## Torque and Equilibrium

**Purpose: To balance a meter stick by hanging various weights on it. **

**Objectives**

- To become familiar with the concepts of torque, leverage arm, and Center of Mass.
- To be able to calculate the torque exerted on the meterstick by the hanging weights.
- To be able to distinguish between experimental results and theoretical calculations.
- To learn how to judge whether comparable quantities agree within their measured uncertainty

**Theory**

**Torque.**

When a force F is applied at a distance r from an axis, and the angle between the two is given as θ, the torque is defined as:

τ = r × F_{⊥}

**Conditions for Equilibrium. **

When an object is in equilibrium, all forces and torques must cancel and it must experience zero net force and torque.

Condition for Forces | Net Force = 0 | |

Condition for Torques | Net Torque = 0 |

In other words, the torques that are trying to rotate the stick in a Counterclock (CCW) direction will be cancelled by the torques try to rotate the stick in a Clockwise (CW) direction.

**Activity 1.** Balance the Meterstick without weights

**Activity 2.** Balance the meterstick with two weights.

- Keep the meterstick clamped at its Center of Mass.
- Take a small clamp, measure its mass and slide it onto the 10 cm mark. Place 100 g on a 50-g hook and hang all on the clamp. Record the total mass of clamp, hook, and weights altogeter:

- Take another small clamp, measure its mass and slide it on the other end of the meterstick.
- Place 150 g on a 50-g hook and hang them on the second clamp. Record their total mass (clamp, hook, and weights altogether):

- Slide the second clamp along the meterstick until it is completely balanced again. Write down the location of the second clamp along the meterstick.

**Challenge.** Balance the meterstick by hanging only one weight.

- Keeping the weight at the 10-cm mark from Activity 2, remove the hanging weights on the right.
- Loosen the meterstick from its hold at its Center of Mass and slide it until it is balanced again.
- Record the position at which you must hold the meterstick in order to balance it:

**Questions and Calculations**

- Calculate the Counterclockwise Torque (right hand) and the Clockwise Torque (left hand). Compare both values? Do they agree? To how many digits?
- For the Challenge: What torque balances the torque due to the weights hanging on the 10-cm mark?