Question

An engine flywheel initially rotates counterclockwise at 6.77 rotations/s. Then, during 23.9 s, its rotation rate changes to 3.51 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

-2.70 rad/s²

Step-by-step explanation:

Given that

ω1 = initial angular velocity of the flywheel, which is 6.77 rev/s

If we convert it to rad/s, we have

(6.77 x 2π) rad/s = 13.54π rad/s

ω2 = final angular velocity of the flywheel = -3.51 rev/s,

On converting to rad/s also, we have

(-3.51 x 2π) rad/s = 7.02π rad/s

α = average angular acceleration of the flywheel = ?

Δt = elapsed time = 23.9 s

Now, using the formula, α = (ω2 - ω1)/Δt. On substituting, we have

α = (-7.02π rad/s - 13.54π rad/s)/23.9 s

α = -20.56π rad/s / 23.9 s

α = -64.59 rad/s / 23.9 s

α = -2.70 rad/s²

Therefore, the average angular acceleration of the flywheel is -2.70 rad/s²