[Physics] Radial Force Understanding

forcesnewtonian-mechanicsrotational-dynamics

I am having trouble understanding how radial force works. I am working in a dynamics course so there's always centripetal acceleration.

My difficulty comes from two cases.

  1. Analyzing a car traveling over a hill, it crosses the peak at maximum possible speed (Normal force is 0 N). Here my professors vector diagram had only weight downwards and no radial force.

  2. A helical slide, having a person traveling down. Here I was asked to work out a radial force which is equal to $mv^2/R$.

My question is why was there no radial force included when the car traveled over the top of the hill, why there is a radial force in case 2 and most importantly, when will there be a radial force?

Best Answer

I consider it helpful to include the phrase "... acts as central force" when talking/thinking about such problems.

There are many forces (gravity, tension in a string, ...) that may or may not act as a central force.

Considering your examples:

  1. Crossing the hill (in the shape of a circle?): An object moves along a circle only if a constant central force is acting on it. Here it is gravity. Gravity always acts on an object on earth and when it's gravity that's keeping the car on the ground on a circular road, gravity acts as central force. One could draw two arrows in the diagram (one for the gravitational force and another one for the central force), but that might be confusing because they are the same thing.
  2. Helical slide: here gravity does not help that much. But there must be a central force because we see the circular motion. Here it's a little bit more complicated: the person exerts an outward force on the outer wall because it "is in the way". The wall therefore exerts a force of equal magnitude and opposite in direction on the person (Newton's third law). This force acts as central force because it points to the center of the helix and forces the person on the circular path. On could draw several arrows in this situation: force of person onto the wall (outwards), reaction force of wall onto person (inwards), central force (again the same thing as the reaction force).
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