Lean Angle
When you ride a bicycle or a motorcycle, to stay balanced means to keep the contact patch where the rubber meets the road, directly beneath your center of gravity. However, when rounding a turn you must lean. As the rider, there is a clear sensation of being pushed outward by the centrifugal force. This is because to you the rider there is a component of effective gravity pointing outward that has a magnitude exactly equal to the centripetal force.
How then should we find the needed lean angle for a given turn? Simple! Effective gravity tells us which way is 'down'. The wheels need to be under you in that direction. Look at the diagram below. From the angle we can easily see the connection between gravity, the centripetal acceleration and the lean angle.