# Help rearranging this equation.

• dwartenb89
In summary, the conversation is about a construction site where a uniform steel beam is suspended and swinging back and forth with a period of 5.00 seconds. The question is asking for the length of the beam, and the person is having trouble rearranging the equation to solve for length. They have attempted to rearrange it and are seeking help.
dwartenb89

## Homework Statement

On the construction site for a new skyscraper, a uniform beam of steel is suspended from one end. If the beam swings back and forth with a period of 5.00 , what is its length?

I know the equation I need to use but I'm having trouble rearranging it to solve for Length (L).

## Homework Equations

T=2pi*sqrt(L/g)*(sqrt2/3)

## The Attempt at a Solution

I tried to rearrange the equation to solve for L and got this.
L=sqrt[g*(T/(2pi*sqrt(2/3)))]

any help would be great!

Welcome to PF.

Why not simply square both sides of the original?

You know all the other values. Plug them in.

First, let's start by writing the equation in a more standard form:

T = 2π√(L/g) * (√2/3)

Next, we can square both sides of the equation to get rid of the square root on the left side:

T^2 = (2π√(L/g) * (√2/3))^2

Simplifying the right side, we get:

T^2 = 4π^2(L/g) * (2/9)

Now, we can divide both sides by 4π^2 to isolate the term for L:

T^2 / (4π^2) = (L/g) * (2/9)

Finally, we can multiply both sides by g and then divide by (2/9) to solve for L:

L = (T^2 * g) / (4π^2 * 2/9)

This gives us the final equation for L:

L = (9T^2 * g) / (8π^2)

So, the length of the beam can be calculated by plugging in the value for T (period) and g (acceleration due to gravity). I hope this helps with your homework!

## 1. "What is the first step in rearranging an equation?"

The first step in rearranging an equation is to identify the variable you want to solve for and isolate it on one side of the equation.

## 2. "Can I rearrange an equation without changing its meaning?"

Yes, as long as you apply the same operations to both sides of the equation, the meaning and solution will remain the same.

## 3. "Are there any rules or guidelines for rearranging equations?"

Yes, when rearranging equations, you should follow the order of operations and perform the same operation on both sides of the equation to maintain balance.

## 4. "Is it possible to rearrange an equation to solve for multiple variables?"

Yes, you can rearrange an equation to solve for multiple variables by isolating one variable at a time and substituting the solved value into the original equation.

## 5. "What is the purpose of rearranging an equation?"

The purpose of rearranging an equation is to solve for a specific variable or to simplify the equation and make it easier to understand and work with.

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