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The Fundamental Equation of Dynamics

Problem 1.115

A small body of mass \(m=0.30 \mathrm{~kg}\) starts sliding down from the top of a smooth sphere of radius \(R=1.00 \mathrm{~m} .\) The sphere rotates with a constant angular velocity \(\omega=6.0 \mathrm{rad} / \mathrm{s}\) about a vertical axis passing through its centre. Find the centrifugal force of inertia and the Coriolis force at the moment when the body breaks off the surface of the sphere in the reference frame fixed to the sphere.

Reveal Answer
 1.115. Fcf=mω2RV5/9‾=8 N,Fcor =2/smω2R5+8g/3ω2R==17 N\begin{aligned} &\text { 1.115. } F_{\mathrm{cf}}=m \omega^{2} R V \overline{5 / 9}=8 \mathrm{~N}, \quad F_{\text {cor }}=2 / \mathrm{s} m \omega^{2} R \sqrt{5+8 g / 3 \omega^{2} R}=\\ &=17 \mathrm{~N} \end{aligned}
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