?Rather than a semicircle that subtends an angle ? = 2? radians, calculate the p

Question

?Rather than a semicircle that subtends an angle ? = 2? radians, calculate the position of the CM of an arc of radius R as a function of ? as ? changes from ~ 0 radians (essentially a point at y = R) to ? = 2? radians (a complete circle). This arc is centered about the y-axis as shown in the figure. Check that your result makes sense; you should be able to predict the position of the CM for ? ~ 0, ? and 2? radians without doing a calculation.

?Rather than a semicircle that subtends an angle ? = 2? radians, calculate the position of the CM of an arc of radius R as a function of ? as ? changes from ~ 0 radians (essentially a point at y = R) to ? = 2? radians (a complete circle). This arc is centered about the y-axis as shown in the figure. Check that your result makes sense; you should be able to predict the position of the CM for ? ~ 0, ? and 2? radians without doing a calculation.

Explanation / Answer

The centre of mass will be of course the origin that is the centre of the circle.

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