# 9.2 The second condition for equilibrium

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## Learning objectives

By the end of this section, you will be able to:

• State the second condition that is necessary to achieve equilibrium.
• Explain torque and the factors on which it depends.
• Describe the role of torque in rotational mechanics.

The information presented in this section supports the following AP® learning objectives and science practices:

• 3.F.1.1 The student is able to use representations of the relationship between force and torque. (S.P. 1.4)
• 3.F.1.2 The student is able to compare the torques on an object caused by various forces. (S.P. 1.4)
• 3.F.1.3 The student is able to estimate the torque on an object caused by various forces in comparison to other situations. (S.P. 2.3)

## Torque

The second condition necessary to achieve equilibrium involves avoiding accelerated rotation (maintaining a constant angular velocity. A rotating body or system can be in equilibrium if its rate of rotation is constant and remains unchanged by the forces acting on it. To understand what factors affect rotation, let us think about what happens when you open an ordinary door by rotating it on its hinges.

Several familiar factors determine how effective you are in opening the door. See [link] . First of all, the larger the force, the more effective it is in opening the door—obviously, the harder you push, the more rapidly the door opens. Also, the point at which you push is crucial. If you apply your force too close to the hinges, the door will open slowly, if at all. Most people have been embarrassed by making this mistake and bumping up against a door when it did not open as quickly as expected. Finally, the direction in which you push is also important. The most effective direction is perpendicular to the door—we push in this direction almost instinctively.

The magnitude, direction, and point of application of the force are incorporated into the definition of the physical quantity called torque. Torque is the rotational equivalent of a force. It is a measure of the effectiveness of a force in changing or accelerating a rotation (changing the angular velocity over a period of time). In equation form, the magnitude of torque is defined to be

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