Question

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

Answer 1

the average angular acceleration is 50.265 rad/s²

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