We study the angular distribution of the radiation from a relativistic charged particle uniformly rotating along an equatorial orbit around a dielectric ball. Earlier it was shown that for some values of the problem parameters and in the case of weak absorption in the ball material, the radiation intensity on a given harmonic can be essentially larger than that for the same charge rotating in the vacuum or in a homogeneous transparent medium having the same real part of dielectric permittivity as the ball material. The generation of such high power radiation is a consequence of the constructive superposition of electromagnetic oscillations of Cherenkov radiation induced near the trajectory of the particle and partially locked inside the ball. The angular distribution of the number of the emitted quanta is investigated for such high power radiation. It is shown that the radiation is mainly located in the angular range near the rotation plane determined by the Cherenkov condition for the velocity of the charge image on the ball surface. The numerical analysis is given for balls made of strontium titanate, melted quartz and teflon in the gigahertz and terahertz frequency ranges.
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