Two gears are adjusted so that the smaller gear with the radius of 2.5 cm drives the larger one with radius of 4.8 cm. If the smaller gear rotates through an angle of 5Pi/4 radians, through what angle measurement in degrees will the larger gear rotate?

Do I need to convert the radians measurement to degrees so I can get the angle measurement?

Question

Two gears are adjusted so that the smaller gear with the radius of 2.5 cm drives the larger one with radius of 4.8 cm. If the  smaller gear rotates through an angle of 5Pi/4 radians, through what angle measurement in degrees will the larger gear rotate?

Do I need to convert the radians measurement to degrees so I can get the angle measurement?

anonymous · Answer

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Do it in whatever angle measurement system you find easiest- I'll do it in degrees and convert to radians.

anonymous · Answer

So: when the small one turns 180+45=225 degrees, how much does the chain move along?
Well, that's just the arc length of the 2.5cm circle with angle 225 degrees. 

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What is it in this case? The arc length of a full circle is $$2 \pi r=5 \pi (cm)$$