HINGED PLATE IN FREE FALL

[CESSNA1]

HELLO ALL: This is a real problem. A uniform rectangular flat steel plate hinged on one side is held at an angle, theta (90<theta>0). The only force acting is earth's gravity. The plate is suddenly released and allowed to fall under th influence of gravity to the horizontal position. ignore friction in the hinge and wind resistance.

The center of gravity of the plate is not necessarily at the midpoint of the plate in the rotational plane. Thus it is distance "A" from the center of the hinge and distance "B" from the other end. It is centered in the direction looking into the paper.

Determine the angular acceleration and angular position as a function of time for the plate.

REGARDS

DAVE

 

[handleman]

You have not given any information regarding the polar moment of inertia, which is required to solve any problem involving angular acceleration.


-handleman, CSWP (The new, easy test)

 

[handleman]

By the way, you're not going to get a closed form solution, if you're after one. What you have is a pendulum. Unusual initial conditions, but a pendulum nonetheless. You'll need numerical methods to solve. Plenty of examples out there.

-handleman, CSWP (The new, easy test)

 

[CESSNA1]

HANDLEMAN: Thank you for your response. I did not give specific numbers becasue I was looking for a solution that would be in general form. I was remiss in not stating that.

Would you please give one or two sources for the numerical method I will need?

Thank you again for your quick response
Cordially

Dave

 

[handleman]

Runge-Kutta is the one normally employed for solving the physical pendulum differential equation.

Goo(gle)d luck!

-handleman, CSWP (The new, easy test)