0

I am trying to understand angular momentum in the same visceral way that I understand linear momentum, e.g., if someone rolls a bowling ball towards me then it is “natural” to me that I must apply a force to divert its path. It’s a little more mysterious that I encounter resistance when I apply torque to the axle of a spinning bicycle wheel.

If I imagine a point mass m rotating on a mass-less rod a distance r from its axis, I understand that I am to take the cross product of r and mv to get the angular momentum vector, but in my readings, this fact always seems to be presented without further explanation.

If I think about what’s going on with this system’s linear momentum, I would predict that it would wobble around as mv changed. In this case, when I apply torque, I think that I can see that I am trying to change mv and the resistance I would encounter is explainable in sort of the same way as the bowling ball above. Am I on the right track with this example? I note that if I add a second mass π radians from the first at the same distance, the linear momentum of the system disappears, but the angular momentum doubles. Should I explain that in this case that I should ignore the total momentum and that I am applying force separately to the 2 mvs?

Qmechanic
  • 201,751
JohnBR
  • 87

1 Answers1

0

The dynamic properties of a spinning body can be understood in a visceral way, but not in the same way as for linear momentum.

In the case of linear momentum the principle one must have in mind first and foremost is the principle of relativity of inertial motion. When you take the case of an object in inertial motion you have the freedom to consider the motion of the object as seen from a co-moving point of view. You imagine yourself co-moving with that object.

In terms of this initially co-moving coordinate system the object is initially stationary. You can subsequently deliver an impulse to the object, and thus cause a velocity with respect to the initial coordinate system.

The principle of relativity of inertial motion gives that there is no inherent distinction between diverting the path of an object and accelerating from a standstill position. The two cases look different, but underneath they are one and the same case.


In the case of a bicycle wheel (or any wheel, or any object) that is rotating, we have that the parts that constitute the object are continuously in accelerated motion. The parts of the wheel are in sustained circumnavigating motion with the structural integrity of the object providing the centripetal force. The involvement of accelerated motion puts the case outside the realm of relativity of inertial motion.

So that is a big difference:
- Linear momentum: for understanding of that the principle of relativity of inertial motion is central.
- Angular momentum of a spinning wheel: not in the realm of relativity of inertial motion.


How to understand the dynamic properties of a spinning wheel is discussed by me in an answer here on stackexchange to a question titled: What determines the direction of precession of a gyroscope?

Cleonis
  • 20,795
  • I am trying to understand angular momentum in [a] visceral way. Go to a playground and find a merry-go-round with a radial handle. Try rotating it by pushing on the rim, and by pushing on a point halfway along the radial handle. It will be easier to rotate it when you push farther from the center. This will give you a visceral understanding of torque, which is what it takes to change angular momentum. – G. Smith Feb 22 '20 at 22:27
  • @G.Smith The OP is asking about the following: " [...] I encounter resistance when I apply torque to the axle of a spinning bicycle wheel." That is, the OP is not asking about spinning up a wheel. The OP is asking about applying a torque such that it forcefully changes the orientation of the spin axis. – Cleonis Feb 22 '20 at 22:56