I’m riding my push bike at 25 km/h and my tyre radius is 30.5 cm.
How many revolutions per min are my wheels travelling at?
Can someone please help with this tricky question, sorry if this is in the wrong category(im new to this forum and wasn't sure which one to put the question in)
You should do a sanity check: how can the circumference be less than the radius? The formula for the length of the circumference is , not . HallsofIvy in post #3 got the correct number of centimeters but converted them to meters as if they were millimeters instead. Therefore, the result in meters from post #3 is 10 times less than what it should be. The notation \pi, which may have confused you, is the TeX command for producing and does not mean division by (for one, that would require a forward slash).
OK, as far as sanity check goes, this is more than 30 revolutions per second: 2170.02 > 1800 and 1800 / 60 = 180 / 6 = 30. I remember watching the shadow from the reflector on my bicycle wheel when I was going about that fast, and it would show the wheel was turning several times a second (maybe four or five), but definitely not 30; otherwise, I would not be able to see it clearly. Recall that movies show about 25 frames per second, and the result is an illusion of smooth motion. So 30 times per second seems about 10 times too much. And indeed, how can dividing 416.67 by something greater than 1 (almost 2) produce more than the original number? The result should be about 2 times less than 416.
Another remark is that to get a final answer with 2 dp, it is not sufficient to round all intermediate results (the number of meters traveled in a minute and the circumference) to 2 dp. You should do all calculations with maximum precision and remove all but 2 dp only from the final answer. It is possible to have less than maximum precision for intermediate results, but to know which precision is sufficient requires a finer analysis.