Radial acceleration and gravity

[chudd88]

This is a very basic question, and not specific to one single homework assignment, but general to many similar types of problems.

If an object is moving in a wheel (like a ferris wheel), I understand how to determine its radial acceleration. But if a problem simply asks for the objects "acceleration", and doesn't specify radial acceleration, does this imply that the radial acceleration vector should be added to the acceleration due to gravity?

For example, when the object is at the lowest point on the wheel, its radial acceleration is directed entirely upward, while the acceleration due to gravity is entirely downward. If the radial acceleration happens to be "g" at that point, would this mean that the object is experiencing no acceleration? It seems intuitive, but it could easily be counterintuitive.

Thanks.

-Dan

 

[Doc Al]

For example, when the object is at the lowest point on the wheel, its radial acceleration is directed entirely upward, while the acceleration due to gravity is entirely downward. If the radial acceleration happens to be "g" at that point, would this mean that the object is experiencing no acceleration?

No, you don't add the acceleration due to gravity to anything. The acceleration at the bottom is whatever it is. If the wheel is rotating, then there will be an upward radial acceleration which you can obtain in the usual manner (from the kinematics of circular motion). That's that.

Note that at any point in its motion, the object may have both a tangential and a radial component of acceleration.

 

[kerimek]

I can understand the confusion and potential counterintuitive nature of this concept. However, in this scenario, the term "acceleration" is often used to refer to the total acceleration experienced by an object, which includes both the radial acceleration and the acceleration due to gravity. This is because both these components are acting on the object and contribute to its overall acceleration.

In the example you provided, at the lowest point on the wheel, the object is experiencing a radial acceleration that is equal in magnitude but opposite in direction to the acceleration due to gravity. This results in a total acceleration of zero, meaning the object is not accelerating in any direction. This concept can be extended to other points on the wheel as well, where the total acceleration will be a combination of both the radial acceleration and the acceleration due to gravity.

It is important to note that while the radial acceleration and the acceleration due to gravity may cancel out at certain points, they are still two distinct components of the object's overall acceleration. In other words, the object is experiencing both of these accelerations simultaneously, but they are just balancing each other out at certain points.

I hope this helps clarify the concept of radial acceleration and its relationship with gravity. It is always important to carefully read and understand the question and its specific requirements in order to provide an accurate answer. Keep up the good work in your studies!