Yes, time runs slower during fast circular motion, specifically when an object is moving at high speeds or undergoing acceleration in a circular path. This phenomenon is known as time dilation.
According to the theory of special relativity, when an object moves at speeds approaching the speed of light, time dilation occurs. Time dilation means that time appears to pass more slowly for the moving object as observed by a stationary observer. This effect becomes more pronounced as the velocity of the object increases.
In the case of circular motion, an object moving in a circular path at high speeds experiences acceleration toward the center of the circle. This acceleration causes time dilation, resulting in a slower passage of time for the moving object compared to a stationary observer.
To illustrate this concept, let's consider an example: Suppose there are two observers, one stationary and another on a fast-moving spaceship that is continuously circling a massive object. The observer on the spaceship will measure time to be passing slower compared to the stationary observer.
This effect has been experimentally confirmed in various contexts, including high-speed particle accelerators and observations of high-speed particles such as cosmic rays. The time dilation resulting from fast circular motion is a consequence of the fundamental principles of special relativity and the behavior of spacetime in the presence of high velocities or acceleration.