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? Choose all that apply. The velocity vector v⃗ �→ must be perpendicular to the axis of rotation. The velocity vector v⃗ �→ must be perpendicular or parallel to the axis of rotation. The moment of inertia must be taken about an axis through the center of mass.
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?
Choose all that apply.
The velocity vector v⃗ �→ must be perpendicular to the axis of rotation.
The velocity vector v⃗ �→ must be perpendicular or parallel to the axis of rotation.
The moment of inertia must be taken about an axis through the center of mass.
The formula for total kinetic energy in a rotating system is
where is the rotational kinetic energy and is the translational kinetic energy.
This formula only takes into account the magnitude of the velocity. The rotating system has velocity which can be in any direction. The center of mass' velocity vector v⃗ can be in any direction for the formula to hold true.
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