# Simple math question for physic problem

1. Jan 3, 2013

### Dragster

How do they get from the Rsinθ the value I have found the one I search: Rθ (extra string length)

I know that sinθ = θ when θ is small but there Rsinθ is the extra height the mass gain when we push it from initial position to a θ angle with vertical, I don't see how it could be the extra string length.

Thank you

2. Jan 3, 2013

### TSny

Hi, Dragster. It would be very helpful if you could describe the physical setup. I think I see what some of the expressions in the figure represent. But I don't understand at all what the small circle with diameter $R\phi$ represents. Is that some physical object?

3. Jan 3, 2013

### Curious3141

Like TSny, I don't get the exact physical setup. But I can tell you that the arc length (length along the curve of the circumference) subtended by an angle $\phi$ along a circle of radius $R$ is $R\phi$. Does that help in relating the "extra string length" to that expression?

4. Jan 3, 2013

### Dragster

I added the black circle with the ''?" on the top right.

Do you mind if I can get the rigorous explanation why the arc is Rθ? Thank you for the fast answers

Oh yea and for the problem, the string is attached on a cylinder. At theta = 0 with the vertical, the length is l0 and the asked result is the potential energy expression if the mass is pushed with an angle theta. I was only blocking on the part where I needed to know what was the extra string length.

5. Jan 3, 2013

### cepheid

Staff Emeritus
It's from the definition of how angles are measured:

6. Jan 3, 2013

### haruspex

When the string is vertical, the 'extra' string is wrapped against the cylinder and subtends angle phi at the centre. Clearly the angle subtended by an arc of a circle at its centre is proportional to the length of the arc, and the radian is defined in such a way that the length is simply radius * angle.

7. Jan 4, 2013

### Dragster

Oh well I am really stupid after all.
Thank you cepheid et harusphex :)
First university session makes me feel like a complete ignorant idiot.