Hello!

I know that for an object at rest, in order to move it, first STATIC FRICTION must be overcome
(F= μ N), where μ is the coefficient of friction between the two surfaces. Afterwards, while the object is in motion, SLIDING FRICTION is the resisting frictional force.

However, is this the same for an object with wheels? Must the same STATIC FRICTION be overcome first? And then when in motion, ROLLING FRICTION becomes the resisting force? If so, is STATIC FRICTION for an object with wheels calculated in the same manner?

Essentially my question boils down to this:
If you had a block weighing 100 kilos, one with wheels (assuming the weight of the wheels to be negligible) and one without, would the STATIC FRICTION at rest be the same in both cases?

I'm quite rusty on my physics concepts and would appreciate any help.

 

In an ideal situation when rolling without slipping, a wheel does not actually move relative to the ground at it's contact point.
Therefore, the very short answer is 'no' - not the same.

 

If it is different is there any way of calculating the static friction, ie the minimum force required to move an object on wheels ?

Is it as simple as:

Force required to move object = (weight) * (coefficient of rolling friction)

(I'm designing a towing hook for a cart and wanted to make a conservative estimate of the force that would be applied on the hook)

Thanks again for your help

 

You're looking at the wrong interface. The wheel contact doesn't have to move relative to the ground. You have to look at the force required to turn the wheel instead.

 

Google 'rolling without slipping'. It should give you a good start. If you don't assume no slipping, you have to calculate twice (basically, you guess, and see if you're right), but assuming no slipping should give you a good approximation.

You're basically dealing with static friction at the wheel axle. The static friction at the ground gives you a reaction force. You have to generate a forward motion at the wheel center, assuming that the point in contact with the ground does not move.

 

Thank you for the suggestion, after reading I realised I had some misunderstandings with regard to the relevant principles. Just to clarify:

For a cart that is at rest, if a torque is applied to the wheel and it is less than the static friction, then it will initiate motion. Then using this torque the driving force applied (ie a push or pull) can be calculated.

However, some sources I read stated that the torque applied must, at the very least, be greater than that of rolling friction in order to initiate motion. While other sources stated that if the wheel and floor were both rigid, then any minimal torque is theoretically enough to initiate motion. Do you know know which is correct?

 

I believe that the 2nd is correct. Without slipping, the contact point has no motion, so you're not overcoming the friction. If you DO overcome friction, then you have some slipping, which complicates things a bit.

However, you can't apply any minute force and get motion. There is friction at the hub of the wheel that needs to be overcome.

Think of it all in terms of a free body diagram. Friction at the bottom of the wheel is a single force. It will not prevent the center of the wheel from moving. It will just create a moment when coupled with a force at the center, causing the wheel to spin.
However, friction around the hub creates a counter-moment to any spinning of the wheel.

So you have two choices if you want motion.
1. Either create a moment to spin the wheel (either a direct torque, or a force forward at the wheel center that couples with the friction reaction force at the wheel base) that is larger than the counter-torque of static friction at the wheel hub. You will then roll without slipping.
2. Create a force at the center of the wheel that is insufficient to spin the wheel, but is larger than the static friction reaction at the wheel base. The wheel will slide forward without turning.

Or you can end up with a combo:
3. A force that is larger than the static friction at the center of the wheel, AND the moment created is enough to spin the wheel. Then you will have motion that is a combination of rolling and slipping.

Usually, 1 is what you're going to get, with 3 happening if you push super hard. Otherwise, your wheels are pretty useless

 

Thank you very much this helped a lot! I do have one last question though, is there a method to calculate estimate friction around the hub/ counter moment to spinning wheels? Or perhaps some rules of thumb to make conservative estimates ?

 

Other factors to ponder, To go from not moving to moving you must accelerate, so mass of cart and accel must be factored in.
A real wheel on a real surface has "rolling resistance" Some of this is because the wheel and the surface deflect because of the weight, other source is hysteresis when the wheel flexes (rubber tire in this instance) Steel wheel on steel rail has low rolling resistance (That is advantage of a train) Wheel in soft sand is opposite case.

 

The system friction is going to depend on your system in question, but if you just have a wheel on an axle, I'd say an initial estimate could simply be mu*Normal Force*diameter of axle