Serious Physics on a Playground Swing—With Toys, Your Own Body, and a Smartphone

What is the acceleration of a swing as it passes the lowest point and as it turns at the highest point? What are the forces acting? These were a couple of the questions students were asked to discuss in small groups during their first week at university, as part of a tutorial session. On one occasion, two students were unable to reconcile their different viewpoints without teacher intervention. One of them emphasized that the swing moves fastest at the bottom, and concluded that the acceleration must be zero. The other student claimed that there must be a force, since you feel heavier at the bottom. They noted the contradiction, but failed to recognize that acceleration is the derivative of velocity, not the derivative of speed: For the lowest point, the speed is maximum, but the direction of motion changes. These students had certainly been taught all the elements of physics needed to calculate the force and acceleration, but forgot to make the connection on their own. A small hint from the teacher, reminding them about centripetal acceleration, was sufficient.