# Pendulum speed given length and angle

1. May 11, 2012

### Kirasagi

1. The problem statement, all variables and given/known data
A circular pendulum of length 1.2 m goes around at an angle of 25 degrees to the vertical.

Predict the speed of the mass at the end of the string. Use g = 9.8 m/s2.

2. Relevant equations

1/2mv^2 = mgh
h = L - Lcosθ

3. The attempt at a solution

I used the above formula doing:
1/2mv^2 = mgh
v = √2g(L - Lcosθ)
Plug n' chug:
v = √2*9.8*(1.2 - 1.2cosθ)
v = 1.448 m/s

I've seen variations of this problem before, but I'm not really sure what I'm doing wrong.

2. May 11, 2012

### Staff: Mentor

What's the difference between a "circular pendulum" and a regular "pendulum"? The difference will make all the difference

3. May 11, 2012

### Infinitum

How did you apply conservation of energy? There was an external force that made the pendulum start its circular revolutions from its initial state.

As I see the problem, the pendulum is revolving about the vertical axis. Drawing a diagram will help

4. May 11, 2012

### Kirasagi

To be honest I'm not really sure, I don't remember paying attention to pendulums too much. I'm assuming it also rotates/spins as it moves? Not sure what can I tie with that.

Am I doing this problem the right way? But having that idea, maybe I should add rotational kinetic energy?:

1/2mv^2 + 1/2IW^2 = mgh

W = v/r

Am I going on the right track?

Initially, another idea I had was to use centripetal force: mv^2/r, and using force diagrams.

5. May 11, 2012

### Staff: Mentor

6. May 11, 2012

### Infinitum

The pendulum only revolves about the vertical axis.

Try this out

Edit : somehow gneill is way faster!

7. May 11, 2012

### Kirasagi

I see, this was the way I saw it at first but I thought it's more complicated.

So:

Fx = Tsinθ = mv^2/r
Fy = Tcosθ = mg

T = mg/cosθ; plugging that in for Fx..
mv^2/r = mgtanθ, so..

v = √rgtanθ, where r = Length ? Not sure if I derived everything correctly.

Assuming I did everything right, final answer came to be v = 2.3417 m/s.. though I tried that a long time ago but got it wrong.

8. May 11, 2012

### Infinitum

r is the radius of the horizontal circle where the pendulum is revolving. So, what component of the length will give you that?

9. May 11, 2012

### Kirasagi

Would that be Lsinθ?

so

v = √g*Lsinθ*tanθ

v = 1.52234 m/s

10. May 11, 2012

### Infinitum

Yep!

11. May 11, 2012

### Kirasagi

Got it right on my last try. Thanks!