Question

A point mass of 3 kg is located at x = 0 m, y = -0.7 m, a point mass of 5 kg is located at x = 0 m, y = +1.9 m, and a point mass of 6 kg is located at x = 0.4 m, y = 0 m. What is rotational kinetic energy of these masses about the y axis if they are spinning at 16 rad/s about the y axis? Answer in Joules.

Answer #1

Rotational kinetic energy of system is given by summation of rotational kinetic energy of individual point masses

rotational kinetic of mass is given by 0.5*mass moment of
inertia*angular velocity^{2}

mass moment of inertia of individual mass is given by
mass*perpendicular distance^{2}

moment of inertia of 3 kg mass = 3*0^{2} = 0

moment of inertia of 5 kg mass = 5*0^{2} = 0

moment of inertia of 6 kg mass = 6*0.4^{2} = 0.96
kg-m^{2}

Total moment of inertia of system = 0+0+0.96=0.96
kg-m^{2}

angular velocity = 16 rad/s

rotationalm kinetic energy = 0.5*0.96*16^{2} = 122.88
J

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