Angular Momentum Conservation -- Rope Problem

[Electric to be]

Say there is a man swinging in space on a rope attached to a pivot. The man is rotating at some constant angular speed w.

Now he climbs up the rope at some constant speed v. Apparently the angular momentum is conserved. As a result his speed increases. However, how does his speed increase if there is no force in the tangential direction, because angular momentum is conserved and there can't be a force here as it would cause torque.I solved it

 

[pixel]

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[Electric to be]

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Basically as soon as the man starts climbing there is a component of velocity that is no longer perpendicular to the rope since he is climbing upward. As a result the tension force can do work and increase speed, however though the speed increases the force still points toward the origin and there is therefore no net torque.