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## Homework Statement:

- I am studying the following exercise from Gregory's CM book (chapter 17th, Example 17.2).

## Relevant Equations:

- Second law in a general non-inertial frame

**Some information**

Newton's second law in a non-inertial frame is given by:

Where:

1) ##A## is the translational acceleration, ##\Omega## the angular velocity and ##\dot \Omega## the angular acceleration (all relative to the inertial frame attached to the ground ##F##).

2) r', v' and a' are the position, velocity and acceleration vectors, all relative to the frame attached to the roundabout ##F'## (and thus ' has nothing to do with derivatives on above equation).

I am studying the following exercise from Gregory's CM book (chapter 17th, Example 17.2).

**Exercise statement:**

OK so I get that:

$$m \vec a = -mg \vec e_3 + \vec X$$

Where ##-mg \vec e_3## is the gravitational force the Earth exerts on the man and ##\vec X## is the normal force the roundabout exerts on the man.

I mathematically understand how we get the final equation for the normal force ##\vec X##,

**but I now want to understand the physics behind it.**

I understand that we expect to get a term due to the gravitational force, another to the centrifugal force and another to the Coriolis Force.

**But why are the last two negative? Why couldn't they be positive?**

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