I just read January issue of the Physics Teacher. There was an article ”Tension in a Pendulum String” in which a relationship between tension force and time was derived. Theoretical relationship was then compared with experimental results; agreement was very good indeed. There was, however, one feature in the article which made me wonder. The article stated that:
”In a simple pendulum the centripetal force on its bob causes the tension in the supporting string to be time dependent. The expression for the tension is the sum of the centripetal force and the bob weight component along the string...”.
Why talk about *centripetal force* as if it were something extra in the system? The same result can be easily derived using Newton’s II law. The component of the net force acting on the bob in the normal direction is given by (using appropriate sign convention):
tension - component of weight = mass * normal acceleration
I avoid using the term ”centripetal force” when teaching this topic to high school students. It may temptate students to believe that there is an extra mysterious force (mysterious because it is not due to any real interaction) acting on the bob. This belief is often manifested as an additional force in a free-body diagram. In addition centripetal force may give an idea that ”turning problems” are fundamentally different from ”straight line problems” in which Newton’s II law is applied.
A fictious centripetal force arises if a non-inertial reference frame is adopted. This approach is implicitly used in the article but I don’t see that it would make a situation easier to handle either from mathematical or conceptual point of view. Perhaps it would have been helpful to state explicitly that the chosen reference frame is non-inertial.
Antti Savinainen
Kuopion Lyseo High School
Finland