As you [[183_notes:rot_ke|read with rotational kinetic energy]], it is often useful to think about the motion of a system about its center. In those notes, you [[183_notes:rot_ke#atoms_in_rotating_objects_can_move_with_different_speeds|read about how the translational kinetic energy of atoms in a solid as the move around some central rotation axis]] can be described with rotational kinetic energy. Rotational angular momentum is a similar construct. It is not that a translating and rotating object has a separate kinds of angular momentum, but that you can mathematically separate the angular momentum due to translation and due to rotation to think about the two parts more easily.
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As you [[183_notes:rot_ke|read with rotational kinetic energy]], it is often useful to think about the motion of a system about its center. In those notes, you [[183_notes:rot_ke#atoms_in_rotating_objects_can_move_with_different_speeds|read about how the translational kinetic energy of atoms in a solid as the move around some central rotation axis]] can be described with rotational kinetic energy. Rotational angular momentum is a similar construct. //It is not that a translating and rotating object has a separate kinds of angular momentum, but that you can mathematically separate the angular momentum due to translation and due to rotation to think about the two parts more easily.//
Consider the spinning ball, person, stool system from the demonstration. In this case, the whole system rotates with the same angular velocity (ω) after the ball was caught. An atom in the ball at a distance of r⊥ from the rotation axis is therefore moving with a linear speed v=r⊥ω. Here, r⊥ is the perpendicular distance from the rotation axis to the atom in the ball.
Consider the spinning ball, person, stool system from the demonstration. In this case, the whole system rotates with the same angular velocity (ω) after the ball was caught. An atom in the ball at a distance of r⊥ from the rotation axis is therefore moving with a linear speed v=r⊥ω. Here, r⊥ is the perpendicular distance from the rotation axis to the atom in the ball.