## Second Week

Â This has been a busy week ðŸ˜›

For a start I made Dino cakes:

For seconds, lectures are already interesting ðŸ˜› I finally found out what people are going on about when they say â€˜centrifugal force isnâ€™t realâ€™ and how Newtonâ€™s laws can apply when we are not in an inertial reference frame. That has bugged me for yearsâ€”being on a spinning planet flying across the solar system, how can we use F=ma if we are already always accelerating?

It turns out when you look down at the Earth from a stableâ€”letâ€™s say relative to the Sun, vantage point, you see things on the surface of Earth moving as you would from Newtonâ€™s laws. However, if translate that co-ordinate system to being on the Earth as it is rotating, you actually see things acting as if they have two extra forces on themâ€”the Coriolis force and Centrifugal force. These are â€˜fictitious forcesâ€™ which only seem to exist because of your choice of spinning co-ordinate system, and donâ€™t have a physical thing causing them to happen. They are always multiplied by the mass of the object, so that the overall acceleration is independent of mass.

Â Hmm, a thing that looks like a force and is proportional to the mass of the object. Does that remind you of anything?

Yep. You are right. Gravity turns out to be one of these fictitious forces in general relativity.

Back to centripetal and centrifugal forces.

The centripetal force is the real, obvious common sense one that pulls spinning things towards the centre of their spinning path e.g. the gravity of the Sun acting on the Earth, or the piece of string connected to a conker you are spinning around your head. If it wasnâ€™t there, the thing would fly off.

Centrifugal force is that feeling you get when you are on a roundabout spinning really fast and your body feels pushed out towards the sides, or the reason why when you spin a bucket of water around your head the water doesnâ€™t fall out. This feels like a real force pushing you out, but from an non-rotating observerâ€™s point of view it can be seen that the outward motion is just from you on the roundabout or the water in the bucket trying to carry on in a straight line and the centripetal force (from the friction in your feet or the sides of the bucket), is struggling to pull that thing inwards.

A more obvious example is maybe if you are in a car turning a tight corner, you will see things on the dashboard sliding outwards away from the direction you are turning. This is because the frictional centripetal force on them pulling them towards the centre of your turning circle isnâ€™t great enough for them to be turned along with you, so they are not actually moving outwards, just continuing to move along in the straight line that you were before you turned the corner.

This means we can now all laugh at this XKCD cartoon in the knowledge that we get it.