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.

Explanation:

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

the area between the graph and the t axis

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