Constant Speeds or Stay
There is an interesting thing you gotta know. Objects that have mass are always moving. But from your point of view it appears as if some things are standing still. Why is that? Its because you and that object are sitting on the same plane, and this plane has a velocity that it shares with both of you. So objects on the earth are moving with the earth, like the mountains, and the houses, and the people etc.
So there are still other objects that move at the velocity you move at and you notice it. How? Its because you can see that the common plane you both are sitting on is moving past like when you are driving a fast car against your friends in a race and you both head -to-head.
When you moving with constant velocity or you moving at the same speed as the earth, you are not accelerating
So there are two times during which you are not accelerating: when you are still or when your speed in a straight line is not changing.
You may need tutorials on solving algebra: Simple Algebra
and vectors: Vectors
and for how forces apply acceleration and vice-versa:Forces
Changes Of Scale Or Direction
So how do you accelerate exactly? You do so by changing your speed in a straight line or you change your direction from a straight line path. Doing so require either an acceleration or a deceleration (which is a negative acceleration).
Circuits Or Partial Circuits
Recall just now I said that a path could change the velocity because of a change in direction. Now we will consider motion on
a curve with constant speed. We will do a short introduction to acceleration in the next part, but for now consider the diagram below:
Assuming this change happens during a short time such that the angle there is very nearly zero or could be taken as that. Now each part of a curve
has a tangent and this tangent could be attached to a particular circle, or you could build out of that point or infinitesimal
portion a circle that can have or own the same tangent. Look below:
The 'owning circle' has been generated in this diagram showing its tangent and also radius of curvature. This is a line showing
how big or small the owning circle is. This line in infinite if the path of motion is a straight line. Now as before imaging that v1 and v2 are close together
which makes the two radii super-imposed on each other making them look like one line. When you look again at the change in velocity using the above diagram:
You will see under close observation that the two velocities must align with the tangents at their the points where the occur. Now since the are very close points it means
they essentially align or super-impose one another. The change in velocity therefore falls into the radius of curvature of the circle. You see, since the velocities
have equal magnitudes(speeds) the triangle they form is an isosceles where the top angle is zero making the vector difference of v1 and v2
perpendicular to v1 and v2.
This is the case for all circular motion where the speed is constant. There is a change in velocity towards the center of motion.
This in turn means that the acceleration of an object in a curve when constant is towards the center of curvature of the path along the radius of the owning circle of that point.
Well. The simple reason is the change in velocity ultimately results in a acceleration, and a curve always produces this acceleration as long as the body is moving along it. Can you build that triangle? The only way to escape this result is stay still on the on any point of that curve.
For other studies in Physics go to: Physics and the needed math: Math
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