In this context, "banking" has nothing to do with money!


It refers to the process of tilting a road surface at a certain
angle to make it less likely that vehicles will skid or slip across
the road when going round a curved part of the road. 



Moving in a Straight Line at Constant Speed 




No problem. 



No tendency to skid off the road. 







Turning on a Horizontal Surface 




In order to follow a curved path, there must be a centripetal force to
provide the necessary acceleration. 



This cannot be provided directly
by R or mg because they both act at 90° to the required
direction (and can therefore have no components along that direction). 



Therefore the required centripetal
acceleration must caused by
the force of friction, F_{f} between the
wheels and the road. 



If the
force of friction is not strong enough, the vehicle
will skid (it will "try to" keep going in a straight line in accordance
with Newton's first law of motion). 



Turning on a Banked Surface 




The normal reaction, R, now
has a component acting towards the centre of the circular path. 



If
the angle, θ is just right, the correct centripetal acceleration
can be provided by the horizontal component of the
normal reaction. 



This means that, even if there is very
little force of friction, the vehicle can still follow the curved path with
no tendency to skid across the road. 








In this diagram, the normal reaction force has been resolved into two
perpendicular components, the vertical component, of magnitude given by 



and the horizontal component (causing the acceleration), given by 







We will now find an equation to calculate the angle needed for a vehicle to
follow the curved path with no tendency to skid. 

Note that this angle will, of course, only be exactly right for a given speed
(because the centripetal acceleration required depends on the speed
of the body). 

As stated above 



but R_{h} must also be given by 



Therefore we have 


equation 1 


The vertical forces are in equilibrium so, considering
magnitudes only, we can write 


equation 2 


Dividing equation 1 by equation 2 gives 



from which the angle required can be calculated. 
