What is linear acceleration in uniform circular motion?

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SUMMARY

Linear acceleration in uniform circular motion refers to the acceleration that acts along the tangent to the circular path, indicating a change in speed. In the discussed scenario, the object is not in uniform circular motion as it is decreasing its velocity, which means it has both radial and tangential components of acceleration. The radial component points towards the center of the circular path, while the tangential component points in the direction of the velocity change. Therefore, the correct representation of linear acceleration in this context is the third diagram, which shows acceleration directed towards the center of the trajectory.

PREREQUISITES
  • Understanding of basic physics concepts such as acceleration and velocity.
  • Familiarity with circular motion dynamics.
  • Knowledge of vector components in two-dimensional motion.
  • Concept of uniform versus non-uniform circular motion.
NEXT STEPS
  • Study the differences between uniform and non-uniform circular motion.
  • Learn about vector decomposition in two-dimensional motion.
  • Explore the concepts of radial and tangential acceleration in circular motion.
  • Review examples of problems involving linear acceleration in circular paths.
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Students studying physics, particularly those focusing on mechanics, as well as educators teaching concepts of circular motion and acceleration.

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What is "linear acceleration" in uniform circular motion?

Yesterday, I took an exam and it was asked a concept that we hadn't studied, at least in the way it was written.

The exercise explained that a circular motion was decreasing its velocity, and we had to be able to identify which of the following diagrams represent linear velocity (no problem, I can identify and calculate it) as well as linear acceleration (problem, a concept that I can't find anywhere, either on Internet)

These were the 3 diagrams:

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I chose the first one because I thought (as well as most of my classmates) that as the acceleration is linear, it must be tangent to the trajectory, as with linear velocity. Moreover, it must have the opposite direction because the velocity is decreasing so acceleration is negative. However, according to my teacher, the correct one is the third one, because linear acceleration always goes to the center of the tragectory.

Which is the correct one?

Thanks.
 
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Linear acceleration is plain old acceleration. The modifier linear is there so you know the problem isn't asking about the rotational acceleration of the object.

You have a two-dimensional problem, so the acceleration a will have two components. For this problem, the most useful way to resolve a is into radial and tangential components. Which way do those components point in this case?

By the way, this isn't uniform circular motion because the object is slowing down. Uniform circular motion occurs when the object moves at a constant speed.
 

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