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 velocity²

mass moment of inertia of individual mass is given by mass*perpendicular distance²

moment of inertia of 3 kg mass = 3*0² = 0

moment of inertia of 5 kg mass = 5*0² = 0

moment of inertia of 6 kg mass = 6*0.4² = 0.96 kg-m²

Total moment of inertia of system = 0+0+0.96=0.96 kg-m²

angular velocity = 16 rad/s

rotationalm kinetic energy = 0.5*0.96*16² = 122.88 J