Mr.p: Good morning.
When we introduced torque, we ignored its direction. Today, we learn how to identify the direction of torque.
"Flipping Physics" Intro
Class, what handy tool are we going to use to identify the direction of torque,
which is the ability of a force to cause an angular acceleration of an object?
BBB: What? Uh? I don't know.
Mr.p: Class, what handy tool are we going to use?
BBB: The right hand rule!
Mr.p: Class, what is step one of the right hand rule?
BBB: Don't be too cool for the right hand rule.
Mr.p: And step two?
BBB: Limber up!
Mr.p: Okay, now that we are limber, let's do an example.
We have an object with an axis of rotation at its right end
and we are applying a force as you can see in the drawing.
Here's how the right hand rule works.
Start with the fingers of your right hand at the axis of rotation.
Point your fingers along a line which goes from the axis of rotation to where the force acts on the object.
Curl your fingers in the direction of the force. Then stick out the thumb of your right hand.
Your right thumb indicates the direction of the torque. In this particular case that is out of the board and
out of the board is considered to be positive.
For this next example, I have only changed the direction of the force applied to the object.
Billy, please determine the direction of the torque in this example.
Billy: Okay. I start with the fingers of my right hand at the axis of rotation,
point my finger is toward where the force acts on the object,
and curl my fingers in the direction of the force and stick out my right thumb.
My thumb is pointing this way, which corresponds to "into the board", which must be negative, right?
Mr.p: That is correct, this torque is into the board, which is negative.
Into the board is considered to be negative because it is opposite from out of the board, which is positive.
Bobby: mr.p?
Mr.p: Yes, Bobby?
Bobby: Is this right hand rule related to the right hand rule for angular displacement and angular velocity?
Mr.p: That is an interesting question. What do y'all think?
Bo: That force would create a torque which would cause the object
to angular accelerate in the same direction as the torque.
Bobby: Right, so the angular displacement of the object would be away from you
or into the board, just like the torque. So, they are related, right?
Mr.p: Yes, that is a very nice observation. Let's do another example.
Now the axis of rotation is on the left side of the object and the force is at an angle.
Bobby, what is the direction of the torque now?
Bobby: Okay. Start with the fingers of my right hand at the axis of rotation.
Point my fingers toward where the force acts on the object. Curl my fingers with the force.
Stick out the the thumb of my right hand and which points into the board, which is negative.
Bo: Right, because this torque causes the object to rotate in the negative direction. That makes sense.
Mr.p: Correct, this torque is into the board and negative.
All I have moved this time is the axis of rotation. Bo?
Bo: Fingers of right hand at the axis of rotation. Point fingers toward the force.
Curl the fingers with the force. And your thumb sticks out from the board, so this is a positive torque.
Mr.p: This next example has the same axis of rotation,
however, I have moved where the force is located and rotated the force by 180 degrees. Billy?
Billy: Fingers of my right hands start at the axis of rotation.
I point my fingers toward where the force acts on the object.
And curl my fingers with the force and stick out my thumb.
Hey, this torque is in the same direction as the last one; out of the board and positive.
How can that be if the force is opposite the direction as the last example?
Bobby: This force is on the other side of the axis of rotation.
Bo: And this right hand rule gives the direction of torque, not the direction of force.
Billy: Right. That makes sense.
Mr.p: Let's do one more.
With the same axis of rotation, only now the force is on the left end of the object and to the left. Bo?
Bo: Okay. Fingers of the right hand start at the axis of rotation.
Point toward where the force is on the object and curl fingers in the direction of the force.
This, this does not... work.
Bobby: Because the angle in the torque equation is zero, so the torque is zero. Zero cannot have a direction.
Billy: That's right. Torque equals r, the position vector from the axis of rotation to where the force is applied,
times the force causing torque,
times the sine of the angle between the r position vector and the force applied vector.
And that angle is zero in this case and the sine of zero is zero! Nice!
Mr.p: That is correct.
The direction of this torque is undefined because zero does not have a direction, therefore,
the right hand rule does not really give logical results when the torque is zero.
Okay, now that we have learned how to use the Right Hand Rule to determine the direction of torque, some-
times my students get overzealous and try to use the Right Hand Rule to determine the directions of forces.
Please, do not do this. The right hand rule is for the direction of torque only, not force.
Billy: This Right Hand Rule is for the direction of torque, not the direction of force.
Bo: I already said that.
Mr.p: Thank you very much for learning with me today. I enjoyed learning with you.