Rotational Symmetry
Samuel went to an exhibition and sat on a giant wheel.
Samuel comes back to his initial position after the completion of every round.
That is, after one complete rotation, the giant wheel comes back to its original position.
If an object looks the same after completion of full or part of a rotation,
Then we say that it has Rotational symmetry.
Letâ€™s learn more about rotational symmetry.
During rotation, the size and shape of the object does not change.
Letâ€™s take an example of a paper windmill that rotates around a fixed point.
The windmill looks exactly the same for each rotation of
$90_{Â°}$
The windmill looks the same at four positions in one complete rotation(
$360Â°$
)
We say that this shape has rotational symmetry of order
$4$
Order of symmetry is the number of times an object looks same in a round of
$360_{Â°}$
The fixed point around which the object rotates is called the center of rotation.
The angle by which the object turns during the rotation is called the angle of rotation.
The angle of rotation for the windmill is
$90_{Â°}$
Let's solve few examples
Consider an equilateral triangle
$PQR$
The angle of symmetry for this triangle is
$120_{Â°}$
The triangle looks the same for
$3$
in one complete rotation. So, the order of symmetry is
$3$
The center of rotation is the centroid of the equilateral triangle.
Consider a square
$ABCD$
The angle of rotational symmetry for this square is
$90_{Â°}$
The square looks the same
$4$
times in one complete rotation, the order of symmetry is
$4$
The centre of rotation is the centre of the square.
Consider a rectangle
$ABCD$
The angle of rotational symmetry for the rectangle is
$180_{Â°}$
The rectangle looks the same
$2$
times in one complete rotation, the order of symmetry is
$2$
The centre of rotation is the centre of the rectangle.
Consider a star named
$PQRST$
The angle of rotational symmetry for this star is
$72_{Â°}$
The star looks the same
$5$
times in one complete rotation, the order of symmetry is
$5$
The centre of rotation for this star is the centre of the star.
Revision
If an object looks the same after completion of full or part of a rotation,
Then we say that it has Rotational symmetry.
The fixed point around which an object rotates is called the center of rotation.
Order of symmetry is number of times an object looks the same in one complete rotation.
The angle by which the object turns during the rotation is called the angle of rotation.
The End