Let me draw a diagram. If you want to swing the mass around with a lower angular velocity, the string will need to be longer. If you want a shorter string, the mass will have to spin around faster.

Spin Ball: The Physics of Polyester String By Ed McGrogan Feb 03, 2011. ATP London, Great Britain. Brits Katie Boulter, Emma Raducau score wins at Queen’s Club Jun 10, 2025. Facts & Stats.

As the ball moves, the tension remains perpendicular to the direction of ball. This means that the angle θ is 90 degrees and the cosine of 90 degrees is zero. See?