How can you prove that turning objects are accelerating?

USE AN ACCELEROMETER!

Water has more inertia (mass) than styrofoam, so a floating piece of foam will be forced into the direction of any applied force....

So if you step forward, the foam goes forward!

What happens if you turn in a circle at a constant speed?

You can see that the styrofoam goes INWARD toward the axis of rotation.

So any change of direction is accelerated motion!