Torque Equilibrium

INTRODuction

Torque is a quantitative measure of a tendency of a force to cause or change the rotational motion of a rigid body. A torque (or moment of force) results from the application of a force acting at a distance from an axis of rotation.

Figure 1. Experimental settings diagram.

In Figure 1 above, F₁ and F₂ (weights of masses 1 and 2) are on the left side of the pivot point, so I place them on the left side of the equation. Of course, the torque depends on the arm r as well (distance from the pivot point), so I include r₁ and r₂, respectively, in the equation. The weight of m₃ is on the right side of the pivot point, therefore I place it on the right side of my equation.

Thus, the physical situation above can be presented in a form of an equation:

F₁ r₁+ F₂ r₂ = F₃r₃

Because F = m g, I can rewrite the equation as

(m₁g) r₁+ (m₂ g) r₂ = (m₃g) r₃

and simplify by dividing all terms by g

m₁r₁+ m₂ r₂ = m₃r₃

If masses m₁and m₂ are known, and arms r₁, r₂, andr₃are known, then m₃can be easily calculated.

m₃= (m₁r₁+ m₂ r₂) /r₃

Example

Let m₁ = 25g and m₂ = 75g.

Let r₁= 60 units, r₂ = 20 units, and r₃ = 55 units.

m₃= (60 units 25 g + 20 units 75 g) / 55 cm = (3000 units g) / 50 units = 60 g

Experimental Settings

Set the yardstick and weights according to the diagram presented in Figure 1. Notice that the way you place the weights on the yardstick depends on the weights, see Figure 2 and Figure 3.

Figure 2. Hooks with weights placed on the yardstick.

Figure 4. Weights placed on the yardstick.

Experimental Settings

In this laboratory exercise, you will determine

Figure 4. Diagram of arms and forces.

As shown in Figure 4, r_L = 26 cm (to determine this, subtract 24 cm from 50 cm); r_R = 13 cm (to determine that, subtract 50 cm from 63 cm). The mathematical representation of that situation is given by the equation:

26 cm 100 g = 13 cm 200 g

Laboratory Procedure

In this experiment we are looking for one of the masses and/or its arm needed to keep the ruler in equilibrium (trial and error method). We will find the mass and/or its arm first, and then calculate both the left and the right side torque (counterclockwise and clockwise one, respectively).