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circumference = 2*pi*radius or diameter*pi
75
A wheel 3.4 meters in radius rotated through 30 radians will move 3.4 metres x 30 = 102 metres along the ground. But hold the phone. You asked how far a point on the circumference would travel if the wheel is rotated through 30 radians. If you plot its path of travel, that point on the circumference makes a quirky trip. Know what a cycloid is? That's where we're going. Ready? Buckle up. A cycloid is the curve defined by a fixed point on a wheel as it rolls. To be more precise, it's the locus of a point fixed on the rim of a circle rolling along a straight line. Use the link to the Wikipedia post to see an aplet of exactly what you asked. All the math is there, too. But make sure you have a bit of knowledge of the calculus.
Since it'll be rolling around the outside of the circle, the distance traveled will be in some multiple of the circumference. So, dividing the distance by the circumference will give the answer. C = πD = 6π revolutions = distance / circumference = 108π / 6π = 18 revolutions
A wheel is in the shape of a circle. The formula for the circumference of a circle is 2πr where r is the radius. But, the diameter of a circle is twice the radius so this equation can be written, Circumference = πd where d is the diameter. The Circumference is therefore π times as big as the diameter, π = 3.142 or 22/7 approx.