An engine flywheel initially rotates counterclockwise at 6.69 rotations/s. Then, during 20.1 s, its rotation rate changes to 2.65 rotations/s clockwise. Find the flywheel's average angular acceleration (including its sign) in radians per second squared. Define counterclockwise rotation as positive.

Given that

We are told to assume counterclockwise to be positive

Then, clockwise will be negative

initial angular velocity counterclockwise

ωi = 6.69 rotation/sec

1 rotation = 1 revolution = 2π rad

Then, ωi = 6.69 * 2π rad/s

ωi = 42.03 rad/s

Final angular velocity clockwise

ωf = 2.65 rotation/sec

ωf = 2.65 * 2π rad/s

ωf = - 16.65 rad/s

Time taken t = 20.1s

Now, we want to find angular acceleration, α

Angular acceleration is given as

α = ∆ω/∆t

α = (ωf - ωi) / t

α = (-16.65-42.03) / 20.1

α = - 58.68 / 20.1

α = - 2.92 rad/s²

So, the angular acceleration is - 2.92 rad/s²