How is this length R(Theta)? I don't see it...

1. Dec 16, 2015

MienTommy

That's the image. I can't see how the edge of that middle triangle's length is Rθ at all. I've tried using similar triangles and law of cosines to figure that out but I'm missing lengths. I thought Rθ was the arc length of a piece of a circle? So if Rθ is a length of a piece of a circle, how is Rθ equal to that edge of the triangle?

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2. Dec 16, 2015

insightful

It looks to me like this is a "given." You might be seeing right angles where none exist.

3. Dec 18, 2015

CWatters

Took me a few moments to figure it out. The answer is that the block started off horizontal then rocks to the left without slipping on the cylinder ... so the red and green lines in this version must be the same length...

4. Dec 18, 2015

insightful

But your green line doesn't equal R*theta as labeled, right?

5. Dec 18, 2015

insightful

I.e., the extension of the radius R to the mid-point line of the bar is not parallel to the line from the top of the cylinder to the big black dot.

6. Dec 19, 2015

CWatters

Why not?

7. Dec 19, 2015