The rotational kinetic energy term is often called the kinetic energy in the center of mass, while the translational kinetic energy term is called the kinetic energy of the center of mass. You found that the total kinetic energy is the sum of the kinetic energy in the center of mass plus the kinetic energy of the center of mass. A similar decomposition exists for angular and linear momentum. There are also related decompositions that work for systems of masses, not just rigid bodies like a dumbbell. It is important to understand the applicability of the formula K_tot= Kr + Kt.
Which of the following conditions are necessary for the formula to be valid?
Check all that apply.

a. The velocity vector V must be perpendicular to the axis of rotation.
b. The velocity vector must be perpendicular or parallel to the axis of rotation.
c. The moment of inertia must be taken about an axis through the center of mass.