# Derivation of angular frequency equation

• AToMic93
In summary, to derive the angular frequency equation (ω=√(g/L)) from the given equations, you can start by using equation (2) to find an expression for the second derivative of θ with respect to time. This can then be set equal to the expression given in equation (1), taking into account that θ = θmaxcos(ωt + δ). From here, you can solve for ω and simplify to get the desired equation. It is important to remember that θmax is a constant in this derivation process.
AToMic93

## Homework Statement

Derive the angular frequency equation (ω=√(g/L) from following equations:

## Homework Equations

1) ((d^2)*θ)/(d*t^2)= (-g/L)*θ
2) θ=θmaxcos(ωt+δ)

## The Attempt at a Solution

I don't even know where to start

AToMic93 said:

## Homework Statement

Derive the angular frequency equation (ω=√(g/L) from following equations:

## Homework Equations

1) ((d^2)*θ)/(d*t^2)= (-g/L)*θ
2) θ=θmaxcos(ωt+δ)

## The Attempt at a Solution

I don't even know where to start

(1) tells you that ##\frac{d^2\theta}{dt^2}## is (-g/L)θ. (2) gives you a formula for θ. If you were only given (2), how would you find an expression for ##\frac{d^2\theta}{dt^2}## from it?

Would you take the second derivative with respect to time? (giving d2/dt2) then set this equal to the other equation?

AToMic93 said:
Would you take the second derivative with respect to time? (giving d2/dt2) then set this equal to the other equation?

I suggest you give it a try

So the main question I have then is for when I'm deriving how do I deal with the θmax? Do I treat it just like θ or do I treat it like a constant?

AToMic93 said:
So the main question I have then is for when I'm deriving how do I deal with the θmax? Do I treat it just like θ or do I treat it like a constant?
It is, of course, a constant. But do keep in mind that θ = θmaxcos(ωt + δ)

Alright I got it. Thanks

Last edited:

## 1. What is angular frequency and why is it important?

Angular frequency is a measure of how quickly an object rotates or oscillates around a fixed point. It is important because it helps us understand the behavior and dynamics of rotating or oscillating systems.

## 2. How is angular frequency related to linear velocity?

Angular frequency is directly proportional to linear velocity. This means that as the angular frequency increases, so does the linear velocity of the object.

## 3. What is the derivation of the angular frequency equation?

The angular frequency equation can be derived from the formula for circular motion, v = rω, where v is the linear velocity, r is the radius, and ω is the angular velocity. By rearranging the formula, we get ω = v/r, which is the equation for angular frequency.

## 4. Can the angular frequency equation be used for all types of rotational motion?

Yes, the angular frequency equation can be applied to any type of rotational motion, as long as the object is moving around a fixed point.

## 5. How is angular frequency different from angular velocity?

Angular frequency is a measure of how quickly an object rotates or oscillates, while angular velocity is a vector quantity that describes the rate of change of angular displacement. In other words, angular frequency is a scalar quantity, while angular velocity is a vector quantity.

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