Freddie is at chess practice waiting on his opponent's next move. He 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 3:35 to 3:55? (Hint: Find the number of degrees per minute first.)
Part 2: How far does the tip of the minute hand travel during that time?

Question

Freddie is at chess practice waiting on his opponent's next move. He 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 3:35 to 3:55? (Hint: Find the number of degrees per minute first.)
Part 2: How far does the tip of the minute hand travel during that time?

Vocaloid · Answer

In one hour, the minute hand will travel 60 minutes. There are 360 degrees on a full circle. So per minute, we get (360/60) = 6 degrees per minute. From 3:35 to 3:55 that’s 20 minutes so 6 degrees * 20 minutes gives 120 degrees. Convert to radians by multiplying by (pi/180)

Vocaloid · Answer

For the distance in part 2, arc length = radius * angle in radians. Simply plug in the angle from part 1 in radians and the radius given in the problem.