Differences in circular and rotatory motion:

            Any turning as if on an axis is rotatory motion.  Any rotatory motion where the radius of gyration length and the axis of rotation are fixed is circular motion. And that’s the difference. Circular motion is just a special case of rotatory motion. That is, there is no fixed axis and radius restriction for rotatory motion, but there is for circular motion.

For example, all planets have rotatory motion around their suns. But most of the orbits are elliptical, so the rotation axis (there are two in an ellipse) and radii of gyration vary as they trek around. So most, if not all, planets do not have circular motion.

Note:

Gyration length:

            A length that represents the distance in a rotating system between the point about which it is rotating and the point to or from which a transfer of energy has the maximum effect.

Mini Exercise

       1. When a body is said to be at rest?

Ans: A body is said to be at rest if it does not change its position concerning its surroundings.

       2. Give an example of a body that is at rest and is in motion at the same time.

Ans: Motion and rest are relative concepts. There is no absolute rest. We can define the state of rest or motion only concerning another object or a point in space taken as reference.

Examples:

• A person inside a train considers himself to be at rest concerning the fellow passengers or the walls of the train. But when he looks outside, he finds himself to be in motion concerning the trees outside.
• A passenger sitting in a moving bus is at rest because he/she is not changing his/her position concerning other passengers or objects inside the bus. But to an observer outside the bus, the passengers and the objects inside the bus are in motion.

      3. Mention the type of motion in each of the following:

• A ball moving vertically upward.

Ans: Linear motion.

• A child moving down a slide.

Ans: Linear motion.

• Movement of a player on a football ground.

Ans: Random motion.

• The flight of a butterfly.

Ans: Random motion.

• An athlete running on a circular track.

Ans: Circular motion.

• The motion of a wheel.

Ans: Circular motion.

• The motion of a cradle.

Ans: Vibratory motion.