Question

A rotating door is made from four rectangular glass panes, as shown in the figure. The mass of each pane is 75.9 kg. A person pushes on the outer edge of one pane with a force of F = 101 N that is directed perpendicular to the pane. Determine the magnitude of the door's angular acceleration.

Answer 1

F =101 N , L = 1.2 m,

Moment of inertia of single rod of length l about an axis passing through its end is = (MR^2/12)

R = 2L

Our given system is combination of 4 thin rods with length

I = 4*(MR²/12) = 4*(M(2L)²/12)= (4/3)*(MLl²)

I = (4/3)[75.9(1.2*1.2)] =145.73 kg.m^2

Net troque :

F*L = I $\alpha$

$\alpha$ = FL/I = (101*1.2)/(145.73)

$\alpha$ = 0.832 rad/s²