When a ball rolls on a table that is rotating, several factors come into play due to the combined effects of the ball's motion and the rotation of the table. Here are a few key observations:
Centrifugal force: As the table rotates, objects on it experience a centrifugal force pushing them away from the center of rotation. This force acts outward and can affect the ball's trajectory. Depending on the speed of rotation and the ball's position, the centrifugal force may cause the ball to move away from the center or be pushed towards the outer edges of the table.
Curved path: The ball follows a curved path due to its rolling motion and the rotation of the table. As the ball rolls forward, the rotation of the table can cause it to deviate from a straight line. The ball tends to move towards the outer edges of the table, following a curved trajectory that combines its rolling motion and the rotational motion of the table.
Combined velocities: The ball's motion is a result of the combined velocities of its rolling and the table's rotation. As a result, the speed and direction of the ball's movement can vary depending on its initial velocity, the direction of rotation, and other factors such as friction between the ball and the table's surface.
Frictional effects: Friction between the ball and the table's surface also comes into play. Depending on the nature of the surface and the ball, friction can either assist or resist the ball's motion. Friction can help the ball maintain its grip on the rotating surface or cause it to slip and slide in a different direction.
Overall, the specific behavior of the ball rolling on a rotating table will depend on factors such as the initial conditions, the speed of rotation, the surface properties, and the interaction between the ball and the table.