Rotation Definition

Rotation can be defined as the circular motion of an object around its centre or some axis. There can be an infinite number of imaginary lines or axes around which an object rotates. When an object undergoes rotation, all the particles comprising the object move at the same velocity around that axis. In general, rotation is one of the 4 types of transformations. Rotational motion is complex as compared to linear motion.

Rotation may be clockwise or anti-clockwise and an object can be rotated at different angles in rotation. When the rotation is in the clockwise direction, the angle of rotation is considered negative whereas it is considered to be positive in the case of anti-clockwise rotation.

The below image shows an object when rotated through different angles in clockwise and anticlockwise directions.

 

Let us have a look at the rotation formula.

Rotation

In real life, we know that the Earth rotates on its own axis and the moon also rotates on its axis. But what basically rotation is? Also, geometry deals with four basic types of transformations that are Rotation, Reflection, Translation, and Resizing. In this article, we shall read about the fundamental concept of rotation.

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Rotation Definition

Rotation can be defined as the circular motion of an object around its centre or some axis. There can be an infinite number of imaginary lines or axes around which an object rotates. When an object undergoes rotation, all the particles comprising the object move at the same velocity around that axis. In general, rotation is one of the 4 types of transformations. Rotational motion is complex as compared to linear motion....

Rotation Formula

We know that rotation can be done in both clockwise and anti-clockwise directions. In mathematics, rotation refers to the circular motion of a figure around a fixed point, particularly the origin. This leads to a change in the coordinates of the point or figure that is rotated. The rotation can be done around any angle. Let us have a look at the rotation formula for some common angles in both directions when the figure is rotated around the origin....

Rotational Matrix

With the help of a rotation matrix, rotation can be performed in Euclidean space. The matrix rotates a point in an anticlockwise direction by an angle θ and provides the coordinates of the point after the rotation through that angle in the Cartesian Plane. The rotation matrix R can be represented as:...

Rotational  Symmetry

Rotational symmetry is the property of the figure due to which its shape remains the same on rotation as compared to the original shape. These figures have an axis of symmetry and are said to possess rotational symmetry. Rotational symmetry can be found using many ways. The easiest way is to start rotating the object from 0° to 360°. If the shape of an object during rotation coincides with its original shape then it is said to possess rotational symmetry at that angle of rotation. For example, a Square possesses rotational symmetry when rotated through angles that are multiples of 90°, a circle possesses rotational symmetry at all angles of rotation whereas a triangle possesses no rotational symmetry....

Solved Examples on Rotational Formula

Example 1: Calculate the coordinates of the point (5, 3) after rotating 90° clockwise....

FAQs on Rotation

Question 1: What is meant by rotation?...

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