Radius/Revolution question

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)

Re: Radius/Revolution question

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Originally Posted by

**mathkid182** 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)

I am not sure which question you are referring to. This question is not tricky. (Smile) Such questions should probably go to Pre-University Algebra.

Find how much the bike travels in 1 minute and divide it by the circumference of the wheel (tyre).

Re: Radius/Revolution question

Quote:

Originally Posted by

**mathkid182** 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)

If the radius of the tyre is 30.5 cm then its circuference is [tex]2\pi(30.5)= 191.6 cm= 0.1916 meters. At 25 km/hr, you would go 25000 m in an hour and so 25000/60= 416.7 meters per minute.

Re: Radius/Revolution question

HI thanks for your help:

Just to confirm:

so i take the 416.7meters/0.1916meters

=2174.84

Therefore the bike will do 2174.85 revolutions per minute?

is this correct

Re: Radius/Revolution question

The number 0.1916 meters from post #3 is incorrect.

Re: Radius/Revolution question

i just recalculated and its 2/pi (30.5) = 19.42169 cm

then to meters its 0.1942169?

so i take the 416.7meters/0.1942meters

=2145.72

?? any luck this time :)

Re: Radius/Revolution question

Quote:

Originally Posted by

**mathkid182** i just recalculated and its 2/pi (30.5) = 19.42169 cm

You should do a sanity check: how can the circumference be less than the radius? The formula for the length of the circumference is $\displaystyle 2\pi r$, not $\displaystyle (2/\pi)r$. 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 $\displaystyle \pi$ and does *not* mean division by $\displaystyle \pi$ (for one, that would require a forward slash).

Re: Radius/Revolution question

Oh i see i though that was a weird equation but thought possibly i have just not seen it before.

thanks for your help i finally got the answer of =

416.67/1.92 = 2170.02 (2dp) revo per minutes?

this is correct i 99% sure

Re: Radius/Revolution question

Quote:

Originally Posted by

**mathkid182** 416.67/1.92 = 2170.02 (2dp) revo per minutes?

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.

Re: Radius/Revolution question

thats great thats for the tip.

so do you think this is correct:

416.6666667/1.916371519

= 217.42? what answer did you get?

Re: Radius/Revolution question

Quote:

Originally Posted by

**mathkid182** so do you think this is correct:

416.6666667/1.916371519

= 217.42?

Yes, this is correct.

Re: Radius/Revolution question

god your a legend! thanks for being so patient and insanely helpful-Im not sure how to "thank" someone on here but if you wanted to let me know i would be happy to do so asap

Re: Radius/Revolution question

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Originally Posted by

**mathkid182** Im not sure how to "thank" someone on here but if you wanted to let me know i would be happy to do so asap

If you hover your mouse in the lower-right corner of a post, just above the multiquote button with a quotation mark and a plus, the link "Thanks" appears. (Blush)