Angular acceleration and it's mass dependancy

[j-e_c]

Homework Statement

A wooden door is closed by applying a perpendicular force to it. If the magnitude of the force is constant and takes 2 seconds for the door to close, how long would it take to close the door with the same amount of force, in the same manner, if the door was made of a material 4 times heavier than the wood? Assume the door is initially at rest and neglect friction.

The Attempt at a Solution

-Angular acceleration is torque/moment of inertia

-$$\alpha$$= $$\frac{N.m}{kg.m.m}$$ so for a constant force and length of door, the angular acceleration is inversely proportional to the mass.

-So, if the door is 4 times the mass, the acceleration is 4 times smaller.

-I then applied a constant acceleration equation: s=ut+$$\frac{1}{2}$$a$$^{2}$$ to circular motion:

-$$\theta$$=$$\frac{1}{2}$$$$\alpha$$t$$^{2}$$

-So, if r is a constant, then $$\alpha$$ is inversely proportional to t$$^{2}$$

-Therefore, if you make $$\alpha$$ 4 times smaller, then t will double.

So, finally, t=4s.

 

[diazona]

Seems to make sense... is 4s the right answer?

 

[j-e_c]

I have no way of knowing. This question is from a university past paper for which there is no mark scheme. That's why I posted it here really.