Basic Static

Torque

How to Determine the Direction of a Torque

To find out the direction of the torque, two important vectors are needed.

The first is the displacement vector ${\displaystyle \mathbf{r}}$, which pointing from the rotating point to the appliance point.

Then is the vector of the force ${\displaystyle \mathbf{f}}$.

We apply the right hand rule on it, use our four fingers pointing from ${\displaystyle \mathbf{r}}$ to ${\displaystyle \mathbf{f}}$, then the direction of the thumb is the direction of the torque.

We define the clockwise torque as negative, and counter-clockwise as positive, equivalently, if the thumb is pointing out from the paper, we say the torque is positive.

Couple

Couple is a couple of force that have opposite directions but the same quantity. The two forces apply at different points, so they can make the object rotate without moving. The couple do have a torque on the object. In a static system, the sum of couples and torques must be ${\displaystyle 0}$.

Support Reactions

The Definition of Support Reactions

To constrain the status of a system, we have some nodes that connect the system to some existed points. The way nodes that restrict the structures through applying forces to them are called supports. And the forces here are called reactions.

Classifications

Cables

Surface

Note that the rough surface have frictions.

Roller

Roller supports have only one reaction which perpendicular to the support surface.

Pin

Fixed

Each fixed supports have two or three reactions: parallel one, perpendicular one, and a moment to prevent rotation(if needed).

Frictions

Dry Frictions

The frictions in ideal systems.

Viscous Frictions