We don't feel the earth moving because of the speed of the earth moving being constant and also because of gravity holding us down.
If it were not for the gravity holding us down then we would be able to feel the earth moving and we would likely get thrown around on the earth.
But thankfully we have gravity holding us firmly down on the earth.
The earth is rotating and spinning at a speed of 1,000 miles per hour and also is tilting towards and away from the sun constantly.
As we approach winter the earth is tilting one way and when summer comes the earth tilts again.
If the earth stopped rotating suddenly you would notice is because all the stuff in your yard and around you would be swept away into the atmosphere such as rocks, topsoil, trees, buildings, your pet dog, and so on.