The very process of cutting a record takes care of the difference in linear track velocity across the disc by laying down undulations whose timings precisely match the sounds they are intended to reproduce. However this doesn't really answer the question of how this occurs.
We need to think of frequencies recorded in terms of angular velocity rather than linear velocity. For example, if we want to record a sine wave at 440Hz on a record rotating at 45RPM, for every full rotation we will cut 586.6 cycles, or 1.63 cycles per degree. At the outer edge of a 30cm record, a one degree arc has a length of 2.62mm, therefore one cycle of the 44oHz tone will be recorded over a linear distance of 1.6mm. If we now move half way towards the spindle, a one degree arc has reduced to a length of 1.31mm, and the 440Hz single cycle is recorded in a linear length of 0.8mm.
The downside to this is that becuase the linear velocity reduces as the stylus makes its way to the centre of the record, more information is crammed into an ever decreasing space. The effect to the listener is that audio quality reduces, it is more difficult to faithfully reproduce high frequencies at the centre of a record, and distortion created by surface irregularities in the groove shift closer to audible frequencies.