# Why are constraint forces assumed to be perpendicular?

In Taylor, it is assumed that the constraint forces are perpendicular to the constraint surface. I am kind of wondering what the justification for this is. Sure, if you mention typical constraint forces (normal force, tension force), they are perpendicular to the motion of the particle. One thing I can think of is that this way, the constraint forces do no work (not sure why that would be desirable though). So, what is the motivation for this assumption in the context of Taylor?

• If the configuration were to move tangentially to the constraint surface then the constraints will continue to hold and there's no need for a force to act... – lemon Oct 20 '17 at 15:56
• Hm ok, I think I get it. The constraint force is the force that keeps the particles confined to the constraint surface - so if a constraint force would have a tangential component, then it wouldn't just be acting as a constraint force. But most importantly, the constraint force has to 'oppose' the particle's motion perpendicular to the surface, while there is no need for that in the parallel direction. Ok yea I got it, thanks! – Sha Vuklia Oct 20 '17 at 16:15
• In general it is false. There is nothing to prove, it depends on the physical situation. A point moving on a surface generally experiences friction constraint forces that are tangent to the surface. – Valter Moretti Oct 20 '17 at 16:38
• Also forces like those due to rigidity constraint are not normal to the motion of the system, though they are not due to friction. – Valter Moretti Oct 20 '17 at 16:41
• @ValterMoretti If the object is free to move in the plane friction acts on, how is friction constraining it? – JMac Oct 20 '17 at 17:07