(Solved): A mechanical speed control system works on the basis of centrifugal force, which is related to ang ...

A mechanical speed control system works on the basis of centrifugal force, which is related to angular velocity through the formula of \( \mathbf{F}=\mathbf{m} \mathbf{r} \mathbf{w}^{2} \), where \( \mathbf{F} \) is force, \( \mathbf{m} \) is the mass of rotating weights, \( \mathbf{r} \) is the radius of rotation, and \( \mathbf{w} \) is the angular velocity of the system. The following values are measured to determine \( \mathbf{w} \); \( r=25 \pm 0.025[\mathrm{~mm}] ; m=150 \pm 1.0[g] ; F=1000 \pm 0.1 \%[N] \). Find the rotational speed in rpm an its absolute uncertainty?