How to Determine the Axis of Rotation

• Diracobama2181
In summary, the rotational kinetic energy of a massless bar with two masses attached can be determined by adding up their kinetic energies.
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?

Diracobama2181 said:
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.

Diracobama2181 said:
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
Diracobama2181 said:
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.

1. What is the axis of rotation?

The axis of rotation is an imaginary line around which an object rotates or spins. It is the center point of rotation for an object.

2. How do you determine the axis of rotation for a rotating object?

To determine the axis of rotation, you can use the right-hand rule. Point your right thumb in the direction of the rotation and your fingers will curl around the axis of rotation.

3. Can the axis of rotation change for a rotating object?

Yes, the axis of rotation can change depending on the forces acting on the object. For example, if a spinning top starts to wobble, the axis of rotation will change to the point where the top is balancing on.

4. Is the axis of rotation always in the center of an object?

No, the axis of rotation can be anywhere in an object, as long as it is the point around which the object rotates. For example, a spinning wheel has its axis of rotation at its center, but a spinning top has its axis of rotation at its tip.

5. Can you determine the axis of rotation for non-circular objects?

Yes, the axis of rotation can be determined for any object that rotates, regardless of its shape. The right-hand rule can still be used to determine the axis of rotation for non-circular objects.

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