Three equal masses m are rigidly connected to each other by massless rods of length l forming an equilateral triangle, as shown above. The assembly is to be given an angular velocity ω about an axis p

Question

Three equal masses m are rigidly connected to each other by massless rods of length l forming an equilateral triangle, as shown above. The assembly is to be given an angular velocity ω about an axis perpendicular to the triangle. For fixed ω , what is the ratio of the kinetic energy of the assembly for an axis through B to an axis through A ?

TestHub · Accepted Answer

I A = m l 3 2 × 3 = m l 2 I B = m l 2 + m l 2 ⇒ I B = 2 m l l 2 KE B = 1 2 I B ω 2 ⇒ KE B = 1 2 2 ml 2 ω 2 KE A = 1 2 I A ω 2 ⇒ KE A = 1 2 ml 2 ω 2 KE B KE A = 1 2 2 ml 2 ω 2 1 2 m l 2 ω 2 = 2 1

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