A bicycle wheel is rotating about a fixed axis at 10 rev/s in a clockwise sense. Five seconds later the wheel is rotating at 50 rev/s also in a clockwise sense. What is the average angular acceleration in this 5 second interval

the average angular acceleration is 50.265 rad/s²

Step-by-step explanation:

since the angular acceleration represents the rate of change of the angular velocity ω with respect to the time t, then:

average angular acceleration = (ω₂-ω₁) / (t₂-t₁)

where 2 represents the final state and 1 the initial one. Also the angular velocity is related with the frequency f through:

angle covered / time = angle covered / revolution * revolutions / time

ω = 2π*f

therefore

average angular acceleration = 2π * (f₂-f₁) / (t₂-t₁)

replacing values

average angular acceleration = 2π * (f₂-f₁) / (t₂-t₁) = 2π rad/rev * (50 rev/s-10 rev/s) / (5 s - 0 s) = 16*π rad/s² = 50.265 rad/s²