A video of this demonstration is available at this link.

You can use the door to the demonstration preparation area to show how, for a given applied force, the magnitude of the torque you exert changes according to where, and in what direction, you push (or pull) on the door.

Torque is a turning or twisting motion. In the case of a door, it is the rotation of the door about its pivot, the hinges. This torque, τ, equals r × F, where r is the displacement vector from the hinge to the point at which you are pushing on the door, and F is the force you apply at that point. The magnitude of the torque is rF sin θ, where θ is the angle between the vectors r and F. By pushing at different places on the door, and by pushing or pulling on the door in different directions, you can vary r, the distance along the door, and θ, the angle at which you apply the force to the door. sin θ goes to 1 as you approach a perpendicular angle to the door, and it goes to 0 as you approach the line along the door (from the door edge to the hinge). This varies the magnitude of the component of the applied force that contributes to the torque.

Torque is often called the moment of force, and r sin θ, the perpendicular distance from the hinge to the point at which you are pushing or pulling on the door, is the moment arm. If you are pushing or pulling the door along a line that is perpendicular to the door, then sin θ = 1, and the moment arm is r.

You can, of course, either apply a constant force at different places and in different directions, or attempt to keep the torque you apply constant and show how much greater force you must apply to do so when r is small or when sin θ is small (or that it is impossible to do so when r or sin θ is 0).

References:

1) Resnick, Robert and Halliday, David. Physics, Part One, Third Edition (New York: John Wiley and Sons, 1977), pp. 231-233.