Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 inches, and the larger gear has a radius of 7 inches. two circles touching at one point. Larger circle has radius of 7 inches. Smaller circle has radius of 4 inches. Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation? Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?
Draw a diagram to illustrate the problem as shown below.
When the smaller gear rotates through a revolution, it sweeps an arc length of 2π(4) = 8π inches.
Part 1 The same arc length is swept by the larger gear. The central angle of the larger gear, x, is 7x = 8π x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°
Answer: 205.7° (nearest tenth)
Part 2 When the larger gear makes one rotation, it sweeps an arc length of 2π(7) = 14π inches. If the central angle for the smaller gear is y radians, then 4y = 14π y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions
