Question

Before coming to lab, consider the following problem: Suppose a solid wheel (cylinder) rolls along a horizontal sandy surface without slipping as it rolls it traces out a path in the sand. We wish to measure the length of the path in the sand, and all we know is the radius of the cylindrical wheel, and the angle through which the wheel rolls. The wheel has a measured radius of 45 + 4 cm is seen to rotate through an angle of 25 +2 a. Draw a detailed sketch (labelled) to illustrate the physical situation described. Include a symbolic label for all measurable quantities along with the numerical values

Answer 1

For full one reduction, the distance covered is equal to perimeter of circle, while it moves for an angle theta, then the distance covered will be perimeter of circle multiplied by ratio theta/360 degree [because for one revolution it covers 360 degree]. S = 2 pi r times theta/360 = 2 pi r(45) times 25/360 = 19.625 cm (c) uncertainty of length of path traced % uncertainty of r = 4/45 times 100 = 8.89 % % uncertainty of theta = 2/25 times 100 = 8% % uncertainty of s = % uncertainty of r + % uncertainty of theta = 8.89% + 8% = 16.89% uncertainty in S = S times % uncertainty in s = s times 16.89% = 19.625 times 16.89/100 = 3.31 cm therefore S = 19.625 plusminus 3.31 cm