T = 2π√I/g but I am getting the wrong answer.Pendulum Periods: A & B (L, m)

In summary, the conversation is discussing two pendulums with the same dimensions and total mass, one with a small ball at the end of a massless bar and the other with half the mass in the ball and half in the bar. The period of pendulum A for small oscillations is found to be 2∏√L/g, while the period of pendulum B is still being determined but the calculation thus far is correct.
  • #1
Mdhiggenz
327
1

Homework Statement


Two pendulums have the same dimensions (length ) L and total mass (m). Pendulum A is a very small ball swinging at the end of a uniform massless bar. In pendulum B , half the mass is in the ball and half is in the uniform bar.

A. Find the period of pendulum A for small oscillations.

B. Find the period of pendulum B for small oscillation

Homework Equations





The Attempt at a Solution



For A. I got 2∏√L/g which is correct however i am struggling for B

What I did was

Pendulum B I= Ibar + Ibar= 1/3 (m/2)L^2+m/2L^2= 2/3mL^2
 
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  • #2
Hi Mdhiggenz! :smile:

(try using the X2 button just above the Reply box :wink:)
Mdhiggenz said:
In pendulum B , half the mass is in the ball and half is in the uniform bar.
…
Pendulum B I= Ibar + Ibar= 1/3 (m/2)L^2+m/2L^2= 2/3mL^2

Looks ok! :smile:
 

1. Why am I getting the wrong answer for the period of my pendulum using the equation T = 2π√I/g?

There are a few possible reasons for this. One common mistake is using the incorrect value for the length of the pendulum, L. It's important to use the length from the point of suspension to the center of mass of the pendulum bob. Another possible error is using the incorrect value for the acceleration due to gravity, g. Make sure you are using the correct value for the location where the pendulum is being tested. Lastly, it's important to ensure that the units for all variables are consistent (e.g. meters for length and seconds squared for acceleration).

2. Can I use the equation T = 2π√I/g for any pendulum, regardless of its mass or length?

Yes, this equation can be used for any pendulum as long as the length and mass are measured correctly and the acceleration due to gravity is accounted for. However, for larger amplitudes (angles greater than 15 degrees), this equation may not be accurate and a more complex equation is needed.

3. What does the variable I represent in the equation T = 2π√I/g?

The variable I represents the moment of inertia of the pendulum, which is a measure of an object's resistance to changes in its rotational motion. It takes into account the mass of the pendulum and its distribution around the point of rotation.

4. How can I measure the period of a pendulum accurately?

The most accurate way to measure the period of a pendulum is by using a stopwatch or timer to measure the time it takes for the pendulum to complete a certain number of swings (e.g. 10 swings). This allows for more precise measurements and reduces the impact of human error. Alternatively, you can use a photogate timer that measures the time it takes for the pendulum to pass through a light beam. This method can be more accurate, but it requires special equipment.

5. Is the equation T = 2π√I/g affected by external factors such as air resistance?

Yes, external factors such as air resistance can affect the accuracy of this equation. If the pendulum is swinging through a fluid medium such as air, the period may be slightly longer due to the resistance of the air. This can be minimized by using a streamlined pendulum bob and conducting the experiment in a vacuum.

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