Calculating acceleration of gravity and inertia of irregular lamina

[KYLESCHOONBEE]

Homework Statement

I have a practical coming up and I have to research the method and calculations. I will be given an irregular lamina that I need to use as a compound pendulum in an experiment to determine the gravitational acceleration, g, as well as the moment of inertia (Io) of the lamina. I will know the mass of the lamina as well as the center of gravity. I need to use the lamina as a pendulum and obtain readings for the period of oscillation and distance between center of gravity and the point of rotation. I then need to perform appropriate calculations and plot a linearised graph to verify the relationship between the variable suggested in equation 3 below. I have no idea what the appropriate calculations are.

Homework Equations

Equation 1: T = 2*pi*(I/mgl)^1/2 (Period of oscillation equation)

Equation 2: I = Io + ml^2 (Parallel axis theorem)

Equation 3: T^2*l = 4*pi^2*(Io/mg + l^2/g) (Insert equation 1 into equation 2 and rearranged)

The Attempt at a Solution

At this stage I have worked out how to calculate where the center of mass is using a plumb line and bob, but I cannot find what appropriate calculations I need to do.

I need to know the process of what calculations I need to perform once I have me readings in order to solve for the two variables g and Io.

 

[Simon Bridge]

Welcome to PF;
The description you have does not talk about a compound pendulum.
A lot will depend on how the compound pendulum is made up.

The lamina itself can be used by itself to find the strength of gravity though - at this looks to be what you want to do. Hang the lamina by some point, let it swing, obtain the period, do some maths.

At this stage I have worked out how to calculate where the center of mass is using a plumb line and bob, but I cannot find what appropriate calculations I need to do.

... to do what?

I need to know the process of what calculations I need to perform once I have me readings in order to solve for the two variables g and Io.

You have a bunch of equations given to you - don't they give you a clue or three?

Usually in experiments you have to take lots of measurements that you put on a graph and you use the properties of the graph to work out the values you need.

It looks to me like part of the exercize is that you have to figure out what measurements to take - for us to help you, then, you will have to tell us how you are thinking about the problems.

You can already find the com, so you can get the distance from the com to wherever the pivot is.
You can measure the period (time 10 swings and divide I hope).
... how were you thinking to use the period to get g?
... what happens if you change the distance from the com to the pivot?

 

[KYLESCHOONBEE]

Thanks Simon.

I know to take the reading of the distance from the center of mass to the axis of roatation and time a number of oscillations and divide by that number to obtain the period.
However, my issue is that I do not know how to solve for g and Io based on the limited information above. I do not know how to calculate The moment of inertia about the axis if rotation so I cannot solve for Io in the second equation. To solve for g, I need to know Io.

I have read around and found that the lamina behaves like a simple pendulum with and effective length L. But I don't know how to calculate that effective length either.

Will I need to know the radius of gyration to calculate the effective length? Because I don't know what that is or how to find it.

 

[Simon Bridge]

I do not know how to calculate The moment of inertia about the axis if rotation

Parallel axis theorem.

I have read around and found that the lamina behaves like a simple pendulum with and effective length L

The moment of inertia about the pivot point for a simple pendulum is $mL^2$ where L is the distance from the bob to the pivot.

Will I need to know the radius of gyration to calculate the effective length?

The radius of gyration is the effective L.

 

[KYLESCHOONBEE]

Ok I'm beginning to understand.

With regards to the parallel axis theorem.

I will know ml^2 but I don't know I or Io.

How would I obtain I or Io?

 

[Simon Bridge]

You will probably need to conduct an experiment to find I ;)

 

[KYLESCHOONBEE]

Alright, got it!
Thank you!

 

[Simon Bridge]

Well done.

 

[peg_leg]

@KYLESCHOONBEE , this link will be quite useful to your practical:



it is basically a video based on the experiment that you are going to conduct entitled:

Measuring the mass moment of inertia - Brian Waves

it sure did help me in the same situation @ UCT

 

[Riyadh Karbary]

@KYLESCHOONBEE , this link will be quite useful to your practical:



it is basically a video based on the experiment that you are going to conduct entitled:

Measuring the mass moment of inertia - Brian Waves

it sure did help me in the same situation @ UCT

Hey there, The video seems to be unavailable. Is there any chance you know of a similar example (or, unlikely, have access to the video?)

 

[robphy]

This is an ancient thread (relatively speaking).

By googling the title of the video,
this seems to be closest match.
(It appears the correct name is "Brain" not "Brian" for the reference posted earlier.)