicates that the propeller is slowing down.
To find the angular acceleration in radians per second squared, we can use the formula:
Angular acceleration (α) = (Final angular speed (ωf) - Initial angular speed (ωi)) / Time taken (t)
However, we are not given the time taken directly. But we know that the propeller rotates through 21 revolutions during this process.
To convert the revolutions into time, we need to use the formula:
Time (t) = Number of revolutions (n) / Angular speed (ω)
1. Calculate the time taken for the propeller to rotate through 21 revolutions:
Time (t) = 21 revolutions / 12.5 revolutions/sec = 1.68 seconds
2. Now we can calculate the angular acceleration:
Angular acceleration (α) = (5.00 revolutions/sec - 12.5 revolutions/sec) / 1.68 seconds
To convert the angular acceleration from revolutions per second squared to radians per second squared, we need to multiply by 2π (since there are 2π radians in one revolution).
Angular acceleration (α) = [(5.00 revolutions/sec - 12.5 revolutions/sec) / 1.68 seconds] × 2π
Simplifying the expression:
Angular acceleration (α) = [-7.50 revolutions/sec / 1.68 seconds] × 2π
Finally, we can calculate the value:
Angular acceleration (α) ≈ -22.38 radians/second²