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Any object flying through space has inertia. Its velocity will only change if an external
force acts on it, and its angular velocity will only change
if an external force generates a torque on it.
In the absence of any external force, the object will continue travelling forward at
the same speed, and continue spinning around its centre of
mass at the same speed, forever.
Although all of this is true, part of it can be misleading. To the chalkboard!
Alright, let me explain. As we watch a completely unsuspicious-looking
chopstick flying through space, we can observe that this it has linear momentum.
Its linear momentum is just its mass times its velocity.
If we were to flick that chopstick at its centre of mass
(because completely unsuspicious-looking chopsticks are infinitely thin),
its linear momentum would change. We could calculate how its momentum should
change according to the size, direction, and duration
of the force. In the presence of any non-zero net external
force, the linear momentum will change. The chopstick's new momentum would be its
old momentum added to the force times the duration.
In other words, the change in momentum, or impulse.
So, the chopstick would continue moving like this.
Similarly, we could look at another completely unsuspicious-looking chopstick spinning in
place. It has angular momentum, which is just its
moment of inertia times its angular velocity. If we were to flick that chopstick at a certain
distance from its centre of mass, we would change its angular velocity.
We could calculate how its angular momentum should change according the size, direction,
duration, and location of the force. The angular momentum will change in the presence
of any non-zero net external torque, which is simply a product of the force and
the distance away from the centre of mass at which the force was applied.
The chopstick's new angular momentum would be its old angular momentum added to the torque times time.
In other words the change in angular momentum. So you might expect the chopstick to continue
moving like this, right? Well sorry, that's wrong!
...or rather, it's only half right. This is what really should happen.
The calculations that we did to find the new angular momentum are all correct,
but we forgot about something else. We said earlier that linear momentum should
change in the presence of an external force. Here's an external force.
Sure, it changed the angular momentum, but according to the laws of physics,
that same force should also change the linear momentum.
Every external force on any object will try to change both linear and angular momentum.
But hang on! If we go back to our first completely unsuspicious-looking
chopstick, we found that the external force only changed
its linear momentum. I thought all forces try to change both types
of momentum. So why didn't that force also change its angular
momentum? Well, it sort of did, it's just that it was
0. The change in angular momentum can be found
with time and torque. As before, torque is just force crossed with distance
But we explicitly flicked the chopstick at
its centre of mass, so radius is 0. This, in turn, means that the torque is 0, and the angular
momentum does not change. But nevertheless, although both types of momentum
are presented separately, they are both always present.
And every external force influences both of them.
Otherwise, they'll just keep on keeping on.