Problem from a quiz...No idea how to start!

[nanahime]

A one-speed bicycle has two sprockets of radii two and five inches respectively. If somebody is riding the bike and the smaller sprocket rotates a complete turn, find the angle in radians rotated by the larger sprocket.

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I know the correct answer, but I couldn't figure out where to even start figuring out this question. I don't understand how to apply the concepts i've learned so far to answer this (radians, degrees to radian conversions, length of an arc, etc.) I'm really sorry I don't have work, but as I said, this question stumped me completely! Please help!

Thank you in advance.

 

[Deleted member 4993]

A one-speed bicycle has two sprockets of radii two and five inches respectively. If somebody is riding the bike and the smaller sprocket rotates a complete turn, find the angle in radians rotated by the larger sprocket.

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I know the correct answer, but I couldn't figure out where to even start figuring out this question. I don't understand how to apply the concepts i've learned so far to answer this (radians, degrees to radian conversions, length of an arc, etc.) I'm really sorry I don't have work, but as I said, this question stumped me completely! Please help!

Thank you in advance.

Do you know:

How does the bi-cycle sprockets work with the chain drive?

The angular speed of each sprocket is inversely proportional to the radius of corresponding sprocket.

Do you understand what does the above statement mean?

 

[HallsofIvy]

The chain running from one sprocket to the next does not stretch or shrink so the distance the chain moves over both sprockets must be the same. now, if a sprocket of radius two inches goes through a complete rotation, the chain covered its entire circumference (which is, remember '\(\displaystyle \pi\) times the diameter' or \(\displaystyle 4\pi\) since the diameter is 4 inches) has run off the sprocket and that same distance must have run off the sprocket of radius 5 inches (so diameter 10 inches). What is the circumference of a circle with diameter 10 inches? \(\displaystyle 4\pi\) is what fraction of that? What fraction of \(\displaystyle 2\pi\) radians, an entire circle, is that?

(You don't need to deal with 'degrees' at all here and so don't need to convert from degrees to radians.)

 

[nanahime]

Ah ok. I understand now! Thank you for the clarification (and sorry for the late thanks!)!! It really helped! I can see where it's going now haha. It was simpler than I expected...sigh.