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