A 30 kg mass and a 20 kg mass are joined by a light rigid rod and this system is free to rotate in the plane of the page about axis through A and perpendicular to the page. The 30 kg mass is 0.2 m from A and the 20-kg mass is 0.4 m from A. Treating the masses as point masses and assuming the system rotates at 5 rad/s about A, what is the total kinetic energy?

  K = 55 J

Explanation:

Kinetic energy is a scalar therefore it is an additive quantity

       K = ½ I₁ w₁² + ½ I₂ w₂²

The moment of inertia of a particular is

      I = m r²

      I₁ = 30 0.2² = 1.2   kg m²

      I₂ = 20 0.4² = 3.2  kg m²

As the body is joined by a rigid rod they both have the same angular velocity

      K = ½ (I₁ + I₂) w²

Let's calculate

      K = ½ (1.2 + 3.2) 5²

       K = 55 J

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