The angle between the clock hands
Set a clock to any time and work out the angle between its hands. Find the times when the hands make a right angle or a straight line, and see why the hour hand is never exactly on the number at half past.
Core concept
The minute hand turns 6° a minute and the hour hand 30° an hour plus 0.5° a minute, so the angle between them is |30h − 5.5m|, or 360° minus that if it is bigger than 180°
Topic: Maths in everyday life
A clock face is a circle of 360°, split by the 12 numbers into 12 equal parts of 30°. The minute hand goes all the way round in 60 minutes, so it turns 360 ÷ 60 = 6° every minute. The hour hand goes round once in 12 hours, so it turns 30° every hour, and it does not jump: it creeps forward 30 ÷ 60 = 0.5° every minute. Measured from 12, the hour hand is at 30h + 0.5m degrees and the minute hand at 6m degrees. The angle: The amount of turn between two lines that meet, measured in degrees (°). All key words between them is the difference, |30h − 5.5m|. There are always two angles between the hands, which add up to 360°; we usually want the smaller one.
What you will learn
- Work out how far each clock hand turns in a minute.
- Find the angle between the hands at any time.
- Name the angle as acute, right, obtuse or straight.
Before you start
- Know that a full turn is 360° and how to read a clock.
Materials
- A real clock or a paper clock with moving hands
Equipment
- A protractor
Procedure
- Record 3:30.
- Set the clock to 3:00 and record.
- Set it to 6:00 and record, then 9:00 and record.