Torque

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

 

At what mark did you have to hold the meterstick to balance it? That is its Center of Mass. Record it position:
Location of Center of Mass:

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?