What part of an object follows a smooth path when the object is made to spin through the air or across a flat smooth surface?

When an object spins through the air or slides across a smooth surface, the part of the object that follows a smooth path is known as the center of mass.

The center of mass is the point in an object where its mass is evenly distributed in all directions. In simpler terms, it is the average location of all the particles that make up the object.

To determine the center of mass of an object, you need to consider both its shape and distribution of mass. For symmetrical objects, the center of mass coincides with the geometric center. However, for irregularly shaped objects, the center of mass may not lie on the axis of symmetry.

To find the center of mass experimentally, you can follow these steps:
1. Hang the object freely from a string or pivot it around a known point.
2. Observe the object's stable equilibrium position.
3. Repeat step 1 and 2 with a different pivot point or hanging location.
4. The center of mass will be the point where the two intersecting lines (formed from the different equilibrium positions) meet.

Knowing the location of the center of mass is essential in understanding the object's rotational motion. When the object spins or slides, the center of mass moves along a straight path, while the other parts rotate or oscillate around it. This smooth path followed by the center of mass contributes to the object's stability and predictable motion.