Rotational Equilibrium Question

[justadream]

If the angular momentum of something = 0, is the thing at rotational equilibrium?

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[Cawolf]

It would not be rotating at all.

L = r x p = mvrsin(theta)

m, r, and theta are constant so unless the particle or object is not moving, L will have some value.

 

[The Brown Knight]

yup rotational equilibrium, but not necessarily translational equilibrium

 

[justadream]

@Cawolf

Can you clarify what those symbols means?
Is that the same as L = Iw

I = intertia
w = angular velocity

@The Brown Knight

Follow-up: What about the converse? If the rotational equilibrium is 0, does that mean the object is still (angular momentum = 0)?

 

[Cawolf]

L = angular momentum

r = distance from axis of rotation

p = translational momentum

I = moment of inertia

w = omega = angular velocity

And yes @justadream it is the same, I just wrote the formula for a particle and the forumla you wrote is for an object.

I am not very familiar with "rotational equilibrium", but I would imagine that it would mean the angular acceleration is constant - so it could have some angular momentum that is constant and not changing.

 

[type12]

I am not very familiar with "rotational equilibrium", but I would imagine that it would mean the angular acceleration is constant - so it could have some angular momentum that is constant and not changing.

This right here is 100% true. If you have rotational equilibrium, your angular momentum is not changing. If you do not, then you will experience a change in your rotation equivalent to your inertia times your angular acceleration (I*alpha).

If you have zero angular momentum, you are in static and rotational equilibrium. Any time the sum of your torques is zero, you are at rotational equilibrium.

This is beyond the scope of the MCAT.

 

[justadream]

@type12

"If you have zero angular momentum, you are in static and rotational equilibrium"

Why would you be at static equilibrium? Is that when nothing is moving (neither translationally nor rotationally)? For example, what if you have a non-spinning object that is being moved from position X to position Y.

 

[type12]

@type12

"If you have zero angular momentum, you are in static and rotational equilibrium"

Why would you be at static equilibrium? Is that when nothing is moving (neither translationally nor rotationally)? For example, what if you have a non-spinning object that is being moved from position X to position Y.

Whoops, you're right. I was thinking velocity. You are in static and rotational equilibrium when your velocity is zero.

 

[The Brown Knight]

@Cawolf

Can you clarify what those symbols means?
Is that the same as L = Iw

I = intertia
w = angular velocity

@The Brown Knight

Follow-up: What about the converse? If the rotational equilibrium is 0, does that mean the object is still (angular momentum = 0)?

If angular momentum is 0, you have no angular speed and so you will be in STATIC rotational equilibrium. If angular momentum was just constant, you could be in NON-STATIC rotational equilibrium as well.
A nonzero angular acceleration means NO rotational equilibrium at all. None of this has any relevance to translational equilibrium.
For completely static equilibrium, you need both rotational and translational equilibria.