• ### Unit 6: Rotational Statics and Dynamics

What do desks, bridges, buildings, trees, and mountains have in common – at least in the eyes of a physicist? The answer is that they are ordinarily motionless relative to the Earth. Consequently, their acceleration, with respect to the Earth as a frame of reference, is zero. Newton's second law states that net F = ma, so the net external force is zero on all stationary objects and for all objects moving at constant velocity. There are forces acting, but they are balanced. That is, the forces are in equilibrium.

Completing this unit should take you approximately 1 hour.

• ### 6.1: Conditions for Equilibrium

When an object is in equilibrium, the forces acting upon the object are balanced. That is, the net force on the object is zero. For this to occur, the object must either not be moving, or it must be moving at a constant velocity.

There are two types of equilibrium: static equilibrium and dynamic equilibrium.

1. Static equilibrium describes a system that is balanced and does not rotate. An example is a seesaw where two children sitting at either end are exactly the same weight. Since the seesaw will not move, it is in static equilibrium.

2. Dynamic equilibrium describes a system that is balanced, but also moving (without any angular acceleration). An example is a planet in perfect circular orbit around its parent star. There is no torque acting on the planet making it orbit faster or slower, but it will keep orbiting for a very long time. The system is in equilibrium, and because it is moving, it is dynamic.

• ### 6.2: Torque

A system is not in equilibrium when a rotational force is acting on it to make it accelerate in its rotation. We call this rotational force torque. We define torque as the force to turn or twist an object, thus changing its rotational velocity. The unit for torque is the Newton-meter (Nm).

We can write the definition of torque as $\tau = rF\sin\theta$, where $\tau$ (the Greek letter tau) is torque, $r$ is how far the force is applied from the axis of rotation, $F$ is the force magnitude, and $\theta$ is the angle between the force and radial vector from the axis of rotation and where the force is being applied.

• ### 6.3: Applications of Statics

When performing calculations, the first step is to determine if the system is, in fact, in equilibrium. Recall from the previous section that two conditions must be met for a system to be in equilibrium: the system must not be accelerating and the torque must be zero. The second step is to draw a free-body diagram of the system. It is important to determine all of the forces acting upon the system. The third step is to solve the problem by applying the relevant conditions of equilibrium: force is zero, and torque is zero.