Mathematics
Mathematics
Problem
An ant walks 0.25 m along the rim of two different circular tracks. Track X has radius 0.50 m and track Y has radius 0.75 m. Answer the following: a. (i) Calculate the angular displacement of the ant on track X, in radians. b. (ii) Calculate the angular displacement of the ant on track Y, in radians. c. (iii) Which track gives the larger angular displacement?Intuitive explanation
The key is understanding that arc length connects the distance walked to the angle swept out, independent of the circle's size. Since the ant walks the same distance on both tracks, you'll use to find how many radians it covers on each circle—then convert to degrees or compare the angles directly. The smaller circle will force the ant to turn through a larger angle for the same path length.
Intuitive explanation
The key is understanding that arc length connects the distance walked to the angle swept out, independent of the circle's size. Since the ant walks the same distance on both tracks, you'll use to find how many radians it covers on each circle—then convert to degrees or compare the angles directly. The smaller circle will force the ant to turn through a larger angle for the same path length.