Question

A body is in translational equilibrium under the action of coplanar forces. If the torque of these forces is zero about a point, is it necessary that it will also be zero about any other point?

Answer 1

Answer:

1) Translational equilibrium: If the net force acting on a body is zero, then the body is said to be in translational equilibrium. In such a case, the center of mass of the body remains either at rest or moves rectilinearly with constant velocity...

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Answer 2

Explanation:

The translational equilibrium is the body here. It is assumed that there are n different particles in n different forces.

$\sum_{i=1}^{n} \vec{F}_{i}=0$

Let us consider that R is the torque and it is zero.

$\vec{\tau}=\sum_{i=1}^{n} \vec{P}_{i} \times \vec{F}_{i}=0$

Now, it is to be found the torque about O is

$\vec{\tau}=\sum_{i=1}^{n} \vec{S}_{i} \times \vec{F}_{i}$

$\vec{\tau}=\sum_{i=1}^{n}\left(\vec{Q}_{i}+\vec{P}_{i}\right) \times \vec{F}_{i}$

$\vec{\tau}=\sum_{i=1}^{n} \vec{Q}_{i} \times \vec{F}_{i}+\sum_{i=1}^{n} \vec{P}_{i} \times \vec{F}_{i}$

$\vec{\tau}=\vec{Q}_{i} \times \sum_{i=1}^{n} \vec{F}_{i}$

$\vec{\tau}=0$

• Hence, it is proved that at any other point, the torque is be zero.  
• It is to be noted that torque, moment of force, rotational force is the linear force’s rotational equivalent.