Using radians to discover the lengths of geometric shapes (circles)

[Elihu5991]

Homework Statement

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Homework Equations

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The Attempt at a Solution

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This is my brothers maths homework. He normally doesn't use online methods to request help and this is his first time.

 

[jedishrfu]

Welcome to the Physics Forums.

So what's your question? We can't just do your homework for you.

 

[Elihu5991]

radians question

sorry about that, if forgot to state my problem.
i was wondering how to get the inner angles of the big and small wheel.
i've been able to get 'alpha' and 'phi' but i don't know how to get 'theta' on the big wheel.
if you can explain how i can get that then i'll be able to get the smaller wheel angle and then find the major arc lengths of both wheels.

 

[jedishrfu]

so first notice the part of band between the two wheels touches tangentially to both that means the radii that touch it both have measure pi/2 and are in fact parallel to one another.

if you extend the 6 cm radius a bit to 16 cm then you have a rectangle containing a right triangle with sides X cm, 10 cm and hypotenuse 26 cm. You can then compute its angles and go from there.

I didn't 21.49 cm for X. I got a nice integer number.

 

[Elihu5991]

Thanks I got the answer of 125cm which I checked in the back of the answers and is right. The way you explained it helped.