How Does Trebuchet Arm Design Affect Moment of Inertia?

[airforce840]

For our AP Physics final project, we must do research on the moment of inertia ... which by that we are looking at a trebuchet's arm design, and also just trebuchet analysis(looking at the body of the trebuchet and how it will need to be for best performance with an arm of certain design).

We have an idea of how to test for the moment of inertia. Here is the set up.

The arm is on this ball bearing thing so that it can spin horizontally, a string is attached at where the axel will be, and pull system is attached to a ramp near by.. A 500g cart has the string attached to it so that when u let the car go... it slowly picks up in speed giving us an angular acceleration. We want to calculate that angular accell. and then use it to find the moment of inertia in that arm that will spin when the car moves down the ramp...

Any ideas? or is there any tips that someone can give us on how to better go about doing this? We have a little less than a month to get this done. We plan to make about 2-5 different arm designs. Also, if anyone knows a good way to make a trebuchet arm.. whether that being drill out holes in the middle or lighten it up in ways... any help is appreciated..if u need pictures of the set up.. i can have that arranged.

thanks in advanced..

-Connerville, Indiana's High School AP Physics Class

 

[Andrew Mason]

The arm is on this ball bearing thing so that it can spin horizontally, a string is attached at where the axel will be, and pull system is attached to a ramp near by.. A 500g cart has the string attached to it so that when u let the car go... it slowly picks up in speed giving us an angular acceleration. We want to calculate that angular accell. and then use it to find the moment of inertia in that arm that will spin when the car moves down the ramp...

Any ideas? or is there any tips that someone can give us on how to better go about doing this? We have a little less than a month to get this done. We plan to make about 2-5 different arm designs. Also, if anyone knows a good way to make a trebuchet arm.. whether that being drill out holes in the middle or lighten it up in ways... any help is appreciated..if u need pictures of the set up.. i can have that arranged.

thanks in advanced..

-Connerville, Indiana's High School AP Physics Class

It would help if you could post a drawing. I don't have a clear idea of the set up. But in order to calculate moment of inertia you have to measure torque and angular acceleration. I is, after all, the ratio of torque to angular acceleration - similar to mass = ratio of force to acceleration.

AM

 

[FredGarvin]

Have you thought about simply using a pendulum to calculate the moments of inertia? Take a look at the attached PDF and perhaps a bit of googling will help. The method has been around for a lot of years. I have used it a couple of times to calculate the MOI of some complicated parts.

One thing as a note...if I remember correctly, the angular displacement has to be relatively small since there is a mathematical approximation involved that states that $$sin \theta = \theta$$