Question

An engine flywheel initially rotates counterclockwise at 6.55 rotations/s. Then, during 20.9 s, its rotation rate changes to 2.19 rotations/s clockwise. Find the flywheel's average angular acceleration (including its sign) in radians per second squared. Define counterclockwise rotation as positive.

Answer 1

The average angular acceleration is -2.628 rad/s²

Step-by-step explanation:

Counterclockwise = positive

Clockwise = -negative

Given;

initial rotation of the flywheel, θ₁ = 6.55 rotation/s

final rotation of the flywheel, θ₂ = - 2.19 rotation/s

The average angular acceleration is given by;

`\alpha = (\delta \theta)/(\delta t)\\\\ \alpha =(\theta _2 - \theta_ 1)/(t)\\\\ \alpha =(-2.19 -6.55)/(20.9) \\\\ \alpha =(-8.74)/(20.9)\\\\ \alpha = -0.4182 \ rotation / s^2\\\\ \alpha = (-0.4182 \ rotation)/(s^2)*(2\pi \ radian)/(rotation)\\\\ \alpha = -2.628 \ rad/s^2`

Therefore, the average angular acceleration is -2.628 rad/s²