Explaining faster spinning without using conservation of angular momentum

Question

Lets take a very big rotating star ,after the finish of the nuclear fuel the star is going to contract under its own gravity.Now to conserve its angular momentum the star is going to rotate faster.

• But how will you explain it in terms of force without involving the concept of torque and angular momentum (Intuitively)?what forces helped to rotate the star faster?

• If you do not like to think about a star,think about twirling ice skater who pulls her arms?

Edit:Let me add here,this is actually a question from the famous book ,The flying circus of physics,and the author is saying the ans is coriolis force. But I did not get it

Answer 1

The Coriolis force is $$F_c = -2m\Omega \times v$$ If your object is moving inward towards the center of the star or dancer's body, then a quick application of the right hand rule indicates that the force is in the $\hat{\phi}$ direction, i.e. east or west, which implies that the force is pushing tangentially on the object, giving it an angular acceleration and helping it rotate faster. I'm not sure I really like that way of thinking about it though, since the Coriolis force is a fictitious force.

Really, you can explain the increase in speed just through the central force in question, whether gravity or the skater. If you have an object moving in a circle, then the central force can't make it move faster or slower because the force is always perpendicular to the object's motion. but if the circle that this object is moving in is contracting, then that something is then no longer moving in a circle, and the central force itself can change the magnitude of the speed of the object, helping it rotate faster.

Answer 2

Here is an intuitive explanation of the rotational force that speeds up an ice skater's rotation upon contracting her arms:

When an ice skater contracts her arms, what she really is doing is contracting her arms radially along a straight line in her own reference frame. However, since her own reference frame is rotating, what she perceives as radial motion in a straight line, is actually curved motion in the inertial non-rotating frame. That is, when the ice skater contracts her arms radially in a straight line, they are actually not traveling along straight lines in the non-rotating frame (see if you can convince yourself of this fact), which means a sideways force must be exerted on her arms to accelerate them in absolute space. She herself must exert this sideways force on her arms when contracting them in, since she and her arms form an isolated system.

Even though she perceives the motion of her arms as along a straight line relative to her, she finds that in order to actually execute this motion in her reference frame, she has to also push her arms sideways with her body when contracting them. Thus, she concludes that there must be a mysterious pseudoforce in her rotating frame that pulls all radially moving objects sideways! This is precisely the Coriolis force (this is incidentally where the Coriolis force comes into play in this whole discussion).

Now, let's look at what happens in the non-rotating frame. Because we know that the ice skater has to push her arms sideways using her body, her arms in turn must exert an opposing tangential force on her body, by Newton's Third Law. This then causes her body to pick up angular speed and spin faster, and this is exactly what we observe!

That is the real fundamental explanation using forces. I hope this is helpful!