Mr.p: Good morning. Let's learn about rotational equilibrium.
"Flipping Physics" Intro
But first, let's review translational equilibrium.
Bo, when is an object in translational equilibrium?
Bo: An object is in translational equilibrium when the net force acting on the object equals zero.
Mr.p: Correct Bo, when the net force acting on an object equals zero, the object is in translational equilibrium.
Bobby, what does it mean physically for an object when it is in translational equilibrium?
Bobby: That means the object is not moving.
Billy: Um. Remember an object that is not moving is in translational equilibrium,
however, an object in translational equilibrium is not necessarily not moving.
Bobby: Um... No
Bo: Net force equals mass times acceleration.
Billy: The translational form of Newton's Second law of Motion.
Bo: Right. So if the net force equals zero, the acceleration of the object equals zero.
So an object in translational equilibrium is not accelerating.
Bobby: Yeah. So an object in translational equilibrium has no linear acceleration.
So it could be at rest or it could be moving with a constant velocity.
Billy: Yes. An object moving at a constant velocity has no acceleration,
therefore the net force acting on it equals zero, so it is in translational equilibrium.
Bobby: Did I not just say that? Bo: Yes. Billy: Kind of.
Mr.p: Okay. Let's visualize that.
This is my dog Buster. When we add up all the forces acting on him, they add up to zero.
So he is in translational equilibrium and you can see he is at rest.
He is an object at rest in translational equilibrium.
This is my car. My car is moving at a constant velocity the sum of all the forces acting on my car equals zero,
therefore the car is moving at a constant velocity,
has zero linear acceleration and is in translational equilibrium.
Okay, that is translational equilibrium.
Billy, please take what we just reviewed about translational equilibrium
and apply it to rotational motion to determine when an object is in rotational equilibrium.
Billy: Well, I bet we start with the rotational form of Newton's Second Law of Motion
only we set it equal to zero just like we did for translational motion.
The net torque acting on an object equals zero which equals rotational inertia times angular acceleration.
That means the angular acceleration of an object in rotational equilibrium equals zero.
Bobby: Right, so an object that is not rotating is in rotational equilibrium
Bo: And an object rotating at a constant angular velocity will also be in translational equilibrium.
Billy: That totally makes sense.
Rotational equilibrium is just like translational equilibrium only rotational.
When the net torque acting on an object equals zero, the angular acceleration of the object equals zero.
Angular acceleration equals change in angular velocity over change in time. And therefore,
if the angular acceleration of the object equals zero
that means the angular velocity of the object is not changing.
Therefore, the object is either not rotating or moving with a constant angular velocity.
Bobby and Bo: Did I not just say that! Jinx, you owe me a soda!
Billy: Uh, sort of.
Mr.p: Again, let's visualize that. This is a ceiling fan which is at rest.
Currently, there is zero torque acting on the fan.
So the fan has zero angular acceleration, is at rest, and is in rotational equilibrium.
If we look at the fan when it is rotating at a constant angular velocity,
there is a constant torque caused by the motor of the ceiling fan and a constant torque
in the opposite direction caused by the internal friction in the fan and the air resistance on the fan blades.
However, the net torque acting on the fan is still zero,
therefore, the angular acceleration of the fan equals zero,
therefore the fan is rotating at a constant angular velocity and is in rotational equilibrium.
Now, I do want to take a moment to review that when we sum the forces,
we need to identify the object or objects we are summing the forces on
and the direction which we are summing the forces.
And when we sum the torques we need to identify not only the object or objects and the direct positive torque,
but we also need to identify the axis of rotation.
Please remember to identify those when using net force equals zero for translational equilibrium
and the net torque equals zero for rotational equilibrium.
Actually, one more thing. When an object is at rest and not rotating it is in what we call static equilibrium.
Static equilibrium is when the object is at rest
and in both translational and rotational equilibrium at the same time.
When this is the case the net torque equals zero about any axis of rotation.
In other words, we can sum the torques and pick any axis of rotation and the net torque will still equals zero.
Just to be clear, class looking at the ceiling fan which is at rest and not rotating
is the fan rotating about its center? BBB: No.
Mr.p: Is the fan rotating about the end of one of its blades?
BBB: No.
Mr.p: Is the fan rotating about any axis of rotation? BBB: No.
Billy: It is not
Mr.p: Then hopefully you can see that,
when an object is in both translational and rotational equilibrium at the same time,
or static equilibrium, then the net torque about any axis of rotation equals zero.
BBB: Yes. Yeah. Sure.
Mr.p: this concept of static or not moving equilibrium is very helpful for analyzing static structures.
We will be delving deeper into static equilibrium in the next few lessons.
Thank you very much for learning with me today, I enjoyed learning with you.