So we know now that we can describe the movement of the political along a line.
By using X, Y and Z components.
But we can do it differently as well.
We can use to coordinate.
A teacup wouldn't stand in court and it was tangential coordinate and a normal court and it.
Now, this is maybe not that intuitive, but it makes a lot of sense once you understand it.
So let me try and explain.
If a particle moves along a path, let's say the path looks something like this.
Here is political.
And it's moving in this direction than if you zoom in.
And this area around the political.
It forms.
The outer edge, it forms the curvature of a circle that has an origin somewhere of their.
So let's call them prime if the particle is over, yeah, then and you zoom in, then there will be
a curvature.
Radius of curvature, O'Brien over there and this distance of a year.
We call this the is now the S is so small that this almost becomes like a straight line.
Calculous.
So the velocity with which the particle moves from here to there, it's just this DETI and that we know
is V.
OK, and that is.
A scalar, but we can give it a direction, we can say this direction is tangential to that point.
So it is a tangent to that circle over there.
So for this case, when the point is there, that would be the direction of the area, the direction
of the Islamic search.
So that is tangential.
So you can immediately see that as this political moves along this path.
The direction of the tangent velocity changes.
Now, because the direction changes of this philosophy as the political moves along this path, that
gives rise to two components for our acceleration.
So there's an acceleration because of the increase in speed of this article as it moves along the path.
And there is also an acceleration due to the fact that these particles velocity changes direction.
So before we get to that, we can say the velocity is V in the tangential direction.
So it is going to write a unit vector with subscript T for the tangential direction.
So as it moves along this line, that direction changes.
It stays tangent to that curvature, the acceleration.
On the other hand, is going to have to component's.
The acceleration is going to have a tangential component in the tangential direction, and it's going
to have a normal component in the normal direction.
So it's going to have acceleration is going to have a component in this direction and it's going to
have a component in that direction.
So now imagine the particle has moved on along this line.
It sits here now.
It's going to have a velocity tangent.
Also, acceleration in that direction, which, of course, can be zero and it's going to have an acceleration
in the normal direction as well.
OK, so this is acceleration in the normal direction, figure of acceleration in the tangent direction,
also velocity in the tangent direction.
Now, a 80.
Is just the DETI, so that is our normal way of writing acceleration like we remember.
So that's the tangential acceleration, this acceleration of a year which is caused by the change in
direction of the velocity as the particle moves along this path, this acceleration of a year is given
by the squared over row.
Now, what is Ro-Ro is that radius of curvature, as you can imagine, as the particle moves along this
line, the radius of curvature changes all the time.
But if we have a particle that moves in a perfect circle, then of course the radius of curvature stays
exactly the same as it moves along.
So as you can imagine, swinging a tennis ball on a on a piece of string, you'll have the normal acceleration
and you'll have the tangential acceleration which goes with your tangential velocity as this ball goes
around the direction of this tangential velocity changes.
This ball can go round with a constant tangential acceleration, but because the direction changes all
the time, you have a normal acceleration, which is also constant.