It doesn't matter whether it's a straight beam or a curve, you calculate moments the same way. The moment is a force multiplied by its perpendicular distance from the point of rotation.
There is one thing you will need to consider while preparing your mobile, the location of the center of mass of the curved pieces. If you are using a rectangular piece of wood, for example, the COM is located at the the midpoint of the length and of the width. So, you can support the piece at the COM.
With a curve, the COM could be at a point in the space around the object. Think of a donut - it's COM is in the middle of the hole. You could have a harder time getting everything into equilibrium.
It's not a monumental challenge to overcome, just something for you to think about as you layout your pieces. Good luck.
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Turning something 'clockwise' would be turning it in the direction the hands on a clock turns. 'Counter-clockwise' would be turning it the opposite direction of a clock. I always remember anti-clockwise from clockwise, by which way a clock turns for clockwise, and the opposite way of a clock turning for anti-clockwise.
An angle is a measure of turn. the amount of turn is the magnitude, measured in degrees, and direction of turn can be clockwise or anti-clockwise. A positive angle turns in an anti-clockwise direction while a negative angle turns in a clockwise direction.
3 quarters clockwise is 270 degrees clockwise or 90 degrees anti(counter)-clocwise
Going clockwise... 210 degrees. Going anti-clockwise... 150 degrees.
Every component: the length of each line, the measure of each angle, the order in which the lines are connected, the order of the angles, whether these orders are clockwise or anti-clockwise.