Of course, both you and I won't live to tell the story, but the implications of this thought experiment gives us a intuitive sense of the role of mass and velocity in classical mechanics.
The concept of power or strength is something that is lodged deeply into our habit of thought. We associate strength with mass (For example, bulging muscles give us an idea of strength) and also velocity i.e. a fast moving object hitting us will do more damage than a slow one. In strict scientific terms, this strength is defined by an object's momentum which is a product of both its mass and velocity. Our earth has massive momentum, by virtue of being massive(5.972 × 10^24 kgs) and rotating at a speed of approximately 1000 miles/hour.
But why don't we feel it motion in our everyday lives?
This is because, everything on earth's surface is moving at the same velocity relative to it. The ground below us, the buildings, trees and even the birds flying in the sky are moving at 1000 miles/hour without feeling a thing. In order to understand what it would feel like when the earth stops, let us consider this common scenario.
When a moving bus stops suddenly, a jerk tends to push us our upper body forward, or jumping out a moving bus, pushes our legs backwards in a direction opposite to the moving bus.
This is because of something known as "moment of inertia". Moment of inertia is a form of resistence offered by bodies which tends to preserve its angular acceleration. In essence, if we push a still object, the object tries to remain still, or if we stop a moving object, it tries to preserve its motion which based on Newton's first law of motion.
An interesting consequence of this, is what we've discussed above in the examples of moving bus. During motion, our body has already adapted to the motion of the bus, and hence we don't feel like its moving. But interesting things happen when it stops in a second. Our legs, which are in close contact with the floor of the bus, experience this halt earlier than the upper part of our body. As a result, a differential in created. Our legs stop almost immediately with the bus, whereas our upper body remains in motion for a while, which makes it move forward.
Same happens with our legs, while jumping out of a moving bus. Our legs, stops immediately after coming in contact with the ground, whereas the upper body continues to remain in motion for a while after.
Source
Coming back to our original discussion, when the earth, stops a small portion of everything in contact with earth's surface will also stop, whereas the majority will continue with an enormous velocity of its rotation i.e. 1000 miles/hour. That's the speed with which the oceans water will rise causing massive flash tsunamis worldwide!
(Source)
Pretty scary, isn't it?