If a wheel has a radius of 3.4 meters how far does a point on the circumference travel if it's rotated through 30 radians?

Answer 1

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.