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Question

Three uniform rods each of mass m and length l are joined to form an equilateral triangle in horizontal plane as shown. Find angular impulse required to rotate the triangle about an axis passing through A and perpendicular to the plane of triangle, with constant angular speed.
1210104_fae84b5c63b04054a46bf474c07fcbef.png

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Solution

The moment of inertia of a single rod about an axis passing through its center and perpendicular to it is

112ML2

That of each side of the equilateral triangle about an axis passing through the triangle's center and perpendicular to its plane is

112ML2+M(L23)2=16ML2

(by the parallel axis theorem).

The moment of inertia of the triangle about this axis is

3×16ML2=12ML2


1316846_1210104_ans_2deb548c2ec6466baf94e03cb9b98f5b.png

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