# How to Determine the Axis of Rotation

• Diracobama2181

#### Diracobama2181

Let's say I have a massless bar of length ##l## with two different masses, ##m_1## and ##m_2##. Suppose an identical spring is attached to each individual mass, with the other end being attached to the ceiling. How would I go about determining the rotational kinetic energy of the system. Do I choose the axis about the center or the center of mass?

Summary: When determining the kinetic energy of a rotating system, which point should I use as an axis to determine rotation kinetic energy.

Let's say I have a massless bar of length ##l## with two different masses, ##m_1## and ##m_2##. Suppose an identical spring is attached to each individual mass, with the other end being attached to the ceiling. How would I go about determining the rotational kinetic energy of the system. Do I choose the axis about the center or the center of mass?
If your goal is to determine the kinetic energy of the system, there is no need to bother with an axis of rotation. You have two masses. Add up their kinetic energies.

When determining the kinetic energy of a rotating system, which point should I use as an axis to determine rotation kinetic energy.
The chosen axis merely determines how much of the kinetic energy is considered "rotational", and how much "linear". Their sum (total KE) won't change.

You should choose an axis which is most convenient. For example, the one for which you know the moment of inertia, which is needed for the rotational KE calculation:
https://en.wikipedia.org/wiki/Rotational_energy

• jbriggs444
Summary: When determining the kinetic energy of a rotating system, which point should I use as an axis to determine rotation kinetic energy.

Let's say I have a massless bar of length ##l## with two different masses, ##m_1## and ##m_2##. Suppose an identical spring is attached to each individual mass, with the other end being attached to the ceiling. How would I go about determining the rotational kinetic energy of the system. Do I choose the axis about the center or the center of mass?

We can assume a flat motion system. Then we have 3 independent variables in the context of an inertial coordinate system : (x,y) for the position of the center of masses and φ for the bar's angle. From this information you can calculate the potential energy due to gravity an due to the strings and complete the Lagrangian as L=KineticEnergy-PotentialEnergy; where KineticEnergy is the sum of the kinetic energy of the center of masses plus rotational energy relative to the center of masses = 1/2 I (dφ/dt)^2 and I= moment of inertia relative to the center of masses.