Clock angle problem

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/clock-angle-problem

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the problem domain?Geometry and Arithmetic, applied to timekeeping mechanisms
2. What is the minute hand angular velocity?6 degrees per minute
3. How do you find the angle between the hour and minute hands?First, find where each hand is: the minute hand is M times 6°, the hour hand is (H mod 12 + M/60) times 30°. Then subtract the two angles. If the result is more than 180°, subtract it from 360° to get the smaller angle.
4. Why does the hour hand move slower than the minute hand?Because the minute hand goes all the way around the clock in 60 minutes, it moves 6 degrees every minute. The hour hand only goes around in 12 hours, so it moves just 0.5 degrees each minute. That’s why the hour hand moves slower.

Angular Velocity: The rate at which an object rotates or revolves, measured in degrees or radians per unit of time.
Horology: The study and measurement of time, including the art and science of making clocks and watches.
Phase Difference: The difference in the timing or position of two periodic phenomena, often expressed as an angle.