The force that holds it on the circle.

Step 1 of 5

What pulls the ball

In the last lesson you saw that the ball is accelerating towards the peg all the time, at $a = \dfrac{v^2}{r}$⁠. By Newton’s second law, $F = m a$⁠, so there has to be a net force on it towards the centre:

$F = \frac{m v^2}{r}$⁠

This force is called the centripetal force. To find out what supplies it, draw a free-body diagram: what touches the ball, and what pulls on it from a distance? The Earth pulls it down, the table pushes it up, and the string pulls it towards the peg. The orange arrow is that pull, and the number on it is its size: 1.33 N for a 0.2 kg ball moving at 2 m/s on a 0.6 m string.

Step 2 of 5

How strong

Swap the ball for a heavier one, of 0.5 kg. The Scene draws it the same size, but works out the pull from the new mass. It moves at 2 m/s on a string 0.8 m long, and the arrows are hidden so that you work it out yourself.

Step 3 of 5

A pull of two newtons

We are back to the 0.2 kg ball, with the arrows showing. Now it is slow, and the string pulls with only 0.33 N. The speed enters the formula squared and the radius sits underneath: work it out before you move anything, then check against the number on the arrow.

Step 4 of 5

A longer string

The ball is moving at 2 m/s on a short string, 0.5 m long, and the string pulls with 1.6 N. What will happen to the pull if the string is made longer, at the same speed? Make your prediction, and the Scene will then switch to a 1 m string.

Step 5 of 5

Who does the string’s job

The centripetal force is not a new kind of force but a job: the net force pointing at the centre. In every circular motion something different does it. Here it is the string. For the Moon it is the Earth’s gravity, in the next two lessons. And for a car going round a bend?

Speaking of cars: in a bend you feel something throwing you outward, and it is tempting to call it a centrifugal force. But there is no such force on your body. Your body simply carries straight on, by Newton’s first law, until the door or the seat belt pulls it inward, onto the circle. The same goes for the ball: the ball pulls the string outward, and the hand holding the string feels that, but it is a force on the string, not on the ball.

Try it: move Forces, then cut all the way, to Cut the string. The moment the string is cut the centripetal force is gone, and the ball goes straight on, just like your body in the car.

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