Lab 9: Torque

What is torque? It is kind of like a force, but different.

Well, then what is a force? How about I say that a force changes the motion of an object – or maybe it changes the momentum of an object. If I go with that definition, then it might be best to say that while forces change the linear motion, torque changes the rotational motion of an object. Torque is like a rotational force.

Ok, now consider the following. Consider opening a door. Which of the two locations would you push on to best open the door?

Please tell me that you would push at location B to open the door. Why would you do that? Also, why is the door handle on the side farthest from the hinge? Why is it not in the middle? Obviously, that would be a bad idea (well, it is a bad idea unless you are a Hobbit).

To open the door, you need it to rotate. The biggest “rotational force” (torque) is when you push at location B. If you play around with this door, it isn’t too difficult to find that the torque depends on :

• The magnitude of the force (F)
• The distance from the point of rotation to the point where the force is applied (r)
• The angle between a line from the point of rotation to the force and the force itself (theta)

The goal of this lab is to show that the following relationship is true:

$\tau = Fr \sin \theta$

Just to be clear, suppose I push on the door above at a different location with a different force. The torque would be:

F and r are really vectors. In the above formula for torque, F and r are the magnitude of the vectors. Technically, torque is also a vector – but that might be a little too much at this point. Just pretend like it is a scalar and everything will work out fine.

Oh, torque can be positive or negative. Let us say that a positive torque would make a stationary object rotate counter clockwise and a negative torque would make it rotate clockwise. If you switched these, it wouldn’t really matter too much. Also, the torque does depend on the point about which it is calculated. When someone says the torque is so and so, technically they should also tell you the point that they are calculating the torque about.

Equilibrium

If we want to look at torque, and clearly we do, it will help if the object in question is in equilibrium. For an object in equilibrium, it neither changes it’s linear motion nor it’s rotation motion. In terms of forces and torques, it can be said that:

$F_\text{net-x} = 0$
$F_\text{net-y} = 0$
$\tau_\text{net-o} = 0$

What to do

First, let us try to have a constant torque and change the angle and force that applies the torque. Try a setup like this:

This is a meter stick on a balance point at the center. Using the center of the meter stick as the balance means that there is no torque due to the weight of the meter stick. On the left side there is a mass hanging a distance L_1 from the pivot. This will make a positive torque. On the other side of the meter stick is a spring scale a distance r from the pivot. If the meter stick is in equilibrium, then:

$L_1 m_1 g = rF \sin \theta$

So, pull on the spring scale to make the thing balanced. Be sure to read the scale in units of Newtons and not grams. Measure the angle theta with a protractor. Change theta and find the new F to make it balance. Since the stuff on the right is a constant, what kind of graph could you make that would show a linear function? Think about it.

Now try something else. This time, just pull straight down so that the angle theta is 90 degrees. Now change the value of r and record the force needed to balance the thing. Make another graph to show relationship between F and r.