How to Measure G with a Compound pendulum

[rossildosil]

For my Advanced Higher Physics Investigation i am measuring acceleration due to gravity. Having already done it with a simple pendulum my teacher says i have to do the same with a "Compound Pendulum". I was wondering how to do this and also how to make a compound pendulum with a steel rod.

Many thanks Ross.

 

[RTW69]

A compound pendulum is one where the rod is not massless, and may have extended size; that is, an arbitrarily shaped rigid body swinging by a pivot. In this case the pendulum's period depends on its moment of inertia I around the pivot point.

T=2*Pi*Sqrt(I/(m*g*L)) where I is the moment of inertia of the rod and L is the distance from the pivot to the center of mass. Measure the period and mass. Locate center of mass and measure distance to pivot. Determining moment of inertia could be the tricky part.

 

[rossildosil]

Hi that's great. Sorry for the slow reply, but i need to clear something up. Is the T the time taken for one oscilation?

Thanks

 

[RTW69]

T is the period or how long to complete one complete cycle

 

[rwisz]

To measure G with a compound pendulum, you will need to follow a similar process as you did with the simple pendulum. However, the key difference is that a compound pendulum consists of a rigid body with multiple points of suspension, rather than a single point like a simple pendulum. This allows for a more accurate measurement of acceleration due to gravity, as the motion of the compound pendulum is less affected by external factors such as air resistance.

To create a compound pendulum using a steel rod, you can follow these steps:

1. Obtain a long steel rod and attach a small mass (e.g. a metal ball) to one end of it.
2. Find a suitable point on the rod to attach a string or wire for suspension. This point should be close to the center of mass of the rod and should be able to support the weight of the rod and the attached mass.
3. Suspend the rod from a fixed point using the string or wire.
4. Adjust the position of the mass on the rod until the pendulum is balanced and the rod hangs vertically.
5. Measure the length of the rod from the point of suspension to the center of mass.
6. Use a timer to record the time for the pendulum to complete one full swing (back and forth).
7. Repeat the measurement multiple times and take an average to improve accuracy.

Once you have your compound pendulum set up, you can use the formula T=2π√(l/g) to calculate the acceleration due to gravity (g), where T is the period of the pendulum and l is the length of the pendulum.

It is important to note that there are other factors that can affect the accuracy of your measurement, such as the quality of the steel rod and the precision of your timing. Therefore, it is recommended to repeat the experiment multiple times and take an average to reduce any errors.

I hope this helps and good luck with your investigation!