# Finding the mass of a ball and a rod using torque

• Physics Person
In summary, the problem involves a diagram of a rod with its center of mass labeled and a ball hanging from it with two applied torques. The task is to find the masses of the ball and the rod. Using the equation for torque, the center of mass of the rod is designated as the axis and the torques applied on either end of the rod are calculated. However, there is confusion regarding the negative value for the torque resulting from the ball's weight and the positive value for another torque in the same direction. More information is needed, such as the direction of the torques and if the system is in equilibrium. A picture is also necessary for a clearer understanding of the problem.
Physics Person

## Homework Statement

There is a diagram of a rod with its center of mass labeled and a ball hanging down from it, attached by a string. Two torques are applied on either side. You are asked to find the mass of the ball and the mass of the rod.

## Homework Equations

Torque = Force * Lever Arm * sine of angle between them

## The Attempt at a Solution

I designated the center of mass of the rod as the axis, and then calculated the torque applied by each force by multiplying the magnitude of the force by the distance between where the force was applied and the center of mass of the rod. There is an angle of 60 degrees on the other side of where one force is being applied, so I calculated that the angle between the force and r (the lever arm, or distance from where that force is applied to the center of mass of the rod) is 120 degrees by subtracting 60 degrees from 180 degrees. What confuses me, though, is that, when I did my calculations, I got a negative value for the torque resulting from the ball's weight. I know torque can be negative, since it is a vector, but what confuses me about this result is that there is another torque that appears to be acting in the same direction as the one caused by the weight of the ball, yet it is positive. So I must have done something wrong. What is it?

Here are my calculations:

9N * 0.09m = 0.81 Nm

5.02N * sin120 degrees * 0.06m = 0.260846852 Nm

0.81 + Tball = 0.260846852

This is where I got the negative result.

There's a lot of information missing here.
Physics Person said:
There is a diagram of a rod with its center of mass labeled and a ball hanging down from it, attached by a string. Two torques are applied on either side.
On either side of what? What direction are the torques? What do we know besides the fact that the torques are acting on it? Is this system in equilibrium? Where is the ball hanging relative to the center of mass? Where is the center of rotation relative to the center of mass and the ball?

The two torques are applied on either end of the rod. It is not specified explicitly whether the system is equilibrium, but it appears to be in equilibrium from the picture. The torques appear to be pushing down on the rod. The ball is seven centimeters from the center of mass. You're supposed to treat a different position as the center of rotation, depending on whether you are trying to find the mass of the ball or the mass of the rod. When I was trying to find the mass of the ball, I treated the center of mass of the rod as the center of rotation. When I try to find the mass of the rod, I guess I'll just pick another point to be the center of rotation -- maybe where the ball is.

Physics Person said:
The torques appear to be pushing down on the rod.
Do you mean that two forces push down on the rod, and these will generate torques?
You describe a ball "hanging" from the rod, so I assume this is in a vertical plane and subject to gravity. Is there anything supporting the rod? Can't be in equilibrium if not!

Edit: maybe they are applied torques, not forces, but in that case it makes no sense to say they push down on the rod. They exert clockwise or anticlockwise torques. These could balance the torques produced by the weights of ball and rod, but still will not lead to equilibrium without an upward force somewhere.

to repeat @RPinPA ' s requst, please post the diagram. The question seems to be ambiguous without more details.

Yes, the rod is shown hanging from something else in the picture. Yes, the ball hanging from the rod is in a vertical plane and, I presume, therefore is subject to gravity. And the magnitudes of the applied forces are given in Newtons, hence why I referred to them as forces. They are forces that tend to cause a rotation. The one on the left seems like it would cause a counterclockwise rotation, whereas the one on the right seems like it would cause a clockwise rotation (assuming the axis of rotation to be the center of mass of the rod, which, in the picture, is shown to be pretty much right smack-dab in the center of the rod).

Physics Person said:
Yes, the rod is shown hanging from something else in the picture. Yes, the ball hanging from the rod is in a vertical plane and, I presume, therefore is subject to gravity. And the magnitudes of the applied forces are given in Newtons, hence why I referred to them as forces. They are forces that tend to cause a rotation. The one on the left seems like it would cause a counterclockwise rotation, whereas the one on the right seems like it would cause a clockwise rotation (assuming the axis of rotation to be the center of mass of the rod, which, in the picture, is shown to be pretty much right smack-dab in the center of the rod).
If there is a single support in the centre of the rod, providing an unknown upward force, it will be impossible to find the mass of the rod.
I can't see that we will get very far with this until you attach an image of the problem as given to you.

gneill
haruspex said:
If there is a single support in the centre of the rod, providing an unknown upward force, it will be impossible to find the mass of the rod.
I can't see that we will get very far with this until you attach an image of the problem as given to you.

I cannot figure out how to insert an image, since, when I click on the image icon when I am typing out my reply, it asks for the URL of the image, and I do not have the image uploaded to any website, but instead have it saved among the images on my phone.

Physics Person said:
I cannot figure out how to insert an image, since, when I click on the image icon when I am typing out my reply, it asks for the URL of the image, and I do not have the image uploaded to any website, but instead have it saved among the images on my phone.
See the UPLOAD button, lower right.

## 1. How do you measure the mass of a ball and a rod using torque?

To find the mass of a ball and a rod using torque, you will need a balance scale, a ruler, and a known weight. First, place the balance scale on a flat surface and zero it out. Next, hang the ball or rod from one end of the ruler and place the known weight on the other end. Adjust the position of the known weight until the ruler is balanced. Then, measure the distance from the center of the ball or rod to the hanging point and record it. Finally, calculate the mass using the formula: mass = (weight of known object * distance) / length of known object.

## 2. What is torque and how does it relate to mass?

Torque is a measure of the force that causes an object to rotate. It is calculated by multiplying the force applied to an object by the distance from the point of rotation. In the case of finding the mass of a ball and a rod, torque is used to balance the object on a ruler and determine the mass based on the distance and weight of a known object.

## 3. Can I use any known weight to find the mass of the ball and rod?

It is recommended to use a known weight that is close in mass to the object being measured. This will provide a more accurate result. Additionally, it is important to have a weight that is evenly distributed, such as a block or cube, to ensure the ruler is balanced properly.

## 4. What are some potential sources of error when measuring mass using torque?

Some potential sources of error when measuring mass using torque include imprecise measurements of the distance from the center of the object to the hanging point, not using a level surface, and not having an evenly distributed weight on the other end of the ruler. These errors can result in an inaccurate measurement of mass.

## 5. Is there a more accurate way to measure the mass of an object?

While using torque is a simple and effective method for measuring mass, there are other ways to obtain a more accurate measurement. These include using a digital scale, a balance scale with smaller increments, or a water displacement method. It is important to choose a method that is appropriate for the size and shape of the object being measured.

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