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We develop a theory of terahertz emission from a slab of a magnetooptic material traversed by a circularly polarized femtosecond laser pulse. The Cherenkov-type radiation is generated by a moving region of ultrafast magnetization optically induced in the slab via the inverse Faraday effect. A prism is used to couple the radiation from the slab to free space. Our theory accounts for transient effects at the slab boundaries and shows their significance for the interpretation of the terahertz waveform emitted from the slab. The theory predicts detectability of the radiation generated by a mJ-level laser pulse in a terbium gallium garnet slab covered with a sapphire prism.