Acceleration in UCM

[EMT313]

In uniform circular motion, I understand that the velocity changes because though the magnitude is the same, the direction changes therefore velocity itself changes. But why does the acceleration change? On Princeton Review's: MCAT Review Online Practice Test 2, question 44, it states that "Acceleration is a vector with both magnitude and direction. It's magnitude remains constant but its direction (towards the center changes)". I thought in a UCM problem the acceleration is constant because the magnitude doesn't change neither does the direction (it's always toward the center). Can someone explain please?

-CM

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[Sammy1024]

I think it's saying that acceleration is a derivative of velocity so if velocity is changing so is the acceleration.

As you said yourself, velocity is changing because the direction is changing. And acceleration is made up of magnitude and direction. If the velocity's direction is changing then so it the acceleration's direction.

 

[EMT313]

It just thew me off because the acceleration is always towards the center but that makes sense thank you. I guess its just all how you look at it.

 

[Natnow]

In uniform circular motion, I understand that the velocity changes because though the magnitude is the same, the direction changes therefore velocity itself changes. But why does the acceleration change? On Princeton Review's: MCAT Review Online Practice Test 2, question 44, it states that "Acceleration is a vector with both magnitude and direction. It's magnitude remains constant but its direction (towards the center changes)". I thought in a UCM problem the acceleration is constant because the magnitude doesn't change neither does the direction (it's always toward the center). Can someone explain please?

-CM

Acceleration is equal to a change in velocity over time, if velocity changes (due to change in direction) then there will be an acceleration and a change in velocity. Think of a projectile at the top of its peak, there is an acceleration at the top because it changes direction although you've also learned that v=0 at that peak for that split second it stops in the air.

A change in direction = an acceleration even if speed is constant.

 

[gublagu3]

So, just because the acceleration is always pointing towards the center, in ucm, does not mean that the direction of acceleration is the same at all points. For instance, if we imagine the Earth rotating around the sun on a horizontal plane, the direction of acceleration when the Earth is left of the sun is towards the right. When the Earth is on the right of the sun, the direction of acceleration would be towards the left. I hope this makes sense!