# Tangental Velocity and Bicycle Wheel Radii

1. Apr 8, 2015

### sciencegem

Hi guys,

This is the silliest thing. I actually solved problem and got the correct answer, but now I'm not sure that my logic was sound--or even what my logic really was!

1. The problem statement, all variables and given/known data

While riding a multispeed bicycle, the rider can select the radius of the rear sprocket that is fixed to the rear axle. The front sprocket of a bicycle has radius A cm. If the angular speed of the front sprocket is B rev/s , what is the radius of the rear sprocket for which the tangential speed of a point on the rim of the rear wheel will be C m/s ? The rear wheel has radius D m .

2. Relevant equations

Honestly, w=v/r is the only one that comes to mind.

3. The attempt at a solution

I don't want to be overly specific about the my equations because this is a Mastering Physics question and I don't want to spoil it, but ultimately I solved it using the above equation and the idea that the tangental speed of the front sprocket and the tangental speed of the back sprocket are equal. Problem is silly me, I'm not sure why I assumed that and I've having trouble visualizing whether it's true. I know (well, think I know) that the centre of mass of both wheels must be moving with the same translational velocity (if that's the right term), so I think that's the idea I was getting at when I solved it, but I'm not really sure how that concept relates to tangental speed. I guess the meat of it is, I'm flummoxed by how the different kinds of speeds of the respective wheels relate to themselves and each other...I'm not sure if I'm making any sense, if anyone wants me to clarify or provide more details please let me know. Thanks for reading this!

D.

2. Apr 8, 2015

### Dick

The tangential speeds are the same because that's the rate at which the chain is passing over each sprocket. If the rates were different then the chain would be getting stretched or bunched up someplace. Agree?

3. Apr 8, 2015

### sciencegem

The chain!! I totally forgot there even was a chain!! Thank you very much. Makes sense now.