explain different types of equilibrium of a rigid body
Answers
Answer:
Equilibrium is a defined as any point where the total amount of external force or torque is zero. This point may be anywhere near the center of mass. ... If the total torque on a rigid body is zero then the body shows rotational equilibrium as the angular momentum does not change with time.
Equilibrium of a Rigid Body
A rigid body is a system of many particles. It is not essential that each of the particles of a rigid body behaves in a similar manner like the other particle. Depending on the type of motion every particle behaves in a specific way. This is where the equilibrium of rigid bodies comes into play.
Equilibrium of Rigid Bodies
Rigid bodies are those bodies in which the distance between particles is constant despite any kind of external force. So while studying the equilibrium of rigid bodies, we mainly aim to define the behavior of these constituting particles in changed conditions of force or torque.Since we are concentrating on the equilibrium of rigid bodies under motion, therefore we need to take both translational and rotational motion into consideration.
Explanation
Equilibrium is a defined as any point where the total amount of external force or torque is zero. This point may be anywhere near the center of mass. External force in translational motion of the rigid body changes the linear momentum of that body. While the external torque in rotational motion can change the angular momentum of the rigid body.
In the mechanical equilibrium of a rigid body, the linear momentum and angular momentum remain unchanged with time. This implies that the body under the influence of external force neither has a linear acceleration nor an angular acceleration. We, therefore, can say that:
If the total force on a rigid body is zero then the body shows translational equilibrium as the linear momentum remains unchanged despite the change in time:
If the total torque on a rigid body is zero then the body shows rotational equilibrium as the angular momentum does not change with time.
Mechanical Equilibrium
When we sum up the above findings of translational and rotational equilibrium we get the following assumptions:
F1+F2+F3+F4+…..Fn= Fi = 0 (For translational equilibrium)
τ1+τ2+τ3+τ4+……τn = τi = 0 (For rotational equilibrium)
These equations are the vector in nature. As scalars the force and torque in their x,y, and z components are:
Fix = 0 , Fiy = 0, and Fiz= 0 and τix = 0 , τiy = 0, and τiz= 0
The independent condition of force and torque helps in reaching the rigid bodies to a state of mechanical equilibrium. Generally, the forces acting on the rigid body are coplanar. The three conditions if satisfied, help the rigid body attain equilibrium. The condition of translational equilibrium arises when any of the two components along any perpendicular axis sum up to be zero.
For rotational equilibrium, it is necessary that all the three components result in a zero. Moreover, as the translational equilibrium is a condition that depends on a particle’s behaviour, therefore, the vector sum of forces on all the particles must be a zero.
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