# Is the spring “constant” still constant if the spring is circular?

Imagine a spring with a spring "constant" $$k$$ which is put on a part of a circular form, say a disc (a slice of a cylinder) with a groove around it to put the spring on. If we stretch the spring it doesn't slip off the disc and friction can be ignored.

What happens to the string constant? Will it get bigger (which is what I think), smaller, stay the same, or isn't it constant anymore?

• Why do you think it would be different than a spring of same length as the circumference? – Aditya Garg Jun 15 at 21:38
• I don't say it will be different, but I'm asking if it will be different. When you stretch a spring on a circular form it's not stretched in the same way as a linear string is stretched. – descheleschilder Jun 15 at 22:04
• What do you mean by circular form? – JMac Jun 15 at 22:18
• That the spring is wrapped, in part (in its "ground" state), around a circular disk, in a way that the spring doesn't slip off the disk when it's stretched. – descheleschilder Jun 15 at 22:34
• I can't think of a way to set this up where ignoring friction is a reasonable assumption, but I did want to point out that the spring constant has always been an idealization. Real springs have a spring constant that varies (oof... okay, I need new wording for that) – Cort Ammon Jun 15 at 22:35