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Answer :
The constant angular acceleration of the wheel is 43.9 rad/[tex]s^2[/tex].
We can use the formula for constant angular acceleration: ωf = ωi + αt
where:
ωi = initial angular velocity = 0 (as the wheel starts from rest)
ωf = final angular velocity = 95.0 rad/s
t = time interval = 6.00 s
α = constant angular acceleration (to be found)
We can also use the formula for the number of revolutions (N) in terms of angular displacement (θ): N = θ / (2π)
where θ is the total angular displacement. Since the wheel completes 25 revolutions, its total angular displacement is: θ = 25 * 2π = 50π
Using the formula for angular displacement with constant angular acceleration: θ = ωit + 0.5α*[tex]t^2[/tex]
Substituting the given values and simplifying:
50π = 0 + 0.5α(6.00)
α = 50π / (0.5*(6.00)^2) = 43.9 rad/[tex]s^2[/tex]
Therefore, the constant angular acceleration of the wheel is 43.9..
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