# Torque and Equilibrium

#### Purpose:

To balance the torque applied to both sides of a meter stick by hanging various weights on it.

#### Objectives

• To learn how to calculate torque exerted on the meterstick by hanging weights.
• To be able to balance the Counterclockwise (CCW) and Clockwise torque for objects in equilibrium.
• To learn how to judge whether comparable quantities agree within their measured uncertainty.

#### Theory

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 sin θ

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 canceled by the torques try to rotate the stick in a Clockwise (CW) direction.

#### Preliminary Setup

Measure the mass of the meterstick and find its center of mass (the  mark about which it is in equilibrium)

#### Experiments

###### Activity 1.

Hang 166 g (100 + 50-g hook + clamp) at the 10-cm mark, and determine where you need to place a 224 g weight (150 g weight + 50 g hook + clamp).

###### Activity 2

Hang 166 g of weight at the 10 cm mark and shift the meterstick until it is balanced.

#### Data and Results

In each activity, calculate the CW torque and the CCW torque. In order to compare whether they agree or not, you must look at their percent difference:

$\text{\% error} = \frac{|\tau_{cw}-\tau_{ccw}|}{\text{average}}$