I How to Determine the Axis of Rotation

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?
 

jbriggs444

Science Advisor
Homework Helper
7,567
2,601
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.
 

A.T.

Science Advisor
9,609
1,477
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:
 
4
0
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.
 

Want to reply to this thread?

"How to Determine the Axis of Rotation" You must log in or register to reply here.

Related Threads for: How to Determine the Axis of Rotation

  • Posted
Replies
7
Views
4K
  • Posted
Replies
8
Views
979
Replies
3
Views
1K
  • Posted
Replies
6
Views
2K
Replies
2
Views
962
Replies
3
Views
609
Replies
6
Views
8K
Replies
2
Views
582

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top