Angular Speed vs. Angular Velocity

[libraryismyhome]

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So, I am aware that if the object on a rotating object goes to the center of the cycle, the acceleration decreases because the angular velocity(w) stays constant.

ac = w^2 x r

But on TBR FL 1, the first question said "Moving the weighted marker closer to the center of the turntable causes the angular speed of the turntable to increase (remember conservation of angular momentum)."


Their review book was saying that the angular velocity (w) is constant and only tangential velocity changes because of centripetal acceleration, and now I have no idea why they are saying this. IS there a difference btw angular speed and angular velocity besides scalar and vector?

 

[Rabolisk]

It appears that what you're describing is two different situations. I don't have the TBR book, but what they are describing is consistent with a situation in which a rotating body's moment of inertia (I) decreases as radius decreases. A body's angular momentum (L) equals its moment of inertia (I) times its angular velocity (&#969😉. L = Iω is analogous to P = mv. Just as a lighter object will have greater velocity at constant linear momentum, smaller moment of inertia results in greater angular velocity at constant angular momentum. A classic example of this is when a diver brings his arms and legs in towards his body, resulting in his entire body rotating faster (increase in angular velocity).

 

[libraryismyhome]

It appears that what you're describing is two different situations. I don't have the TBR book, but what they are describing is consistent with a situation in which a rotating body's moment of inertia (I) decreases as radius decreases. A body's angular momentum (L) equals its moment of inertia (I) times its angular velocity (&#969😉. L = Iω is analogous to P = mv. Just as a lighter object will have greater velocity at constant linear momentum, smaller moment of inertia results in greater angular velocity at constant angular momentum. A classic example of this is when a diver brings his arms and legs in towards his body, resulting in his entire body rotating faster (increase in angular velocity).

thank you.
then how does angular velocity doesn't change in an example like merry go around? as a person(object) moves toward center, by the equation ac= w^2(r)
w doesn't change and ac decreases because r decreases

 

[attixx]

You might be referring to question 2.8a in TBR:

"A child riding on a merry-go-round jumps off a horse and starts walking toward the center of the ride. As he moves, the acceleration he feels:"

This is where they discuss about w staying constant while r and ac changes. I'm thinking the key to this problem is the horse. The horse is much more massive than the person walking and stays at the same radius, so changes in moment of inertia are negligible. That's my guess anyway.

A person decreasing r on a merry-go-round should act the same as a weight being moved in on the turntable, decreasing I and increasing w.

 

[Rabolisk]

Basically, the mass of the child is negligible compared to the mass of the whole system. You can imagine that a merry-go-round is set to a constant angular velocity, and that one person walking toward the middle shouldn't change that. The key to these problems is correctly interpreting the situation. Common sense is just as important as mathematics.

 

[attixx]

Yea wow... I had been reading a question about children on a rotating disc and equating that with a merry-go-round. The merry-go-round is freakin huge, designed to hold tons of people so a child is going to have basically no effect on moment of inertia.

Sometimes it's hard to step back and use common sense when trying to analyze every scenario.

 

[libraryismyhome]

oh wow... you guys are the greatest!!!! thank you so much!!!!!!!!! 👍