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Answer :
The angular acceleration of the rotating wheel is 9.73 rad/s^2.
Known Values
Given data:
Number of revolutions (n) = 42.5 revolutions
Time taken (t) = 4.1 s
Final angular speed (ω_f) = 97.6 rad/s
Angular Acceleration Formula
The angular acceleration (α) of a rotating object can be calculated using the formula:
α = (ω_f - ω_i) / t
Where:
ω_f = final angular speed
ω_i = initial angular speed (which is 0 rad/s in this case, as the wheel starts from rest)
t = time interval
Calculating Angular Acceleration
Substitute the known values into the formula:
α = (97.6 rad/s - 0 rad/s) / 4.1 s
α = 97.6 rad/s / 4.1 s
α ≈ 23.8 rad/s^2
Therefore, the angular acceleration of the rotating wheel is approximately 23.8 rad/s^2.
The correct answer is option d: 23.8 rad/s^2.
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