# Can an object be in equilibrium if it is in motion?

• linhison
In summary, an object in rotational equilibrium is not at rest or in motion, but an object in translational equilibrium is at rest or in motion.

#### linhison

Homework Statement
Can an object be in equilibrium if it is in motion? Explain
* This is a prelab question to a lab that deals with equilibrium and torque

The attempt at a solution
My thought process:

- Equilibrium means that:
1) Net external forces = 0
2) Net torque = 0
- Net torque is related to angular acceleration, so if net torque = 0, then angular acceleration = 0.
0 acceleration could mean constant velocity which would mean that the object is in motion.
*Not sure if this second point is correct*
-If an object is at constant velocity around an axis of rotation, are the external forces at equilibrium?

Welcome to PF !

linhison said:
Homework Statement
Can an object be in equilibrium if it is in motion? Explain
* This is a prelab question to a lab that deals with equilibrium and torque

The attempt at a solution
My thought process:

- Equilibrium means that:
1) Net external forces = 0
2) Net torque = 0
- Net torque is related to angular acceleration, so if net torque = 0, then angular acceleration = 0.
0 acceleration could mean constant velocity which would mean that the object is in motion.
*Not sure if this second point is correct*

Either the object is at rest or is moving with constant velocity . In the former case we say it is in static equilibrium . In the later it is in dynamic equilibrium .
linhison said:
-If an object is at constant velocity around an axis of rotation, are the external forces at equilibrium?

If the object is moving with constant speed around an axis of rotation then there must be a net centripetal force acting on it . The object is not at equilibrium .

conscience said:
Welcome to PF !
Either the object is at rest ...
Actually, there is no such thing, in and of itself and as a stand-alone statement like that. This may sound like nitpicking (and possibly for the purposes of this problem it is) but it is a very important point. All motion is relative. Something may be at rest in the frame of reference of the lab bench on which it is sitting, but it is not "at rest" or "in motion" in any absolute sense (unless it's accelerating, but that's a different story).

conscience said:
If the object is moving with constant speed around an axis of rotation then there must be a net centripetal force acting on it . The object is not at equilibrium .

phinds said:
unless it's accelerating, but that's a different story
From a little Googling, the general view seems to be that one should distinguish translational from rotational equilibrium. An object spinning about its mass centre at a constant rate is considered to be in rotational equilibrium. If its mass centre is not accelerating then it would also be in translational equilibrium. This seems to fit with the OP's view.

In fact, I added the 'mass centre' qualifier, others don't. But maybe the thinking is that if it is spinning about some other axis at constant speed then it is in rotational equilibrium (no net torque) but not translational equilibrium.

Last edited:
linhison

## 1. Can an object be in equilibrium if it is in motion?

No, an object cannot be in equilibrium if it is in motion. Equilibrium refers to a state of balance where all forces acting on an object are equal and opposite, resulting in a net force of zero. If an object is in motion, there must be a net force acting on it, therefore it cannot be in equilibrium.

## 2. What is the difference between static and dynamic equilibrium?

Static equilibrium refers to a state where an object is at rest and all forces acting on it are balanced. This means there is no net force acting on the object. Dynamic equilibrium, on the other hand, refers to a state where an object is in motion at a constant velocity with all forces balanced. In this case, there is no net force or net torque acting on the object.

## 3. Can an object be in both static and dynamic equilibrium at the same time?

No, an object cannot be in both static and dynamic equilibrium at the same time. These two types of equilibrium are mutually exclusive. An object can either be at rest (static equilibrium) or moving at a constant velocity (dynamic equilibrium), but not both simultaneously.

## 4. How does the concept of equilibrium apply to objects on an inclined plane?

On an inclined plane, objects can be in equilibrium if the forces acting on it are balanced. This means that the weight of the object is balanced by the normal force acting perpendicular to the plane, and the force of gravity acting parallel to the plane is balanced by the force of friction. The angle of the incline and the coefficients of friction will determine the magnitude of these forces.

## 5. Can an object be in equilibrium if there is an unbalanced force acting on it?

No, an object cannot be in equilibrium if there is an unbalanced force acting on it. In order for an object to be in equilibrium, all forces acting on it must be balanced. If there is an unbalanced force, the object will accelerate in the direction of that force, breaking the state of equilibrium.