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Definition of Inertia:
Inertia is the property of an object that describes its natural tendency to keep on doing whatever it is doing.
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An object in motion will continue in motion with the same speed and direction unless acted upon by an unbalanced force. If your are driving a car upward toward the crest of a hill, then the direction of your motion is upward (probably at an angle). As your car makes a turn over the crest of a hill, it is your tendency to keep on traveling along the upward trajectory. This is inertia - the tendency of an object to keep on doing whatever it is doing. If you were to try this driving feat at high speeds (not suggested), then you would likely feel your body lifted off your seat. A force is not needed for this to be accomplished. After all, straight line motions do not require a force. To stay on the curve of the hill, a force would be required. Thanks to gravity, you are pulled downward towards the center of the curved hill and are able to travel along the curved path.
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Try this: Draw a circle and put a dot on the circle at the 10:30 position. The top section of the circle represents the curve of the hill and the dot represents your location as you approach the crest of the hill. Draw a straight line tangent to the circle at this position (it would be directed up and towards the right). Observe that the tangent line is directed away from the center of the circle. This is the direction which you tend to move as you approach the crest of the hill. But you would never need a force to move in this straight line direction; it happens naturally. To stay on the circular path, you would need a force directed towards the center.
There is no need to believe in the notion of a centrifugal force. Centrifugal is an adjective which means outward. The incorrect conception is that a force pushes the passengers in the outwards direction. But don't be fooled! There is no such outward force. The sensation of moving outwards is simply explained by an object's tendency to continue moving straight. Your diagram makes this clear (I hope).
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