Let me change the person in the chair, for a mass attached to a string. Take a look to escalar definition of angular momentum $L=r\, p = r \, mv$ where $r$ is the string longitude and $p$ is the mass linear momentum. The angular momentum is a conserved cuantity. Then if, the string longitude changes, the linear momentum have to changes too for maintain the angular momentum as at the first. ($\omega = \frac{v}{r}$)

Let me change the person in the chair, for a mass attached to a string. Take a look to escalar definition of angular momentum $L=r\, p = r \, mv$ where $r$ is the string longitude and $p$ is the mass linear momentum. The angular momentum is a conserved cuantity. Then if, the string longitude changes, the linear momentum have to changes too for maintain the angular momentum as at the first. ($\omega = \frac{v}{r}$) The force that you are looking force is exerted by the boy, because he is changing the movement radius thus the centripetal acceleration.