In a downtown office building you notice each of the four sections of a rotating door has a mass of 85 kg. What is the width of each section of the door if a force of 58 N applied to the outer edge of a section produces an angular acceleration of 0.400 rad/s2?

width = 1.28 m

Explanation:

To do this exercise, you need to apply the following expression:

T = F * d (1)

T: torque

F: Force

d: distance or width in this case

But T can be also:

T = 4Iα (2)

α: angular acceleration

And I (moment of innertia) is:

I = md²/3 (3)

Then, replacing (2) and (3) in the equation (1) you have:

4md²α/3 = F * d - --> two d cancel themselves

Solving for d:

4mdα/3 = F

d = 3F/4mα

Now, let's replace the data in this equation:

d = 3*58 / 4 * 85 * 0.4

d = 1.28 m