9.2 The Second Condition for Equilibrium

9.2 The Second Condition for Equilibrium

• The stick rotates when the same forces are applied at other points.
• The system isn't at equilibrium.
• It is a necessary condition for achieving equilibrium.

• Torque causes an object to move.

• The second condition to achieve equilibrium is avoiding accelerated rotation.
• If the rate of rotation is constant, the system can be in equilibrium.
• Let's think about what happens when you open an ordinary door by rotating it on its hinges.

• How effective you are in opening the door is determined by a number of factors.
• The bigger the force, the more effective it is in opening the door.
• The point at which you push is crucial.
• The door will open slowly if you apply force too close to the hinges.
• Most people have been embarrassed by bumping up against a door that did not open as expected.
• The direction in which you push is important.
• We push in this direction almost instinctively.

• Torque is the turning or twisting effectiveness of a force, illustrated here for door rotation on its hinges.
• There is both magnitude and direction.
• That is the distance from the pivot to the action of the force.

• Torque is defined by the magnitude, direction, and point of application of the force.
• It is a measure of the effectiveness of a force in changing a rotation.

• Torque can be produced by a force applied to an object.
• If the object rotates around point A, it will do socounterclockwise.
• Torque is counterclockwise relative to pivot A.
• The clockwise rotation around point B is caused by the Torque from the applied force.

• As the name implies, the line segment that defines the distance is not straight.
• It may be more convenient to use, but both are valid.

• If you push the door with a force of 40 N at a distance of 0.800 m from the hinges, you exert a Torque of 32 N*m. If you reduce the force to 20 N, the Torque is reduced as well.

• The pivot point is used to calculate the Torque.
• Since both the location of the pivot and the applied force are variables, a different choice for the location of the pivot will give you a different value for the Torque.
• Any point in an object can be used to calculate the Torque.

• There are two possible directions for rotation in a plane.
• The Torque for the force is shown as counterclockwise relative to A if the object can rotation about point A.
• The force shown is relative to B if the object can rotation about point B.
• The magnitude of the Torque is greater when the lever arm is longer.

• The second condition needed to achieve equilibrium is that the net external Torque on the system must be zero.
• An external Torque is created by an external force.
• The point at which the Torque is calculated can be chosen.
• The point is the physical pivot point of a system or any other point in space.
• If the second condition is satisfied for one choice of pivot point, it will also hold true for any other choice of pivot point in or out of the system of interest.

• Torques are assigned opposite signs.
• The counterclockwise (ccw) and clockwise (cw) Torques are referred to as negative.

• Most people know that a heavier child can keep a lighter one off the ground indefinitely, and that a lighter child can sit farther from the pivot.

• Two children balance a seesaw.
• The lighter child sits farther from the pivot to create a Torque equal to that of the heavier child.

• The first child has a mass of 26.0 kg and sits at the pivot.

• There are two conditions for equilibrium.
• Since the first condition has no distances in it, the second must be used.
• The system of interest is the seesaw plus the two children.
• The pivot is where the Torques are calculated.
• All external forces are identified on the system.

• The supporting force of the pivot is one of the external forces acting on the system.
• Let's look at the Torque produced by each.

• The second equation has a minus sign in it because it is negative by convention.
• The distance is zero since acts directly on the pivot point.
• A force on the pivot can't cause a rotation, just as a force on the door can't cause a rotation.
• The second condition for equilibrium is that the Torques on both children are zero.

• The acceleration is due to gravity.

• The heavier child needs to sit closer to the pivot to balance the seesaw.

• This part requires a force.

• The results make sense.
• The two children are supported by the pivot.

• There are a number of aspects of the preceding example that have broad implications.
• The pivot is the point at which the Torques are calculated.
• The lever arm is zero since it is exerted on the pivot point.
• The supporting force exerts zero Torque relative to that pivot point.
• We chose the pivot point to simplify the solution of the problem because of the second condition for equilibrium.

• We were left with a ratio of mass after the cancellation of the acceleration due to gravity.
• This won't always be the case.
• Don't jump ahead to enter some ratio of mass.

• The weight of each child is distributed over an area of the seesaw, yet we treated the weights as if each force were exerted at a single point.