How Does a Compound Pendulum Behave When Dropped and Restrained?

[irishmts]

a rectangular plate of length 300mm and depth 200mm, whose top left corner is attached to a wire of 200mm is dropped lengthways. What is the angular velocity of the plate and the speed of the corner opposite to the one the wire is attached to, just after the wire is pulled taut (it doesn't lengthen due to the stress). I've attached the diagram we were provided with to the bottom of this post.



I have been trying to use the compound pendulum equation: T = 2âˆsqrt(I/mgh), where I is the Inertia of the plate ( i used I = bd³/12, where b is the length and d is the depth), m is the mass of the plate, which was not provided, g is acceleration due to gravity and h is the distance from the top of the pendulum to the center of mass. T, the period can then be converted into ω using T = 2âˆ/ω. I also used the equations of linear motion to get the linear acceleration of the plate: v² = u²+2as



I had gone down the route of assuming I could do it in two parts, ie, find the angular velocity of the plate about the end of the wire, and then relate it in some way to the angular velocity of a bob that would be on the end of the wire, but I got a little lost along the way.


Thank you for any help you can give me on this, mechanics is not my strong point at all.

 

[jedishrfu]

It seems that when the plate drops both points drop straight down too until the wire is taut. Once taut, then point b continues downward but in a circular arc of radius sqrt(200^2+300^2) mm and point a remains stationary.

 

[irishmts]

Would there not be any kind of rotation about the top of the wire though?