A circular wheel, while completing a full turn, fits exactly into its original position 12 times. find the angle of rotational symmetry of the wheel.
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Answer:
object or shape is said to have rotational symmetry if it looks exactly the same at least once during a complete rotation through three hundred and sixty degrees.
In a full turn, there are precisely four positions (on rotation through the angles 90°, 180°, 270° and 360°) when the windmill looks exactly the same. Because of this, we say it has a rotational symmetry of order 4.
Here is one more example for rotational symmetry. Consider a square with P as one of its corners. Let us perform quarter-turns about the centre of the square marked x .
(i) is the initial position. Rotation by 90° about the centre leads to (ii). Note the position of P now. Rotate again through 90° and you get (iii). In this way, when you complete four quarter-turns, the square reaches its original position. It now looks the same as (i). This can be seen with the help of the positions taken by P.
Thus a square has a rotational symmetry of order 4 about its centre. Observe that in this case,
The centre of rotation is the centre of the square.
The angle of rotation is 90°.
The direction of rotation is clockwise.
The order of rotational symmetry is 4.
Draw two identical parallelograms, one-ABCD on a piece of paper and the other A' B' C' D' on a transparent sheet. Mark the points of intersection of their diagonals, O and O' respectively .
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