If both of these conditions are met, then scientists and engineers say, "The body is in mechanical equilibrium." There are two other forms of eqilibrium called static and dynamic equilibrium. Static equilibrium means the body is moving at a constant velocity. Mechanical equilibrium is a subset of static equilibrium. Dynamic equilibrium is where a body is accelerating and moving at constant velocity at the same time. An example of this is a ball that is spinning while not moving linearly. Every spinning object experiences a centripetal acceleration. In the example the object is spinning but not experiencing any translational motion.

The red car is in mechanical and static equilibrium.

The blue car is only in static equilibrium

The spinning "eight ball" is in dynamic equalibrium

This unit will only deal with mechanical equilibrium.

Putting it All Together

When you solved free body problems, in a previous unit, you were applying one of the conditions of mechanical and dynamic equilibrium by summing up the forces. This is called the first condition of equilibrium. It looked like this...

The second conidition of equilibrium states that a body is not rotating. This is mathematically stated by saying that, "The sum of torques about any point is zero." This means you have an tool that can be used when solving problems. It looks like this...

Here is a video describing how the math sentence above makes sense.

When do you use the summing up the torques
technique?

Use summing up the forces and torques when the question asks how far away from a point a force is applied.This includes questions that ask...

how far a person can walk on a board or beam.

Or where can a weight be placed on beam

Or where the lifting force needs to be placed. All these questions involve a force(s) and a distance. -and that's a torque.

General strategy when solving equilibrium problems

Draw an extended free body diagram, "EFBD."

Sum up the forces in the "x" and "y" directions.

Try to solve with this information.

Sum up the torques

Choose an axis of rotation where you don't know a variable.

Solve

Example 1: Using a torques to write a math sentence

Question

Solution

Video Solution

Below is an extended free body diagram for a beam that is held horizontally. Each letter represents a force. Write the math sentence that sums up all the torques.

Sum up the torques about a point on the beam. You can pick ANY point on the beam. Wherever the point is located, all force that point towards or away from the point will not exert a torque about this point. Mathematically this means that the force in toque equaiton will dissappear. Therefore, pick a pivot point where an unknown force points towards or away from. This is one of the secrets to using toque to solve equilibrium problems.

Use some or all of the three eqautions you created to solve for an unknown.

A 5.00 m, 200.0 N, long ladder rests on a wall. The ladderâ€™s center of mass is 3.00 m from the bottom of the ladder, along the ladder. There is no friction on the wall, but there a coefficient of friction along the ground of 0.300. How far along the ladder can a 750. N person climb above the ground?

by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)

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