What it shows
A body moving in a circle needs an inward force of m ω² r. Whirling a bung on a string with a hanging weight pulling it inwards shows that this force equals the weight.
The science
A mass m moving in a circle of radius r at angular speed ω needs a net inward (centripetal) force F = m ω² r = m (2π / T)² r = 4π² m r / T², where T is the period. In the experiment the thread runs through the tube and carries a hanging weight M g that provides this force. If the formula is right, the measured 4π² m r / T² will equal M g. The bung does not fly outwards; the thread merely pulls it round, and it would move along a straight line if the thread broke.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A rubber bung or a ball of about 20 g (weigh it)
- About 1.5 m of strong thread
- A smooth plastic pen barrel or a glass tube (with the ends smoothed) to hold in the hand
- A set of washers or small weights as the hanging load
- A paper clip or marker tape on the string to fix the radius
- A phone stopwatch
- A ruler and a calculator
Safety
For this project: Whirl the bung in an open area, away from people and windows; an adult must supervise. Wear safety glasses if possible.
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.
Tie the bung to one end of the thread, pass the thread through the tube and tie the washers to the other end.
Put a marker tape on the thread 60 cm from the bung so you can keep the radius constant by letting the tape sit just under the tube.
Whirl the bung round above your head at a steady speed so that the marker just stays still below the tube.
Time 20 revolutions with the stopwatch and calculate the period T; repeat three times and average.
Calculate the centripetal force 4π² m r / T² and compare with the weight M g of the washers.
Change the hanging weight to a different number of washers and repeat the measurement.
Plot M g against 1 / T² for different loads and show that it is a straight line with slope 4π² m r.
What you should see
The calculated force agrees with the hanging weight to within about 10 percent for each load, and the graph of M g against 1 / T² is a straight line through the origin.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What provides the centripetal force in this experiment?
The tension in the thread, which equals the hanging weight.
2What happens to the period if the weight is increased at fixed radius?
The period falls, because a larger force needs a faster rotation.
3Which way does the bung move if the thread breaks?
In a straight line along the tangent to the circle.
4Name an everyday example of centripetal force.
The friction of tyres on a curving road, or the Moon’s gravitational pull on its orbit.
Take it further
Keep the weight fixed and plot T² against r to show that T² is proportional to r.
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.
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