A 0.12-m-radius grinding wheel takes 5.5 s to speed up from 2.0 rad/s to 11.0 rad/s. What is the wheel's average angular acceleration?

The wheel's average angular acceleration is equal to 1.64 .

Given the following data:

To determine the wheel's average angular acceleration, we would apply the first equation of kinematics:

Mathematically, the angular acceleration of an object is given by the formula:

Where:

Substituting the given parameters into the formula, we have;

Angular acceleration = 1.64

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0.56rad/s²

Explanation:

Using the equation of motion

wf = wi + αt

wf is the final angular velocity

wi is the initial angular velocity

α is the angular acceleration

t is the time

Given

wf = 11.0rad/s

wi =2.0rad/s

t = 5.5secs

Substitute into the formula and get α

11.0 = 2.0+5α

11.0-2.0 = 5α

9.0 = 5α

α = 5/9.0

α ≈ 0.56rad/s²

Hence the wheel's average angular acceleration is 0.56rad/s²

true tan speed = ang vel x radius