Determine the Angular Acceleration of a Rotating Door

[wchvball13]

Homework Statement

A rotating door is made from four rectangular glass panes, as shown in the drawing. The mass of each pane is 92 kg. A person pushes on the outer edge of one pane with a force of F = 79 N that is directed perpendicular to the pane. Determine the magnitude of the door's angular acceleration.

http://h1.ripway.com/wchvball13/09_34.gif

Homework Equations

$$\sum T = I\alpha$$

$$I = (1/12)ML^{2}$$

The Attempt at a Solution

$$T$$ = 79(1.2) = 94.8

So...
94.8 = (1/12)(92)(2.4)$$^{2}$$ $$\alpha$$
94.8 = 44.16$$\alpha$$
2.15 = $$\alpha$$

the alphas aren't supposed to be superscript...anyway...this is my answer and it's wrong...don't know what I'm doing ...or not doing...

 

[Astronuc]

The torque imposed by the person pushing with a force of 79N is correct.

 

[wchvball13]

Where am I going wrong?

 

[wchvball13]

nevermind...I got it..I didn't realize I would take 92 x 4 to use as the weight

 

[Astronuc]

nevermind...I got it..I didn't realize I would take 92 x 4 to use as the weight

Yes, be careful on the calculation of I with respect to geometry and total mass.

See http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod and more generally,

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#cmi

Note L and the position of the rotational axis w.r.t. center of mass.