What is linear acceleration in uniform circular motion?

In summary, linear acceleration is simply acceleration and in this case, it is the component of acceleration in the direction of motion. In the given problem, the acceleration is decreasing and therefore, the correct diagram is the third one where the acceleration points towards the center of the circular trajectory. This is different from uniform circular motion, where the acceleration is constant and always perpendicular to the velocity.
  • #1
Capde10
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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:

15hg4qq.jpg


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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  • #2


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.
 

What is linear acceleration in uniform circular motion?

Linear acceleration in uniform circular motion is the rate of change of an object's linear velocity as it moves in a circular path at a constant speed. It is the acceleration that is experienced by the object along the tangent of the circle at any point.

How is linear acceleration related to angular acceleration?

In uniform circular motion, linear acceleration and angular acceleration are directly proportional. This means that as the angular acceleration increases, the linear acceleration also increases, and vice versa.

What is the difference between linear and tangential acceleration?

Linear acceleration is the acceleration experienced by an object in a straight line, while tangential acceleration is the component of acceleration that is tangent to the circular path of the object. In uniform circular motion, tangential acceleration is equal to the linear acceleration.

How do you calculate linear acceleration in uniform circular motion?

The formula for linear acceleration in uniform circular motion is a = v^2/r, where a is the linear acceleration, v is the linear velocity, and r is the radius of the circular path. Alternatively, it can also be calculated as a = ω^2r, where ω is the angular velocity.

What is the significance of linear acceleration in uniform circular motion?

Linear acceleration in uniform circular motion is important because it allows us to determine the force acting on an object in circular motion. This acceleration is always directed towards the center of the circle, and is caused by a centripetal force that keeps the object moving in its circular path.

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