Final answer:
Yes, a set of forces can have a net force that is zero and a net torque that is not zero.
Step-by-step explanation:
Yes, a set of forces can have a net force that is zero and a net torque that is not zero. The net force on an object is the vector sum of all the individual forces acting on it, and it is calculated by adding up the magnitudes and directions of each force. If the forces are balanced such that their magnitudes and directions cancel each other out, the net force will be zero. However, even if the net force is zero, the net torque can still be nonzero if the forces do not act at the same point or if they act perpendicular to the lever arm.
For example, consider a seesaw with two children of different weights sitting on opposite ends. If the seesaw is perfectly balanced, the net force is zero because the downward forces from each child cancel each other out. However, the torques exerted by the forces are not zero because the lever arm (distance from the pivot point to the point where the force is applied) is different for each child. In this case, the torques created by the unequal forces cause the seesaw to rotate.
On the other hand, if you have two forces of equal magnitude acting in opposite directions at the same point, their torques will cancel each other out, resulting in a net torque of zero. This can occur, for example, when two people push or pull on an object with equal but opposite forces.