Question

if you have a wheel 900mm dia and one from 880 how much faster does the smaller wheel have to turn to cover the same distance

Answer 1

Okay, distance a wheel travels in one revolution is its circumference. What is the equation for circumference?

Answer 2

C = 2 * pi * r
OR
C = pi * d,
where r = radius, pi = 3.14, and d = diameter

Answer 3

So, circumference of first wheel is 900*pi, and the rate it will travel at is 900*pi mm/unit (of time). Lets assume it travels at 900*pi mm/second.

Answer 4

Formula for distance is Distance = Rate * Time, OR D = R * T

Answer 5

So, in one second, the first wheel travels a distance of D = (900 * pi mm / sec) * (1sec) = 900 * pi mm.

Answer 6

We want the second wheel to cover the SAME distance in the SAME amount of time, so 900 * pi mm = R * 1 sec, which means the second wheel must have the same rate of 900 * pi mm/sec.

Answer 7

However, the second wheel must spin faster to achieve this rate!

Answer 8

The circumference of the second wheel is 880 mm * pi, which is the distance it will travel in one revolution. However, we want the second wheel to travel 900 * pi mm in a single revolution (or second), and in order to do this it must spin faster than the larger wheel. How much faster must it spin? (880 mm * pi) * X = 900 * pi mm / second. Solve for X and get 900/880, which equals 90/88, or 45/44 times faster.

Answer 9

The answer 45/44 can be written as an improper fraction, a proper fraction (1+1/44), and as a decimal 1.0227.

Answer 10

Really you only need to look at the last two posts. The rest just shows my long though process...

Answer 11

Please, ask me a question if this does not make sense.

Answer 12

no that makes sense to me ty.can i ask another ?

Answer 13

you just did. but, yes, i grant that you may ask a third question.

Answer 14

i will sent it next week with all the measurement.and a drawing if you like.the problem is i have a machine that is driven by 4 rollers as said there is a difference in size of the rollers, but also one of the big roller is smaller and i need to get it to revolve at at the same speed . thank you for helping

Answer 15

Yes, send it in next week with a drawing.