# moments about two points of an object

**1. The problem statement, all variables and given/known data**

hi guys this is an image of the rear wheel of a push bike going into a corner as well as what i think are relevant forces,

i need to calculate the moments or torque at A (the contact patch) and B (the hub centre)

this is to calculate the force on the left hand side of the frame and right hand side of the frame while in a corner

Fsr = the force going through the suspension

Fc = lateral cornering forcer on the rear wheel

phi = lean angle

MG = mass & gravity

t = the cross sectional radius of the tyre

CoG(y) = centre of gravity height

**2. Relevant equations**

this is my question what is the relevant equation to find the moments for A and B??

i can and have calculated the above parameters through lot of prior equations that take into account the wheelbase, velocity, friction, radius of the turn ect. but i think that the above are the require ones to calculate this… if there is an easier way please let me know

i said thought im not 100% these are the relevant forces but i am fairly confident also to point out this is assuming that it is a 2d diagram should be a simple moments equation really (i think) also it can be assumed the bike is stationary and that it is simple leant over with a machine applying the forces if it makes it easier to calculate…

thats the torque or moments about point A ( contact patch ) and B the wheel spindle centre

but any help would be great whether in motion stationary or anything, if you ignore the forces i have written and know another way very happy to listen to that too thanks alot

**3. The attempt at a solution**

ive tried looking at the centripetal forces as uniformaly distributed loads, along the height of the bike,

ive tried looking at it as basic moments but as the main force im considering (Fsr) is going from CoG to contact patch through A&B the torque would equal 0

and ive also tried looking at it as though Fc (cornering force) is acting at the CoG this gave moderatly good results but exceed the torque of A in regards to MG meaning the bike would be rolling and self righting as such the bike would not be in equilibrium so also wrong

there are no definitive numbers to input as it would take the best part of an hour if i gave all prior equations, forces, geometric aspects velocities ect. but if you could tell me what i need and where i need to be looking (if you could explain your reasoning too would be useful) i will figure the relevant forces ect. myself… thanks very much guys

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