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 ktot=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.

c.The moment of inertia must be taken about an axis through the center of mass.

Explanation:

The movements of rigid bodies can always be divided into the translation movement of the center of mass and that of rotation around the center of mass. However, we can demonstrate that this is true for the kinetic energy of a rigid body that has both translational and rotational movement.

In this case the kinetic energy of the body is the sum of a part associated with the movement of the center of mass and another part associated with the rotation about an axis passing through the center of mass. This is all represented by the form Ktot = Kr + Kt, however we must consider that the moment of inertia must be taken around an axis through the center of mass, since rigid bodies at rest tend to remain at rest.

firearm identification is the process of analyzing the bullets and cartridge cases left at a crime scene to determine if they came from a particular firearm. marks on the bullets and cartridges may be common to every firearm of that type. these are called class characteristics.

force tends to be low and long diustance masses are high