A Question About Uniform Acceleration

[The Student]

Imagine looking down at a fly flying in a circle with a constant speed, so that it is uniform acceleration. Let's reference the fly's position on a posistion/time graph of y/t. When the velocity of the y component is maximum, which means that the derivitive of Vy' = 0 with respect to time, does this mean that the Y component of this uniform acceleration is not uniform? Why or why not?

 

[DrPhil]

Imagine looking down at a fly flying in a circle with a constant speed, so that it is uniform acceleration. Let's reference the fly's position on a posistion/time graph of y/t. When the velocity of the y component is maximum, which means that the derivitive of Vy' = 0 with respect to time, does this mean that the Y component of this uniform acceleration is not uniform? Why or why not?

Notice that the acceleration is referred to as "uniform," not "constant." What is the fly (insect) doing that a fly ball does not? What are the x,y-components of the position, the velocity, and the acceleration? In what sense is the motion "uniform"?

[Are you starting a unit on angular motion?]

 

[The Student]

Notice that the acceleration is referred to as "uniform," not "constant."

The textbook has not distinguished the difference between uniform and constant, so I assumed that they were the same for our purposes.

What is the fly (insect) doing that a fly ball does not? What are the x,y-components of the position, the velocity, and the acceleration?

X(position) = cos(t), and Y(position) = sin(t); (where t = radians). Vx = -sin(t), and Vy = cos(t). Ax = -cos(t), and
Ay = sin(t). Ahhhh, so, are you saying that "acceleration is a change in velocity" does not apply to acceleration that is not constant?

In what sense is the motion "uniform"?

Is it by speed and not acceleration?

[Are you starting a unit on angular motion?]

I am not sure, but it is the first part of a first-year-physics textbook for university. It is only the 3rd chapter of 30 chapters, and it is called "Motion in Two Or Three Dimentions".

 

[DrPhil]

What the fly is doing is flying. It is exerting a force, always toward the center of the circle. Because that force is perpendicular to the instantaneous direction of motion, the acceleration vector has constant magnitude - but it is always changing direction to point toward the center of the circle. Likewise the speed (magnitude of the velocity) is constant, and the position vector also has constant magnitude (the radius) but changing direction.

All those directions are quantified by sines and cosines, as you showed.

 

[The Student]

What the fly is doing is flying. It is exerting a force, always toward the center of the circle. Because that force is perpendicular to the instantaneous direction of motion, the acceleration vector has constant magnitude - but it is always changing direction to point toward the center of the circle. Likewise the speed (magnitude of the velocity) is constant, and the position vector also has constant magnitude (the radius) but changing direction.

All those directions are quantified by sines and cosines, as you showed.

Ok, so is "acceleration is a change in velocity" not necessarily true when dealing with accelerations that are not contstant?

The fly scenerio is mine, and should not have used it - we have not got to force yet; it's the next chapter.

 

[DrPhil]

Ok, so is "acceleration is a change in velocity" not necessarily true when dealing with accelerations that are not contstant?

The fly scenerio is mine, and should not have used it - we have not got to force yet; it's the next chapter.

By DEFINITION acceleration is rate of change of velocity. That is, the acceleration vector is the rate of change of the velocity vector. In circular motion, the acceleration is perpendicular to the velocity, so it can't change the speed. Rather, it acts to change the direction of the velocity, leaving the speed constant.

Force is also a vector, and Force produces an acceleration: F = ma (where m is mass).

 

[Bob Brown MSEE]

Ok, so is "acceleration is a change in velocity" not necessarily true when dealing with accelerations that are not contstant?

The "vector" business, comes into problems of more than one dimension.
You will initially study 2-dimensions by separating the problem into 2 parts.
1) Motion in x-direction
2) Motion in y-direction
Later in your studies, you will find problems that are difficult to partition in that way.
You will use vectors to simplify these problems.

You have (so far) treated speed and velocity as the same thing.
They are not. Speed is the magnitude of the velocity, but velocity also has direction.
Your problems have involved changing speed, but always in the same direction.

Circular motion can have constant speed, but will have constantly changing direction.
Therefore constantly changing velocity.
Therefore non-zero acceleration.
Because as Dr. Phil said, "By DEFINITION acceleration is rate of change of velocity."