Answer :
The formula for angular acceleration is:
α = (ωf - ωi) / t
where α is the angular acceleration, ωi is the initial angular speed, ωf is the final angular speed, and t is the time interval.
In this case, we know that the time interval is 2.98 s, the final angular speed is 97.6 rad/s, and the initial angular speed is 0 (since the wheel starts from rest). We also know that the wheel rotates through 37.0 revolutions, which is equivalent to 2π × 37.0 = 231.2 radians.
Using the formula for angular speed :
ωf = θ / t
where θ is the angle of rotation and t is the time interval, we can find the angle of rotation:
θ = ωf × t = 97.6 rad/s × 2.98 s = 291.04 radians
Now we can plug in the values into the formula for angular acceleration:
α = (ωf - ωi) / t = (97.6 rad/s - 0) / 2.98 s = 32.77 rad/s²
Therefore, the constant angular acceleration of the wheel is 32.77 rad/s².
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