This rule also applies to rotational motion. If the resultant moment about a particular axis is zero, the object will have no rotational acceleration about the axis. If the object is not spinning, it will not start to spin. If the object is spinning, it will continue to spin at the same constant angular velocity.
Again, we can extend this to moments about the y -axis as well. We can represent this rule mathematically with the following equations:. Privacy Policy. Skip to main content. Static Equilibrium, Elasticity, and Torque. Search for:. Conditions for Equilibrium.
First Condition The first condition of equilibrium is that the net force in all directions must be zero. Learning Objectives Identify the first condition of equilibrium. Key Takeaways Key Points There are two conditions that must be met for an object to be in equilibrium.
The first condition is that the net force on the object must be zero for the object to be in equilibrium. If net force is zero, then net force along any direction is zero. It is possible to split a force into its horizontal and vertical components.
This can be done by forming a triangle, with the hypotenuse as the resultant. If two equal and opposite forces act on an object, the object is in equilibrium or constant velocity. An example of this is an object resting on a horizontal surface. The weight of the object is equal and opposite to the resistive force acting upwards.
In general, an object can be acted on by several forces at the same time. A force is a vector quantity which means that it has both a magnitude size and a direction associated with it.
If the size and direction of the forces acting on an object are exactly balanced, then there is no net force acting on the object and the object is said to be in equilibrium. Because there is no net force acting on an object in equilibrium, then from Newton's first law of motion, an object at rest will stay at rest, and an object in motion will stay in motion.
Let us start with the simplest example of two forces acting on an object. Sample data for such a lab are shown below. For most students, the resultant was 0 Newton or at least very close to 0 N.
This is what we expected - since the object was at equilibrium , the net force vector sum of all the forces should be 0 N. Another way of determining the net force vector sum of all the forces involves using the trigonometric functions to resolve each force into its horizontal and vertical components. Once the components are known, they can be compared to see if the vertical forces are balanced and if the horizontal forces are balanced.
The diagram below shows vectors A, B, and C and their respective components. For vectors A and B, the vertical components can be determined using the sine of the angle and the horizontal components can be analyzed using the cosine of the angle. The magnitude and direction of each component for the sample data are shown in the table below the diagram.
The data in the table above show that the forces nearly balance. An analysis of the horizontal components shows that the leftward component of A nearly balances the rightward component of B. The vector sum of all the forces is nearly equal to 0 Newton. But what about the 0. Why do the components of force only nearly balance? The sample data used in this analysis are the result of measured data from an actual experimental setup.
The difference between the actual results and the expected results is due to the error incurred when measuring force A and force B. We would have to conclude that this low margin of experimental error reflects an experiment with excellent results. We could say it's "close enough for government work. The above analysis of the forces acting upon an object in equilibrium is commonly used to analyze situations involving objects at static equilibrium.
The most common application involves the analysis of the forces acting upon a sign that is at rest. For example, consider the picture at the right that hangs on a wall. The picture is in a state of equilibrium, and thus all the forces acting upon the picture must be balanced. That is, all horizontal components must add to 0 Newton and all vertical components must add to 0 Newton.
The leftward pull of cable A must balance the rightward pull of cable B and the sum of the upward pull of cable A and cable B must balance the weight of the sign. Suppose the tension in both of the cables is measured to be 50 N and that the angle that each cable makes with the horizontal is known to be 30 degrees. What is the weight of the sign? This question can be answered by conducting a force analysis using trigonometric functions.
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