A wheel turns through an angle of 188 radians in 8.0 s; and its angular speed at the end of the period is 44 rad/s. If the angular acceleration is constant, what was the angular speed of the wheel at the beginning of the 8.0 s interval?
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The formula for angular displacement is θ = ωi*t + 0.5*α*t^2, where θ is the angular displacement, ωi is the initial angular speed, α is the angular acceleration, and t is the time.
We also know that the final angular speed (ωf) is given by ωf = ωi + α*t.
We can solve the second equation for α: α = (ωf - ωi) / t.
Substituting this into the first equation gives us θ = ωi*t + 0.5*(ωf - ωi)*t.
Solving for ωi gives us ωi = (θ - 0.5*ωf*t) / t.
Substituting the given values gives us ωi = (188 rad - 0.5*44 rad/s*8.0 s) / 8.0 s = 15 rad/s.
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