penny farthing had a large front wheel radius 65cm and a small back wheel radius 25 cm. how many times did the back wheel turn for each turn of the front wheel?
65/25 = 13/5 = 2.6/1
To find out how many times the back wheel turns for each turn of the front wheel, we need to calculate the ratio of their circumferences.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
For the front wheel:
C1 = 2π(65 cm) = 130π cm
For the back wheel:
C2 = 2π(25 cm) = 50π cm
Now, to determine how many times the back wheel turns for each turn of the front wheel, we divide the circumference of the front wheel by the circumference of the back wheel:
Number of back wheel turns = C1 / C2 = (130π cm) / (50π cm) = 13/5 or 2.6
Therefore, for each turn of the front wheel, the back wheel will turn approximately 2.6 times.
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