# Find an Expression for the Frequency - Pendulum

• AbigailG
In summary: I thought the moment of inertia would be that of a sphere about an axis through the center. ..am I just not visualizing this correctly?No, check out this page and pay particular attention to the meaning of ##I_{\rm support}##.
AbigailG

## Homework Statement

[/B]
A solid sphere of mass M and radius R is suspended from a thin rod. The sphere can swing back and forth at the bottom of the rod. Find an expression for the frequency of small angle oscillations.

## Homework Equations

f = 1/2(pi) sqrt(MgR/I)

I for a solid sphere 2/5MR^2

## The Attempt at a Solution

[/B]
I simply plugged the moment of inertia into the equation for the frequency and that yielded:

1/2(pi) sqrt(5g/2R)

1/2(pi) sqrt(5g/7R)

Does anyone know what my missing is?

Review the meaning of R and I in the equation f = 1/2(pi) sqrt(MgR/I). R is not the radius of the sphere and I is not the moment of inertia of the sphere about an axis through the center of the sphere.

EDIT: It could be that R does in fact equal the radius of the sphere depending on the interpretation of the problem. It's not clear how the rod is arranged in the problem.

TSny said:
Review the meaning of R and I in the equation f = 1/2(pi) sqrt(MgR/I). R is not the radius of the sphere and I is not the moment of inertia of the sphere about an axis through the center of the sphere.

Generically, R = l which is the distance from the pivot point to the center of mass. I thought the moment of inertia would be that of a sphere about an axis through the center. ..am I just not visualizing this correctly?

Is the setup like either of the pictures below?

#### Attachments

4.4 KB · Views: 2,111
AbigailG said:
Generically, R = l which is the distance from the pivot point to the center of mass.
Yes
I thought the moment of inertia would be that of a sphere about an axis through the center.
No, check out this page and pay particular attention to the meaning of ##I_{\rm support}##.

http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html

## What is the equation for the frequency of a pendulum?

The equation for the frequency of a pendulum is f = 1/T, where f is frequency and T is the period of the pendulum.

## How is the length of a pendulum related to its frequency?

The frequency of a pendulum is inversely proportional to the square root of its length. This means that as the length of the pendulum increases, its frequency decreases.

## What factors affect the frequency of a pendulum?

The main factors that affect the frequency of a pendulum are its length, the acceleration due to gravity, and the mass of the pendulum bob. Other factors such as air resistance and friction can also have a slight effect on the frequency.

## How does the mass of the pendulum bob affect its frequency?

The mass of the pendulum bob does not affect its frequency. As long as the length and acceleration due to gravity remain constant, the mass of the bob will not change the frequency of the pendulum.

## Can the frequency of a pendulum be changed?

Yes, the frequency of a pendulum can be changed by altering its length, the acceleration due to gravity, or the mass of the pendulum bob. However, these changes will only have a significant effect on the frequency if they are large enough.

• Introductory Physics Homework Help
Replies
9
Views
961
• Introductory Physics Homework Help
Replies
17
Views
741
• Introductory Physics Homework Help
Replies
16
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
300
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
7
Views
951
• Introductory Physics Homework Help
Replies
14
Views
1K