What it shows
The minute hand turns 6 degrees per minute and the hour hand half a degree per minute, so the angle between them at any time is the difference of 30 times the hours and 5.5 times the minutes. At 3:00 the angle is 90 degrees and at 3:30 it is 75 degrees, not 90, because the hour hand has moved on.
The science
In 60 minutes the minute hand makes one full turn of 360 degrees, which is 6 degrees per minute. In the same hour the hour hand moves from one number to the next, 30 degrees, which is half a degree per minute. At H hours and M minutes the minute hand is at 6M degrees from 12 and the hour hand at 30H + 0.5M degrees. The angle between them is the difference, 30H minus 5.5M, taken as a positive number and subtracted from 360 if it is over 180. The hands overlap 11 times in 12 hours, roughly every 65 and a half minutes.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A card clock face with a degree scale round the edge
- Two card hands on a split pin
- A protractor
- A table of times to test
- Optional: two toothed wheels from a broken toy with a 12 to 1 ratio
Safety
For this project: An adult must push the split pin through the card.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Draw the clock face with the twelve numbers and a fine scale of 0 to 360 degrees round the rim, 30 degrees between numbers.
Cut a long minute hand and a short hour hand and fix both at the centre with the split pin so they turn independently.
Set the hands to 3:00 and measure with the protractor: 90 degrees.
Set 3:30 by moving the minute hand to 6 and the hour hand half way between 3 and 4. Measure: 75 degrees. Compare with 30 times 3 minus 5.5 times 30, which is 90 minus 165, giving minus 75, so the angle is 75.
Test 6:00 (180 degrees), 9:45 (22.5 degrees) and 12:20 (110 degrees) and record each measured and calculated angle.
Find the first time after 12:00 when the hands overlap: 12:05 and 27 seconds, when 6M = 0.5M, which gives M = 0 and then the next solution at M = 360/5.5 = 65.45 minutes past 12, that is about 1:05:27.
Make a table of all eleven overlap times in 12 hours and mount it beside the clock.
What you should see
The measured angles match the formula at every tested time, 90 at 3:00, 75 at 3:30, 180 at 6:00, and the hands overlap at the predicted times.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1How many degrees does the minute hand turn in one minute?
6 degrees.
2What is the angle between the hands at 3:30?
75 degrees, because the hour hand has moved 15 degrees past the 3.
3How many times do the hands overlap in 12 hours?
Eleven times.
4At what time between 6 and 7 are the hands opposite each other?
At 6:00 exactly, since 180 degrees apart is the starting angle at 6:00.
Take it further
Add a second hand and work out how often all three hands line up: only at 12:00.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
Science projects
Maths Working Models and Activities
Make maths visible: models for number, geometry, algebra and data
Science projects
Science Projects for Class 6 to 8
Working models matched to middle-school science topics