A car wheel is being tested for balance. It is spinning at 750 rpm and the machine then accelerates it to 1500 rpm over a period of 3 s.  What is the angular acceleration.

First, we will find the angular velocity:

ω₁ = 2π × (750 / 60) = 25π = 78.5 rad/s

Now, find the angular velocity at the end:

ω₂ = 2π × (1500 / 60) = 50π = 157 rad/s

Using the formula:

ω₂ = ω₁ + αt

∴ 157 rad/s = 78.5 rad/s + α × 3 s

On rearranging, we get:

α = (78.5 rad/s) / 3 s = 26.2 rad/s²