Mr.p: Good morning.
Let's start with me sitting on a stool
which is free to rotate around a vertical axis through the center of the stool
There is no net external torque acting on the stool and me system,
so angular momentum of the system is conserved.
Initial momentum of the system is zero, so as much as I wave my arms and legs around,
I cannot cause the system to rotate because the angular momentum of the system will stay zero.
"Flipping Physics" Intro
However, if I am holding a spinning wheel, the wheel has an angular momentum
and if I rotate the spinning wheel by applying a torque to it,
the spinning wheel will apply an equal but opposite torque back on me, which will cause me to rotate.
Now realize, the angular momentum of the system is still conserved
because the two torques, which are equal and opposite, will cancel one another out
and results in a net torque on the system of zero.
In other words, both of these two torques,
the torque I applied to the wheel and the equal but opposite torque the wheel applies on me,
are internal to the person, chair, and wheel system.
Now, let's do a problem. Bo, please read the problem and Bobby, please translate.
A person is holding a spinning wheel while sitting on a stool which is free to rotate.
If the person rotates the wheel 180 degrees about a horizontal axis,
in terms of the initial angular momentum of the wheel,
what is the final angular momentum of the person and stool? (assume no friction)
Bobby: Okay. We already showed that about a vertical axis of rotation through the centre of the stool
angular momentum is conserved.
Because the stool and persons start out with zero initial angular velocity
and angular momentum of a rigid object with shape equals rotational inertia times angular velocity,
the initial angular momentum of the person and stool is zero.
We are solving for the final angular momentum of the person and stool
in terms of the initial angular momentum of the wheel.
So final angular momentum of the person and stool equals
x times the initial angular momentum of the wheel, where x equals question mark.
Bo: Ya know, you did not do anything with the fact that the wheel is rotated by 180 degrees. Right?
Bobby: Right...
Billy: Oh that means the final angular momentum of the wheel
equals the negative of the initial angular momentum of the wheel.
Bobby: Right! The final angular momentum of the wheel will have the same magnitude
because nothing will be slowing it down, however,
it's angular momentum will be opposite in direction form where it started,
which is why the negative is there.
Bo: Right. So when we use the right hand rule,
you can see the wheel initially has an upward angular momentum.
And after being rotated 180 degrees, the wheel has a downward angular momentum.
Billy: Oh and conservation of angular momentum
means the initial angular momentum of the wheel plus the initial angular momentum of the stool and person
equals the final angular momentum of the wheel plus the final angular momentum of the stool and person.
The initial angular momentum of the stool and person equals zero
and the final angular momentum of the wheel equals the
negative of the initial angle momentum of the wheel.
Add the initial angular momentum of the wheel to both sides and, voila!
The final angular momentum of the stool and person equals
two times the initial angular momentum of the wheel.
Mr.p: That was really great. Notice there is an interesting result to our solution,
the direction of the final angular momentum of the stool and person
is the same as the direction of the initial angular momentum of the wheel.
But the interesting piece is that, this is true regardless of the direction the person rotates the spinning wheel.
Bill: I'm sorry, what? Bobby: Umm.
Bp: Okay, I'm sorry. Wait, wait wait. When we look at it, initially the wheel has an upward angular momentum
and as you rotate the wheel you gain an upward angular momentum.
And even when you rotate the wheel the other direction, you still gain an upward angular momentum.
Bobby: That is weird.
Billy: But, that is what our solution says will happen.
I mean nowhere in the problem did it say which direction the person rotates the wheel, right?
Bo: Yeah. Mr.p: I'm glad y'all appreciate it.
Okay, just you know this same physics concept is how NASA rotates the Hubble Space Telescope.
In space there's nothing to push off of to cause a net external torque on the telescope.
Therefore, there are near frictionless gyroscopes constantly spinning on the satellite
which can be rotated, which in turn rotates the direction the Hubble Space Telescope is pointing.
The International Space Station also has onboard gyroscopes which are used to control its rotation,
which is pretty darn cool if you ask me.
Thank you very much for learning with me today. I enjoyed learning with you.