Angular vs centripital acceleration from TBR

[Meredith92]

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Can someone help clarify the difference? Tbr says if you assume you're moving uniformly around the circle, then angular acceleration is zero and the velocity vector always has the same length. (chap 2 of tbr physics ) How can we assume angular acceleration is zero when the velocity vector is changing directions each instant?

They use this logic to then introduce centripital acceleration but since I don't understand this last point I'm getting confused on how the two concepts are related.

Thank you

 

[Meredith92]

Hmm I may be slowly figuring this out ) but could still use some help! So maybe angular accel is zero ( when an object is moving around a circle at a constant velocity) because ANGULAR VELOCITY is constant ( stays in clockwise direc for ex) but the linear velocity is changing because it is changing direction. Therefore linear acceleration for this object would be toward the center (centripital acceleration) and accounts for the change in linear velocity.

I think where I get confused is that both these concepts relate to rotational/ circular motion but only one is for angular motion , whereas the other is linear

 

[noobtech]

there are 2 types of accelerations:
1. the object's acceleration v^2/r which is constantly changing; hence changing velocity
2. angular acceleration, keyword : "angle" a = speed/r, since speed is constant, this angular acceleration is constant.

 

[Meredith92]

Not just would it be constant... But it would also be zero? And by "speed "do you mean angular velocity? (theta)

Thanks!

 

[NuttyEngDude]

acceleration vector is constantly changing (pointing to the center of the circle from your current location), so the velocity vector is always changing (pointing tangential to the circle).

angular velocity is constant, so the angular acceleration is zero. otherwise you would be going faster or slower in the angular path.

 

[noobtech]

Oops, i messed up. Sorry. You are right.

Angular velocity is speed/r = constant. So a = 0


🙂

 

[justhanging]

You can have an acceleration without changing speed, that's centteipical accel

 

[PhysMatMan]

Angular acceleration is an increase or decrease in angular velocity (it changes how fast you are spinning). Centripetal acceleration is the acceleration associated with changing direction (always present when you are going in a circle =v^2/r). So if I have a train that goes in a circle, and I start it up from rest, there will be angular acceleration since its angular velocity was 0 and now I'm increasing that. The centripetal acceleration will be increasing during this time as well since it equals w^2r where w=angular velocity and this is increasing due to angular acceleration. If I stop increasing the speed of the train, w will stop changing, so angular acceleration will be 0. However, centripetal acceleration will still be w^2r.

 

[Meredith92]

Thanks for your help! I also saw an equation in my text book that linear acceleration = angential acceleration + centripital acceleration. How does tangential acceleration come into play here?

And just to tie together these concepts- what is the point/ when is it necessary to convert from
Angular to linear velocity? In some tbr questions when talking about the effect of radius on velocity I was getting confused about when to use the angular or linear velocity term.

Thanks again ( and sorry if I'm over thinking this - this topic has always confused me)