I have a formula which is $\text{G-force} = \frac{v\omega}{9.8}$, where $v$ is speed and $\omega$ is the angular velocity. I've seen on the internet that G-force is actually $\text{acceleration}/9.8$. I'm confused as to which formula is correct. For simulating the motion of particle taking a turn, would omega simply be velocity divided by radius of turn? Assuming Cartesian coordinates.
Another funny thing I noticed is that while simulating particle motion, a 7G turn showed up as an almost straight line (while using a constant turn motion model) with a velocity of 900m/s and time interval of 1second. Am I simulating wrong or is my use of the first equation wrong?
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The g force is a unit of acceleration. 1 g is equal to 9.80665 m s-2. So the correct formula is $$ \text{G force} = \frac{\text{Acceleration in m s}^{-2}}{9.8}. $$ However, when describing uniform circular motion (i.e. $\boldsymbol\omega$ is constant) in free space, the only acceleration felt by the person rotating (in their frame of reference) is the centrifugal acceleration, which is exactly $$ a = \frac{v^2}r = v\omega = \omega^2 r,$$ so the first expression is also correct for centrifugal acceleration of uniform circular motion. (If the motion is not a uniform circular motion, only $a = \omega^2 r$ can be used to describe the centrifugal acceleration.) (I don't know how do you get the 7 g.) |
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