Question

If the net force on a system is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zero? Explain and give examples.

Short answer

If the net force on a system is zero, the net torque is not zero. If the net torque on a system is zero, the net force is not zero.

Step-by-step solution

Understanding the net force and the net torque acting on the system 

The net force acting on the system can be calculated by the sum of each force acting on it.

The net torque acting on the system can be obtained by the sum of each torque acting on it.

Determine the net torque if the net force on a system is zero 

Consider that a system consists of two equal and opposite forces acting on it. This can be shown as follows:

The net force acting on the system can be calculated as:

\begin{align*}{F_{net}} &= F - F\\ &= 0\end{align*}

The net torque acting on the system can be calculated as:

T_net= F x X

Thus, from the above analysis, it is clear that if the net force on a system is zero, then the net torque is not equal to zero.

Determine the net force if the net torque on a system is zero 

Consider the case of frictionless free fall of any object (zero air resistance). Then, the net torque acting on the system is zero. However, the net force acting on the system is downward, that is, the gravitational force.

Another example is when someone pushes a crate with some force along the center of mass. There is no torque on the system about its center of mass.

Thus, from the analysis, it is clear that if the net torque on a system is zero, the net force is not zero.