# Homework Help: Swinging door

1. Nov 8, 2008

### vincisonfire

1. The problem statement, all variables and given/known data
A truck has acceleration A. Its door has a width w and a heigth h. We want to find the angular speed of the door when it reaches the horizontal. (I attached the problem as an image)
2. Relevant equations
See solution attempt.
3. The attempt at a solution
There is a fictitious force acting on the center of mass of the door. It is situated at w/2.
This force is F = MA
Let T be the symbol for torque and y the angle from the horizontal.
T = r x F = w/2 * MA sin(pi/2 - y) = w/2 * MA cos(y)
Let L be the angular momentum and I the moment of inertia
T = dL/dt = d(I y')/dt
Chain rule gives us
T = I/2 d(y'^2)/dy
T = I/2 d(y'^2)/dy = w/2 * MA cos(y)
T = d(y'^2) = w/I * MA cos(y) dy
y'^2 = w/I * MA sin(y)
I = 1/2*m*w^2
y'^2 = 2*A*sin(y)/w
y' = sqrt(2*A*sin(y)/w)
PS : can't we use latex on this forum?

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Last edited: Nov 8, 2008