SOLUTION: two friction wheels are of diameter 20mm and 200mm respectively. they connect at P and rotate without slipping. calculate the number of turns made by the small wheel when the large

Question 1133030: two friction wheels are of diameter 20mm and 200mm respectively. they connect at P and rotate without slipping. calculate the number of turns made by the small wheel when the large wheel rotate through 60°
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula for circumfernce of a circle is 2 * pi * r or pi * d.

the small wheel has a diameter of 20 millimeters.
the large wheel has a diameter of 200 millimeters.

the circumference of the small wheel is equal to 20 * pi millimeters.
the circumference of the large wheel is equal to 200 * pi millimeters.

if the large wheel is rotating the small wheel, then the large wheel will make the small wheel turn 10 times for one turn of the large wheel.

one turn is equal to 360 degrees.

60 degrees is equal to 60 / 360 = 1/6 times one turn.

when the large wheel is rotating 1/6 of a turn, then the small wheel is rotating 10 * 1/6 of a turn which is equal to 10 / 6 turns

10 / 6 turns is equivalent to 5 / 3 turns.

1/6 turns of the large wheel therefore causes 1 and 2/3 turns of the small wheel.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
"respectively" is superfluous.
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The author thinks it makes him/her look smart, but it's just the opposite.
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It's similar to "What's your present location?" rather than, "Where are you?"
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The ratio is 10:1
10*60 = 600 degrees
600/360 = 5/3 turns
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