Why Is the Mass of the Equal-Arm Balance Neglected in Torque Calculations?

[Ginny Mac]

In my lab assignment, we used an equal-arm balance to demonstrate rotational equilibrium by balancing torques using different mass quantities. A 100 g mass hangs from one end of the EAB, and a 185.18 g mass hangs from a thread at a 50 degree angle on the other end. The EAB is horizontal and we achieve rotational equilibrium. Here is my question:

When we sum all of the torques acting on the EAB, we neglect the mass of the equal arm balance (EAB). Is this simply because the torque acting on the EAB is zero? (Since the torques are balanced and in equilibrium). I understand this, but I suppose I am simply trying to really know "why."

Also, if the EAB were not horizontal, and we still were able to achieve rot. equil., its mass would still be negligible, correct? I believe this is because this only means the EAB's center of mass is in a different location. But where? I am confused about this concept. Where is the fulcrum located then?
Thank you for your time and help!
Ginny

 

[Nate810]

Yes, the mass of the EAB is negligible because the torques are balanced and in equilibrium. The torque acting on the EAB is zero because the masses on each side of the EAB are equal and opposite. Therefore, the sum of all the torques acting on the EAB is zero. If the EAB were not horizontal and we still achieved rotational equilibrium, its mass would still be negligible. This is because the center of mass of the EAB would be located at the point of equilibrium. In this case, the fulcrum would be located at the center of mass of the EAB.

 

[quicknote]

Dear Ginny,

Thank you for sharing your lab assignment and question about rotational equilibrium. I am happy to provide a response and further explanation to your inquiries.

Firstly, you are correct in understanding that we neglect the mass of the EAB when summing the torques acting on the system. This is because, as you mentioned, the torque acting on the EAB is zero. In order for an object to experience a torque, there must be a force acting at a distance from the axis of rotation. In the case of the EAB, the equal arms are symmetrically positioned on either side of the axis of rotation, resulting in equal and opposite forces that cancel out and do not create a torque.

To further explain why the EAB's mass is neglected, we can look at the equation for torque, which is torque = force x distance. Since the distance from the axis of rotation to the EAB's center of mass is zero, the torque created by the EAB's mass is also zero. Therefore, it can be omitted from the calculation without affecting the overall equilibrium of the system.

As for your question about the EAB's position, you are correct in understanding that the center of mass will be in a different location if the EAB is not horizontal. The center of mass is the point at which an object's mass is evenly distributed in all directions, and it is also the point where the object will balance. In the case of the EAB, the fulcrum will be located at the center of mass, which will shift depending on the angle of the EAB.

I hope this explanation helps clarify the concept of rotational equilibrium and the role of the EAB's mass in this scenario. Keep up the good work in your lab assignments and continue to ask questions to deepen your understanding of scientific concepts. Best of luck!

Sincerely,