Rotational equilibrium

Consider the see-saw problem in the diagram below. Where should the 8 kg mass be placed so the see-saw balances? A see-saw is an example of a lever which is a board free to rotate around a point called the fulcrum. This is a typical problem applying equilibrium of torques.
Where should the mass be placed so that the see-saw is in equilibrium?
  1. Draw the free body diagram and choose a center of rotation.
  2. Draw each force at approximately the right distance. Label the known and unknown distances.
  3. Write a relationship for the torque created by each force, including positive and negative directions.
  4. Solve the problem by setting the net torque to zero.
The first step is to draw the free body diagram of the lever with its center support replaced by the support force it exerts. Choose the center of rotation to be the fulcrum. This choice means the support force, F, produces no torque because its line of action passes through the center of rotation. In many problems the center of rotation is often chosen to eliminate the torque from one or more forces.
The next step is to calculate the torque from each force about the center of rotation you have chosen. For the see-saw there are two torques and they tend to cause rotation in opposite directions. One common choice to make the positive rotation direction counterclockwise, in the direction of increasing angle. That makes the clockwise direction negative.
How to calculate torque to solve equilibrium problems
Five kilograms at two meters creates a positive torque of +98 Nm. Eight kilograms at 1.25 m creates a negative torque of −98 Nm. The heavier mass sits closer to the fulcrum than the lighter mass to create equal and opposite torques that cancel out in equilibrium. This is consistent with what you know about see-saws.
If you have a 3 m long seesaw with a 5 kg weight placed right on top of the fulcrum, where would you put a 4 kg weight to balance it. Show


72 Previous Page Next Page