I’m sure anyone who has ever used a top-loading washing machine will have seen this phenomenon occasionally: you lift the lid after the machine has been spinning and you find one item of clothing (such as your favourite most expensive shirt) stretched across the diameter. It happened to me last night. What’s happened is, right at the beginning of the cycle, the shirt has been lying most probably across the diameter of the machine (OK, so there’s a spindle in the middle so it can be exactly across the diameter) and then as the machine has begun to spin instead of being squashed against the drum at single point it’s been squashed simultaneously at two opposite points. It’s probably not doing the clothing much good when this happens.
It’s interesting though to ask the question – if we put a piece of clothing at the centre – and, as I’ve already said, you can’t, because there’s the central spindle in the way – but if you did, what force would the clothing experience here? We’ll use a rotating frame of reference, what you’d see and measure if you were in the machine with the clothing, so centrifugal force is the dominating factor here. The centripetal force is directly proportional to radius times rotation rate squared, so the larger the radius, the greater the force. This means a bit of clothing right at the centre experiences no centrifugal force at all – so it will stay where it is. Of course, if it is slightly off centre, it will experience a force towards the outside of the drum, and off it moves. It’s a bit like balancing a ball right on top of a hill – in theory you can balance it, but in practice, any small displacement away from the top and it will roll down. It’s an unstable equilibrium point.
Now, with the shirt that’s pulled both ways, it’s a bit like having two balls joined together by string at the top of the hill. One ball rolls one way, one the other. We end up with the string stretched out, and the two under tension. So although the centrifugal force at the centre of the machine is low, the shirt is still under tension at that point (and so could be damaged), as it gets pulled two ways at once.
We can contrast this to what happens with gravity as we head towards the centre of the earth, Jules Verne style. This is a fun question to ask students to see if they’ve grasped the idea of Gauss’ Law. (If you don’t know what that is, don’t worry). What is the strength of the field at the centre of the earth? By symmetry, it’s going to be zero. So what would you feel if you were there? (Apart from very warm?). Is it like the washing machine – would gravity pull you all ways at once leaving each arm and leg stretched outwards beyond your control?
In this case, no, because the physical system is different. The gravitational force will always be towards the centre of the earth (not away from the centre as in the washing machine), and, as you go downwards through the earth, it gets less. If the centre of your body were at the exact centre of the earth, your limbs would feel almost no force at all – it would be like weightlessness. Throw your shirt off here, and it wouldn’t get pulled in all directions, in fact, the opposite, it would (very slowly) get squashed towards the centre, as the bits further out experience would experience a tiny bit of inwards gravity. Different system, different result.
Unfortunately, unlike the washing machine example, doing this experiment probably is confined to the realm of fiction.