Here's why:

* Tangential Speed: The speed of a point on the object moving along a circular path is called tangential speed.

* Rotational Speed: The rate at which an object rotates is called rotational speed. It's usually measured in revolutions per minute (RPM).

* Relationship: Tangential speed is directly proportional to the radius and rotational speed:

* Tangential Speed = Radius x Rotational Speed

Let's break down the relationship:

1. Larger radius: If the radius of the circle is larger, the object has to travel a greater distance to complete one revolution. To keep the tangential speed constant, the rotational speed needs to decrease.

2. Smaller radius: If the radius is smaller, the object has to travel a shorter distance for one revolution. To keep the tangential speed constant, the rotational speed needs to increase.

Example:

Imagine a merry-go-round with a radius of 5 meters. You stand at the edge and are moving at a constant tangential speed of 5 meters per second. If the merry-go-round's radius doubles to 10 meters, you'll still be moving at 5 meters per second tangentially. However, the rotational speed will have to decrease to maintain that speed.

In summary:

* Larger radius = slower rotational speed

* Smaller radius = faster rotational speed

This relationship is important in various fields like engineering, physics, and astronomy. For example, in mechanics, understanding this relationship helps in designing gears and other rotating machinery.