# What is linear acceleration in uniform circular motion?

1. Feb 8, 2012

### Capde10

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:

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.

2. Feb 8, 2012

### vela

Staff Emeritus
Re: What is "linear acceleration" in uniform circular motion?

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.