# Question about torque and center of mass

• AGC
In summary, the conversation discusses the concepts of torque and how it is applicable to rotating objects. The first question is whether torque can be calculated if the particle is not rotating at a fixed distance around a fixed axis. The second question is about the treatment of a rigid body as a particle-like object and how gravitational forces are replaced by a resultant force at the center of mass. The final clarification is whether torque is only applicable to objects rotating around a fixed axis or if it can also apply to objects rotating around a fixed point.

#### AGC

I am a beginner and this is my first post.

We know torque ## \vec T = \vec r × \vec F ## Now, should r be fixed in magnitude? I mean can I calculate torque only if the particle is rotating at a fixed distance around a fixed axis? I am having this idea because torque is explained (from where I read) using an analogy with doors.

Second question. I read that generally a system of forces acting on a rigid body can not be reduced to a single force equal to the vector sum of the forces. Then I get confused because in case of weight, we replace gravitational forces on each particle of a rigid body with a resultant force through the center of mass.

about your first question , your question is how can we deal with torque when r is variable 'not constant in magnitude' ?

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About your second question , [As I know] we treat the rigid body as a particle-like object so that the gravitational force will act only on its center of mass.

Maged Saeed said:
about your first question , your question is how can we deal with work when r is variable not constant 'in magnitude' ?
I think my first question was not clear enough. I asked if the concept of torque is applicable only if the particle (or body) is rotating about an axis? And should it rotate in a fixed radius? Sorry if the question is of very intro level.

No , [As far I know] The concept of torque can be applied if the rigid body is rotating about either a fixed point or a fixed axis , where the point 'similarly to the axis of rotation ' is allocated on an axis vertical to the xy-plane.

See this vedio:

## 1) What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

## 2) How is torque related to center of mass?

The center of mass is the point where the entire mass of an object can be considered to be concentrated. Torque is calculated using the distance from the axis of rotation to the center of mass, which means that the location of the center of mass can affect the amount of torque produced.

## 3) How does the center of mass affect stability?

The lower an object's center of mass is, the more stable it will be. This is because a lower center of mass means there is less potential for the object to tip over or fall.

## 4) Can torque and center of mass be used to determine the stability of an object?

Yes, torque and center of mass can be used to determine the stability of an object. By calculating the amount of torque produced by the object's weight and its distance from the center of mass, we can determine if the object will remain stable or if it is at risk of tipping over.

## 5) How can torque and center of mass be applied in real life situations?

Torque and center of mass are important concepts in engineering and physics, and they are used in many real life situations. For example, they are used in designing structures such as buildings and bridges to ensure their stability, and they are also used in sports equipment design to improve performance and prevent injury.