Calculating Torque on a Shaft: What Factors Need to be Considered?

[2slowtogofast]

This is more of a general question i want apply to a problem i am working on. If i was standing on a cart with four wheels an i am holding a string that is wound around the axel of the back wheels. So as i pull the string it unravels around the back axel turning the axel and moving the cart. I want to find the tourque that this is putting on the axel. So i am looking for some advice on how to attack this. I would know how much force i am pulling up on the string with. but would i also need to know the mass moment inertia of the wheels and the friction between the wheels and the ground so i know what i have to over come to get the cart moving. Because right when i start pulling on the string its going to put a greater torque on the axel because it has to overcome static friction and inertia but then once it is moving the torque will be less because the only thing resisting motion is kinetic friction. So i am looking for ideas on how to model this.

 

[Danger]

I'm not one for formlae, but it seems to me that you can easily determine your answer by working out what is required to move both you and your support structure for a given distance.

 

[K^2]

You only need to know moment of inertia if you want to know acceleration rate. Realistically, the two main sources of torque will be you pulling on the string and rolling resistance.

So are you trying to measure or predict the results? If former, all you need is the force with which you pull the string and diameter of the axle. If later, you need a way to estimate the rolling resistance, which you'd do by estimating deformation of the surface and/or wheel under the total weight.

 

[gneill]

This is more of a general question i want apply to a problem i am working on. If i was standing on a cart with four wheels an i am holding a string that is wound around the axel of the back wheels. So as i pull the string it unravels around the back axel turning the axel and moving the cart. I want to find the tourque that this is putting on the axel. So i am looking for some advice on how to attack this. I would know how much force i am pulling up on the string with. but would i also need to know the mass moment inertia of the wheels and the friction between the wheels and the ground so i know what i have to over come to get the cart moving. Because right when i start pulling on the string its going to put a greater torque on the axel because it has to overcome static friction and inertia but then once it is moving the torque will be less because the only thing resisting motion is kinetic friction. So i am looking for ideas on how to model this.

If all you want to know is the torque applied to the axle for a given pulling force (tension)
on the string, then that's easy:

t = F * R

where R is the radius of the axle shaft. This works because the string is always tangential
to the axle (making a 90 degree angle with a radius vector) and the lever-arm for the
applied force is radius of the axle.

As for determining the resulting motion of the cart, you'll need to do some thinking about
what the wheel having a different radius than the axle will do the the torque as it is
'translated' to a ground force. Friction may also rear its head...