This question already has an answer here:
A block tied to a string is rotating with an angular velocity $\omega$ on a frictionless table. The string passes through a hole in the center of the table. If the string is pulled and the length of the string reduces to half, find the new angular velocity of the block.
I know this question can be easily solved using conservation of angular momentum of the block because no external torque acts on it. The answer to this question will be $4 \omega$.
What I wanted to know was that why would the the speed change at all? The tension due to string acts perpendicular to the direction of motion so it cannot change the angular velocity. So which force changed the angular velocity of the block??