Changes to a spinning skater's angular velocity

[Rosenthal]

Can we describe what is happening as the skater's angular velocity increases/decreases using F=ma rather than invoking L = constant?

 

[kuruman]

Can you be more specific about "what" it is that is "happening"?

 

[Lnewqban]

Welcome!
"When a body is acted upon by a force, the time rate of change of its momentum equals the force."
Would you explain the meaning of L to us?

 

[Vanadium 50]

using F=ma rather than invoking L = constant?

Why would you want to?

 

[jbriggs444]

Can we describe what is happening as the skater's angular velocity increases/decreases using F=ma rather than invoking L = constant?

Yes. We could. For instance, we could consider a force of each hand on the other (mediated through the arms and body). In the starting configuration, this centripetal force is sufficient to accelerate each hand in its circular path around the axis of the skater's body. $F=ma$ is upheld and the hands circle as predicted.

We could consider what happens if that centripetal force is increased. The skater pulls her arms in. Now the hands accelerate inward more strongly than their previous centripetal acceleration. They assume an inward spiral trajectory. $F=ma$ in the radial direction conforms with this and predicts the result.

Significantly, in the absence of any resisting tangential force from the body, the hands would retain their original tangential velocity. With a new position nearer to the axis of the skater's body, the retained tangential velocity means that the hands would then have an angular velocity greater than that of the rest of the skater's body. Again, this would be consistent with $F=ma$ in the tangential direction together with the supposition of zero tangential force.

But the arms resist that relative motion with a rearward tangential force. This force decellerates the hands in their tangential motion around the body. Again, $F=ma$ is upheld and predicts the observed result.

Newton's third law means that the body is subject to forward tangential force from the hands. The arms are accelerated and acquire a greater tangential velocity as a result. Again, $F=ma$ is upheld and predicts the more rapid rotation of the skater as a whole.