How does the length of the Lever Arm effect Torque?

As you could see from the video, the door was more difficult for Lauren to push when she pushes it from the inner side of the door rather than the outer side. This concept goes back to the equation
T (torque) = r (lever arm) x F (force). When Lauren pushes the door from the inner edge, she is shortening the lever arm, which then requires more force to exert the same amount of torque. For example, if a very large door requires a torque of 100 NxM (newtons per meter) to move, and Lauren is pushing the door at 10 M from the fulcrum, Lauren needs to provide 10 N of force. However, to push the same door with a torque of 100 NxM from 2 M from the fulcrum, Lauren needs to provide 50N of force. So, it would make sense that it is easier for Lauren to push the door from the outside because she is extending the lever arm and requiring less force.

How does the Angle of Force effect Torque?

The angle of the force applied is important in measuring the amount of torque. A force that is applied perpendicularly to the fulcrum will provide the most torque. As the angle gets farther and farther from being perpendicular to the fulcrum, it exerts less torque. This goes to the point at which the force is applied directly towards the fulcrum, which, as stated below, exerts no torque.

How to Calculate Torque

Torque is calculated by multiplying the lever arm (or radius) by the force applied to the object.

               T = r x F

Center of Mass

What is the center-of-mass? How is it related to Torque?

The center of mass is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In relation to torque, when an object is supported at its center of mass there is no net torque acting on the body, it will remain in static equilibrium.
Below is a diagram to help you better understand.