Simplify this expression for the period

In summary, the conversation discusses a homework problem involving the expression for T and the steps to simplify it. The person asking for help has consulted their notes but still needs assistance. After some discussion, it is determined that squaring the denominator can help simplify the expression, and this is referred to as "taking the square root" or "squaring". The final simplified answer is 2π * √(Lcosθ / g).
  • #1
15
2
Homework Statement
A bob of mass m is suspended from a fixed point with a massless string of length L. You are to investigate the motion in which the string moves in a cone with half-angle, 𝜃. Express your answers in terms of some or all of the variables m, L, and 𝜃, and g.

v = √Lgsin𝜃tan𝜃

How long does it take the bob to make one full revolution (one complete trip around the circle)?
Relevant Equations
T = 2πr / v
r = Lsin𝜃
hi ! I'm having a lot of trouble simplifying my expression for one of my homework questions. I know someone asked about this homework problem already, but the answers didn't really help me figure out how to simplify it.. I really have no idea what steps to take, and I've even consulted all my math notes too.

my expression for T is:

T = 2πLsinθ / √(Lgsinθtanθ)
T = 2πLsinθ * √(Lgsinθtanθ) / Lgsinθtanθ
T = 2π * √(Lgsinθtanθ) / gtanθ

final answer

[ 2π * √(Lgsinθtanθ) ] / gtanθ

the correct answer should be:

2π * √( Lcosθ / g )thank you in advance
 

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  • #2
Hi,

How about the forces that act on the bob ? Can you draw a diagram ?

##\ ##
 
  • #3
If you square the denominator, you can put it inside the radical. What do you get?
 
  • #4
kuruman said:
If you square the denominator, you can put it inside the radical. What do you get?
tried that, and it worked, thank u ! what is that rule called though? I don't remember learning it
 
  • #5
crememars said:
tried that, and it worked, thank u ! what is that rule called though? I don't remember learning it
It's called "taking the square root" or "squaring". You can go back and forth in what is shown below.
$$\sqrt{\frac{A}{B^2}}=\frac{\sqrt{A}}{\sqrt{B^2}}=\frac{\sqrt{A}}{B}$$
 
  • Like
Likes crememars

What does it mean to "simplify" an expression?

Simplifying an expression means to rewrite it in a way that is easier to understand and work with. This often involves combining like terms, reducing fractions, and eliminating unnecessary symbols or parentheses.

Why is it important to simplify expressions?

Simplifying expressions can make them easier to work with and can help to identify patterns and relationships within the expression. It can also make it easier to solve equations and perform calculations.

What is the "period" in an expression?

The period in an expression refers to the length of one complete cycle or repetition of the expression. It is often used in trigonometric functions and can help to determine the frequency or wavelength of a wave.

How do I know when an expression is fully simplified?

An expression is considered fully simplified when there are no more like terms that can be combined, no more fractions that can be reduced, and no more unnecessary symbols or parentheses. It should be in its most simplified form and cannot be simplified any further.

Can I use different methods to simplify an expression?

Yes, there are often multiple ways to simplify an expression. Some common methods include using the distributive property, combining like terms, and reducing fractions. It is important to choose the method that works best for the specific expression and to check your answer for accuracy.

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