The mysterious centripetal force

Last week I came face to face with another physics misconception with some of my students. I do think that, as I get more experienced teaching, I’m getting better at picking up on where students are having problems. But it’s a very difficult thing to do.

Last week it was circular motion The students were looking at a fairly simple problem (well, I thought so, they are third year mechanical engineering students after all). In a nutshell, it’s this: Imagine you have a T-shirt in a spin dryer (top loading). If you know the coefficient of friction between the T-shirt and the wall of the drum, and the drum’s radius, you should be able to work out the minimum rotation speed for the T-shirt to stick to the wall of the drum, rather than slide down to the bottom. So, what is it?

As with all force problems, a good way to start is by drawing a free-body diagram, where we put in arrows for every force acting on the body. The total of these arrows (added as vectors), or the net force, is just the mass times acceleration, by Newton’s 2nd law. So, I put a sketch on the board and asked the students to tell me what forces are acting on the T-shirt.  There is of course gravity on the T-shirt. That’s balanced by the frictional force of the wall on the shirt (otherwise it would slide down.) Then there’s the inward force exerted by the reaction of the wall on the T-shirt. Now, that’s all the forces there are. I could have just carried on with the analysis,  but instead I asked the class whether that was it  "Have we got all the forces?"  I expected a ‘yes’ answer, but a student gave me the response "There’s the centripetal force as well." 

There’s a clearly a misconception about circular motion buried in that comment.   Yes, there is centripetal force, but it’s the reaction of the wall on the T-shirt that provides this force. We’ve got it already. The centripetal force isn’t an ‘extra’ force – that would be counting it twice. This is a tricky concept to present clearly. The best I can manage now is that it’s the fact that there exists a force towards the centre of rotation that CAUSES the object to move in the circle, not that the fact that an object moves in a circle causes it to have a centripetal force. 

Centripetal force is not a ‘magic’ force, that mysteriously appears when you turn corners. There is always a very physical force that provides the centripetal force, whether it’s the tension in a string (for whirling a mass-on-a-string) around, friction from the road on your car tyres (for driving a car around a circle), the lift force from an aeroplane’s wings (for an aeroplane banking) or gravitational attraction (for the earth orbiting the sun).

I’m not sure I did a great job during class of explaining this, but at least I know now to look out for this misunderstanding with students in first year. And it also demonstrates that if you don’t ask questions of the students, you really don’t have a clue what they are thinking.

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