Earth moves very fast. It spins at a speed of about 1,000 miles per hour at the equator and orbits around the sun at a speed of about 67,000 miles per hour. We do not feel any of this motion because these speeds are constant. The spinning and orbital speeds of Earth stay the same so we do not feel any acceleration or deceleration. You can only feel motion if your speed changes. For example, if you are in a car which is moving at a constant speed on a smooth surface, you will not feel much motion. However, when the car accelerates or when the brakes are applied, you do feel motion. Hope this makes sense!
How are you sure that we can’t? Maybe the “normal” way we feel is because always feel the Earth spinning. And perhaps the “space sickness” that astronauts get for the first few days when they leave the Earth is because they have to adjust to not feeling it any more?
The earth is spinning on its axis at a rate of one revolution per day, so if you’re at the equator you’re travelling at about 1000 miles an hour! There’s also the earth orbiting around the sun at around 67,000 miles an hour. So we should be able to feel that, right?
The reason we don’t is because we’re travelling at a constant speed* – and we can only feel *changes* in velocity when we speed up or slow down. For instance, you can feel it when you’re in an accelerating car because you’re pushed back against your seat, but if you’re in an aeroplane going at a constant 500 miles an hour, you can’t really tell you’re moving at all.
But our speed isn’t completely constant, because we’re not moving in a straight line, we’re rotating, which actually means we are accelerating (I won’t go into the maths of this, but let me know if you want me to!) and are therefore subject to a force. This is the same force that you feel when going round a sharp corner in a car, or on a merry-go-round, that makes us feel as though we’re being pushed away from the centre of the curve.
The reason we don’t feel this force pushing us away from the earth is because it’s very weak. The strength of this rotational force depends on how long it takes to make a rotation, not on how fast we’re actually moving. It takes a whole day for the earth to make one rotation, which is actually quite slow! If the earth rotated faster, we’d feel this force more strongly. And as this force is strongest at the equator (because the radius of the rotation is greatest there) and weakest at the poles, this means if you go and stand near the equator you will weigh (a tiny bit) less!