Step by Step rearranging with square roots

In summary, the conversation is about solving for the length of a pendulum in an equation given its period and gravitational constant. The process involves dividing by 2pi, squaring both sides, and multiplying by g. The discussion also touches on the relationship between mass, weight, and the period of a pendulum, as well as the use of LaTeX to format equations.
  • #1
SLiM6y
10
0
Hello,

I have a simple equation (maybe simple for some) that I can't understand how to get from one point to the next when re-arranging. If you can help by giving an answer in english I would be thankful...

The equation T = 2 pi square root L / g (sorry couldn't find the square root etc...)

I want to solve for L

So the answer will be L = g / T 4 pi^2

Why is that? How do I get from the first equation to solving for L. Can you please explain in simplistic terms that way I can see my errors.

Thanks.

Maybe you can tell me how to do the square root and pi symbols...
 
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  • #2
i don't know how to use LaTeX, so i can't make the equations loko nice:

:P

Anyways (this the eq'n for the period of a simple pendulum?):

T = 2pi * sqrt(L/g)

Divide by 2pi on both sides:

T / 2pi = sqrt(L/g) = [L/g]^(1/2)

Square both sides (i.e. raise to the exponent 2):

[T/2pi]^2 = [L/g]^{(1/2)(2)}

Then multiply by g:

L = g * [T/2pi]^2

I didn't get your L = g / T 4 pi^2

just checking over my work for any errors right now
 
Last edited:
  • #3
Thanks for the reply... I got the same as you the first and the second time, but the book got something different...
 
  • #4
OK - I have looked through it and I can't get the same answer as the book...

The question is Calculate the length of cable required to give a clock (grandfather clock) a frequency of 1.0 Hz. So T = 2 pi * sq rt L / g

They work the answer through as L = g / T 4 pi^2 = 9.8 / 4 pi^2 = 0.25 m (a reasonable answer, but how the hell do we get to it?)
 
  • #5
DOH - I get it!
 
  • #6
But then in that case... that would mean EVERY grandfather clock has a pendulum with a cable length of 0.25 m - does that sound correct? Because the mass doesn't change the period, and the height it is dropped doesn't change the period so then only the length of the cable will change the period... Is this true?
 
  • #7
SLiM6y said:
Because the mass doesn't change the period, and the height it is dropped doesn't change the period so then only the length of the cable will change the period... Is this true?
Yes. That's why pendulum clocks keep good time, while mechanical watches (which use springs instead) eventually have to be adjusted. You are basically asking a physics question. It is related to the fact that different weights fall at the same speed. A more massive object is harder to get moving, but OTOH since its weight is basically the force that drives it, a more massive object falls with greater force. The two effects exactly cancel. This is sometimes called Einstein's equivalence principle.
 
  • #8
NSX said:
i don't know how to use LaTeX, so i can't make the equations loko nice:...
You are almost there! Just put backslashes in front of pi and sqrt, and use tex in square brackets where you have b in square brackets. That's it!
 

1. How do I rearrange an equation involving square roots?

To rearrange an equation with square roots, you need to isolate the square root term on one side of the equation and square both sides to eliminate the square root. Then, solve for the remaining variable.

2. Can I rearrange equations with square roots in the same way as equations without square roots?

No, equations with square roots require an extra step of squaring both sides in order to eliminate the square root. This is because the inverse operation of a square root is to square a number.

3. What if the equation has more than one square root term?

If the equation has multiple square root terms, you can follow the same steps as for one square root term. Isolate one square root term on one side, square both sides, and then solve for the remaining variable. Repeat this process for each additional square root term until you have solved for all variables.

4. Can I rearrange equations with square roots if there is a variable under the square root?

Yes, you can still rearrange equations with a variable under the square root. Just make sure to isolate the square root term on one side and then square both sides to eliminate the square root. This will allow you to solve for the variable.

5. Are there any special rules or exceptions when rearranging with square roots?

One important rule to remember when rearranging with square roots is that you cannot square a negative number. If your equation has a negative number under the square root, you will need to use the imaginary number i to solve for the variable.

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