# Torque: Swinging Door; mass, I, r, t and Angular Displacement Given

1. Feb 28, 2008

### JFlash

Hello. The question reads, "...This is the world's heaviest hinged door. The door has a mass of 44,000kg, a rotational inertia about an axis through its hinges of 8.7X10^4 kg*m^2, and a width of 2.4m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90 degrees in 30s? Assume no friction acts on the hinges."

The work I did below followed 4 steps:
1. Use this equation: $$\Theta = (1/2)(\omega initial + \omega)t$$ to find the angular velocity at 30s.
2. Find the average angular acceleration over the 30s period of applied force.
3. Set the torque equal to the rotational inertia of the door times its angular acceleration.
4. Set torque equal to r X F, and solve for F.

My answer came to 40.27N, which is about a third of the actual answer: 130N. As I look over my work, I realize that I never used the mass of the door, which is probably a reason why my answer is wrong. Anyway, here's what I did:

$$\Theta = \pi/2 = (1/2)(0 + \omega)30s... \omega = \pi/30 rad/s$$
$$\alpha = (\pi/30 rad/s)/(30s-0s) = \pi/900 rad/s^2$$
$$\tau = 87000kgm^2 * \pi/900 rad/s^2 = 96.67$$
$$\tau = rF sin \phi = 2.4m * F * sin(90 degrees) F = 40.27N$$

Does anyone know where I went wrong?