A bicycle wheel has a circumfrence of 1m and it rotates 1 revolution per second why is the speed 1m/s?

princess_abecca07 - 2009-02-26 13:47:39 - Physics

I know this sounds so obvious but I have to explain why this is. So a good explanation would be amazing.

Best Answer:

You could tackle it on the basis of the equations of motion. C ( circumference ) = 2 . π . R so R (the radius) = C / 2 .π Angular speed (w) = 2 . π (the distance in radians round 1 turn) ÷ T ( the time taken for 1 turn) T = 1/F ( where F is the number of turns in 1 second, the frequency) so w = 2 . π . F V ( tangential speed ) = w . R ( well known , standard relationship) V = (2 . π . F) . ( C / 2 . π ) the 2 . π's cancel and V = F . C . Since F = 1 and C = 1 then V must =1 Or, you could try it in words. The point where the rim meets the road moves one meter when the wheel rotates 1 full turn ( assuming there is no slipping). One full turn takes 1 second. Therefore the point of contact with the road has moved 1 meter in 1 second. That is a speed of 1 m/s. It does seem too obvious to bother with BUT...as an exercise in practicing explaining it is probably worthwhile to have a go at something where you are sure you know what is correct. Now you should really try another, for yourself. Something like" Why do flags flutter in the wind?" .....go on....amaze yourself.

Answer:

The circumference is 1 m and in 1 sec it travels 1 m. Therefore its speed is 1 m/s

As the wheel turns, visualize a dot on the outside of the wheel. That dot travels 1 meter every time the wheel turns, and the path it traces on the floor is also 1 meter. .

You could tackle it on the basis of the equations of motion. C ( circumference ) = 2 . π . R so R (the radius) = C / 2 .π Angular speed (w) = 2 . π (the distance in radians round 1 turn) ÷ T ( the time taken for 1 turn) T = 1/F ( where F is the number of turns in 1 second, the frequency) so w = 2 . π . F V ( tangential speed ) = w . R ( well known , standard relationship) V = (2 . π . F) . ( C / 2 . π ) the 2 . π's cancel and V = F . C . Since F = 1 and C = 1 then V must =1 Or, you could try it in words. The point where the rim meets the road moves one meter when the wheel rotates 1 full turn ( assuming there is no slipping). One full turn takes 1 second. Therefore the point of contact with the road has moved 1 meter in 1 second. That is a speed of 1 m/s. It does seem too obvious to bother with BUT...as an exercise in practicing explaining it is probably worthwhile to have a go at something where you are sure you know what is correct. Now you should really try another, for yourself. Something like" Why do flags flutter in the wind?" .....go on....amaze yourself.