When do we use angular velosity to calculate centripetal acceleration?

[libraryismyhome]

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Instead of using this formula,
Centripetal Acceleration = (tangential velosty)^2 / r

Sometimes, I need to use this to get the question right.

Centripetal Acceleration = (angular velosity)^2 x r

My prep book explained that when the speed is fixed or velosity is same for all rotating body, we use this, but I still don't get it.

Thank you.

 

[Rabolisk]

Whichever one is more convenient for the problem at hand. For example, a problem asks you to calculate the change in centripetal acceleration as r doubles. Then you have to ask yourself if angular velocity remains constant or tangential velocity remains constant. Whichever one remains constant is the equation you use, simply because it's easier. There are many types of problems that can be asked about centripetal acceleration, and the key is that you understand the difference between angular velocity and tangential velocity.

 

[RogueUnicorn]

don't worry too much about it, the second equation is merely a derivative of the first using the relationship that w (angular v) = v/r.

this specifically applies to constant rotational motion, which is the only kind of rotational motion you will solve quantitatively on the MCAT

 

[libraryismyhome]

how do I know which one is constant when I see a question? tangential velocity or angular velocity?

 

[Rabolisk]

If you know what tangential velocity and angular velocity are, then you should be able to figure it out.

For example, if I have a merry-go-round, and I vary radius by sitting near or far from the center, do I have constant tangential velocity or constant angular velocity?

 

[libraryismyhome]

ah... a classic BR example. yeah in that circumstance, I must use angular velocity equation cause the book was saying that angular velocity is constant.

yeah, this was the exact part I was confused on. how can I tell whether Vt or W is constant?

 

[RogueUnicorn]

how do I know which one is constant when I see a question? tangential velocity or angular velocity?

they should both be constant in magnitude

i am afraid you might be missing on some fundamental points of circular motion

 

[Rabolisk]

they should both be constant in magnitude

i am afraid you might be missing on some fundamental points of circular motion

We mean constant with respect to radius, not time. In the merry-go-round example, angular velocity is independent of radius, while tangential velocity is not.

To the OP, you should know the difference between angular velocity and tangential velocity. Angular velocity is dθ/dt. It's a measure of how fast something is revolving in a circular orbit, independent of how big that orbit is. If you are still confused, post some questions where you were unsure of which equation to use.

 

[RogueUnicorn]

We mean constant with respect to radius, not time. In the merry-go-round example, angular velocity is independent of radius, while tangential velocity is not.

oh word. i didn't read your previous post

 

[libraryismyhome]

Angular velocity is dθ/dt. It's a measure of how fast something is revolving in a circular orbit, independent of how big that orbit is. If you are still confused, post some questions where you were unsure of which equation to use.

Here is the necessary concept I had forgotten completely. Indeed, Vt decreases as the orbit size decreases. So in Merry-go around example, as the child moves to the center, r decreases, but Vt decreases as well. However, w doesn't change cause dθ/dt doesn't change.

BR CH Force Motion Gravitation Passage IV
#23 If a person starts at the rim of the space station and moves radially towards the central axis in an elevator, what happen to the normal force felt by that person?

Answer: N = mac = w^2r so, N decreases.
Just as the merrygoaround example


BR CH Equilibrium and Momentum Passage X
#68 As the crane rotates, it increases its speed. What effect will this have on the tension in the cable and on the angle the cable makes with the vertical?

- Previously, this I could answer just by imagining, but was not able to answer in an intuitive way, and drawing diagram and playing with equations took too much time.
- Let's see whether my understanding is correct. Increasing its speed in this question means increasing its angular velocity, cause it's rotating faster. so this increases the centripetal force which is tension?



#69 As the crane rotates, and linearly increases its speed, what can be said about the torque aciting on the load?

How could a crane linearly increase its speed?? It's saying that it won't change the angular acceleration, so no change in torque as well. 😕

 

[Rabolisk]

Can't help you out without a diagram. I'm having trouble imagining exactly what is going on.

 

[libraryismyhome]

ahh. sorry,, thought you have BR books since you used merro-go-around example. but it's cool. I figured out everything. thanks a lot.

 

[RogueUnicorn]

as a courtesy to the people who answer Qs, it's a good idea to put up as much info as possible. even if we have the books, they may not be readily available at the location we use SDN, like work.