Question

Celia is staring at the clock waiting for school to end so that she can go to track practice. She notices that the 4-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:25 to 1:50? (Hint: Find the number of degrees per minute first.) Part 2: How far does the tip of the minute hand travel during that time? You must show all of your work.

Answer 1

Part 1: There are 2π radians in a circle, so that is the angle the minute hand travels in 60 minutes. In 25 minutes (from 1:25 to 1:50), the minute hand travels
(25/60)*2π = (5/6)π radians

Part 2:The distance the tip of the minute hand travels is this angle multiplied by the raidus of the hand, 4 in.
(4 in)(5/6)π = 10π/3 in ≈ 10.47 in