Changes to a spinning skater's angular velocity

In summary, the conversation discusses the use of F=ma instead of L = constant to describe the change in angular velocity of a skater. It is suggested that a change in centripetal force can lead to a change in the skater's angular velocity, and that Newton's third law explains the resulting changes in the skater's motion.
  • #1
Rosenthal
2
0
Can we describe what is happening as the skater's angular velocity increases/decreases using F=ma rather than invoking L = constant?
 
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  • #2
Can you be more specific about "what" it is that is "happening"?
 
  • #3
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?
 
  • #4
Rosenthal said:
using F=ma rather than invoking L = constant?
Why would you want to?
 
  • #5
Rosenthal said:
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.
 
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1. How does a spinning skater change their angular velocity?

The angular velocity of a spinning skater can be changed by altering their moment of inertia or their angular momentum. This can be done by changing the position of their arms, legs, or body, or by applying external torques.

2. What factors affect a spinning skater's angular velocity?

The main factors that affect a spinning skater's angular velocity are their moment of inertia, angular momentum, and external torques. Other factors that may play a role include air resistance, friction, and the skater's body composition.

3. How does a skater's angular velocity change when they pull their arms in?

When a skater pulls their arms in, their moment of inertia decreases, causing their angular velocity to increase. This is due to the conservation of angular momentum, which states that the product of moment of inertia and angular velocity must remain constant unless acted upon by an external torque.

4. Can a skater change their angular velocity without changing their moment of inertia?

Yes, a skater can change their angular velocity without changing their moment of inertia by applying external torques. These torques can come from the skater's muscles, the friction between their skates and the ice, or other external forces.

5. How does a skater's angular velocity affect their stability?

A skater's angular velocity affects their stability by determining how easy it is for them to maintain their balance. Higher angular velocities can make it more difficult for a skater to maintain their balance, as they may have less time to react to external forces. However, skilled skaters can use their angular velocity to their advantage, using it to perform spins and other tricks.

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