Centripetal Force Acting on a Belt and Pulley System Just a warning: I am an A Level student looking for a simple but thorough explanation. I am happy to be introduced to new ideas, but a sesquipedalian answer with formulae that aren't derived will only confuse me further.
This question concerns a past paper question given to me for a topic test on Circular Motion. I did ask my teacher about this but they weren't sure. The question asks about the following diagram of a washing machine:
 
The question is this:

When the motor speed is increased, the belt can start to slip on the motor pulley. Explain why the belt slips. [2]

The marking scheme is:


*

*the belt tension is insufficient to provide the centripetal force

*so the belt does not 'grip' the pulley/does not hold the belt against the pulley/there is insufficient friction to pull/push/move the belt.

alternative argument:

*

*the belt does not 'grip' the pulley/there is insufficient friction to pull/push/move the belt

*because of its inertia/insufficient to provide force for acceleration of (belt)-drum


My question(s) are:

*

*Where does circular motion apply in this question? I am assuming it is referring to the section at X that is in contact with the motor. This section would be moving in a circle about the motor for the duration of its contact.

*What provides the centripetal force required for this circular motion? I am thinking the friction must cause the belt's movement, but this force is tangential to the circle (not towards its centre). The only explanation I can think of is that the force caused by the elasticity of the belt causes the centripetal motion as this seems like it would act towards the centre at all times. But the mark scheme clearly says the centripetal force is provided by the friction. I just don't see how the friction can be acting towards the centre of the circle.

*This is a question I thought of when trying to think of the answer (I'd imagine they're somehow related): Consider an elastic band tightly wrapped around the full circumference of a tennis ball. When the ball rotates about its centre, the elastic band rotates with it. What is providing the centripetal force for the particles in the elastic band that are moving in a circle? Is there something about friction on curved surfaces that explains this?

I have researched this but cannot find anything explaining this in terms I can understand. I apologise in advance if I have missed anything. I've been thinking about this for a while now and can't find the solution.
I'm sorry if I've asked a simple question, but I would be most grateful to anyone who could provide an intelligible answer. Thanks in advance to anyone that does.
Also, please do let me know if there is an error or if I have missed something. This is my first time asking a question, so I apologise if I've inadvertently broken a rule.
Question Paper: https://papers.xtremepape.rs/OCR/AS%20and%20A%20Level/Physics/Physics-A-158-558/2007-Jan/A_GCE_Physics_A_2824_01_January_2007_Question_Paper.pdf
Mark Scheme: https://bengoad.co.uk/userfiles/file/ffe_07_jan_ms.pdf
 A: *

*The circular motion applies to the part of the belt that is in contact with the motor pulley (there is a similar section undergoing circular motion on the drum pulley also).


*the centripetal force is provided by the tension in the pulley. Calculus is required to calculate the precise inward force resulting from tension in a circular section of a belt - but it may be easier to look up hoop stresses as they follow the same maths. The tension is locally always tangent to the pulley but, as you move arount the circumference, the direction of that tension changes and there is a resultant force that is radially inwards and provides a centripetal force so the belt follows a cirular path. Note that the radial inwards force is typically larger than the centripetal force required for circular motion. For example, even when the belt is static on the pulley there will still be an inwards (centripetal) force. When in motion, the excess inwards force over the ~v^2/r part necessary for circular motion is the part that produces friction. That is to say - the belt will apply a force inwards on the pulley which results in a circumfrential tension in the belt.  The following is an 'armwaving' picture of how that works. Note that if the tension in the belt was reduced to zero while it was moving (for example if you cut the belt into lots of tiny pieces), then each piece of the belt would undergo linear motion. Or if you just reduced teh tension so it was only just enough to keep it in circular motion then there woul dbe no excess inwards force to provide friction and the belt would slip.



*yes - the same forces are in action. Once again, I suggets you look up hoop stress (it is almost exactly the same thing except that in hoop stresses a radial force induces a tension rather than a tension inducing a radial force).

A: Quick answers. 1. Circular motion applies to the sections of the belt turning around the pulleys. 2. and 3. Centripetal force is provided by tension in a bent (curvature radius is finite) elastic medium.
Brief description of the physical phenomenon
Without any formula:

*

*you need tension in the belt: when you provide some tension to a elastic component that is rolled up around a pulley, each section of belt acts with a locally normal elementary force on the pulley which reacts with a normal force to the section of the belt in contact with it;


*this normal reaction is needed to get the tangential force by friction


*when you make the pulleys rotate, the normal force acting on the belt must equilibrate the centrifugal force on the rotating section of the belt as well (it's like you in a car, when you turn the steering wheel on the left and the car turns to the left, you feel an "apparent" force to the right; the same here for the belt turning around the pulley, that feels a force towards the outside that reduces the reaction between the belt and the pulley)


*if the pulleys start rotating very fast, the apparent centrifugal force could be so strong that the normal reaction between tjhe belt and the pulley becomes so weak that it can sustain friction and thus any change in the rotational speed (acceleration) without friction
