Chapter 8, Problem 5Q

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

To determine

To Explain: The two situations mentioned in the question with examples.

Answer to Problem 5Q

Solution:

No, for both situations

Explanation of Solution

1. Consider a rod of length l , which has its weight ( mg ) acting in the downward direction, while an upward force of equal magnitude F acts on one of its ends to keep it steady.
The net force acting on the rod is $F_{net}{}_{}=mg–F=0$ . Taking torque about the center of the rod:

  $\begin{array}{c}\tau =mg\times 0–F\times \frac{l}{2}\\ =\frac{-mgl}{2}\end{array}$ (Since $F=mg$ )

Therefore, even though the forces are balanced and the net force is zero on the rod, there is net upward torque acting on it.

2. Consider a rod of length l, which has its weight ( mg ) acting in the downward direction, while two upward forces of equal magnitude F act on it, one at each end.
F is still equal to mg . One of these forces tries to rotate the rod in the clockwise direction (positive), while the other tries to rotate it in counter-clockwise direction (negative)

Therefore, net force,

  $\begin{array}{c}{F}_{net}=mg–F–F\\ =mg–2mg\\ =-mg\end{array}$ .

Taking torque about the center of the rod,

  $\tau =mg\times 0+F\times \frac{l}{2}–F\times \frac{l}{2}=0$

Thus, even though the net torque is zero, there is net upward force acting on the rod.

Conclusion

Therefore, if the net force on a system is zero, there can still be net torque acting on it, and even if the net torque is zero, there can be net force acting on it.