#mainpage --- ## Base of support and critical angle - All objects have what is known **as a base of support** on which it rests when in static equilibrium. If you tilt the object, one edge of their base of support **becomes a pivot point. Therefore, you can find the bounds of an object's base of support by finding out where the object pivots when tilted in different directions**. - An object is considered to be **stable as long as its center of gravity remains vertically above its base of support.** When an object is stable it will **always** tend back towards its stable equilibrium position. - The critical angle, denoted $\theta_c$ is reached when the center of gravity of an object **is directly over the pivot point.** For objects this will always be directly above *the edge* of their base of support. - **When an object has uniform mass distribution** you can calculate the critical angle using just its width and height. - The critical angle **is measured from the vertical axis**. - The critical angle of a square - *Note: We can only use the object dimension equation if the object is a rectangle. If the object is not one of these two shapes we MUST use the position of its center of gravity to determine the critical angle.* $\newline$ $\text{Critical angle}$ $\text{Using COG position: }\;{\color{LightCyan}\theta_c=\tan^{-1}\Biggl(\frac{\frac{1}{2}w}{h}\Biggl)}\;\;\text{Using object dimmensions: }{\color{LightCyan}\;\theta_c=\tan^{-1}\Biggl(\frac{h}{w}\Biggl)}$ $\small\color{grey}\text{Using COG position }w\text{ is the base of support width}$ $\newline$ - If more than one object is involved, *like a man on a ladder*, the **combined center of gravity of the *two objects* must be over the base of support of the object ==that is in contact with the ground==**. >[!tip] >##### *Increasing stability* >- To increase the stability of an object you can either **lower its center of gravity** or **widen its base of support**. >- The **static stability factor** is a number that represents the general stability of an object **(higher is better)**. The equation for an object's static stability factor is as follows, where $w$ is the base of support width and $w$ is the height of the COG. > >$\Huge\boxed{\normalsize\text{Static stability factor: }=\frac{\frac{1}{2}w}{h}}$ >[!quote] >##### *Stability example* >![[Rotational and Circular motionstabilty.png|850]] --- ## Calculator <iframe src="https://app.calconic.com/api/embed/calculator/648873d428c7470029d3e3ea" sandbox="allow-same-origin allow-forms allow-scripts allow-top-navigation allow-popups-to-escape-sandbox allow-popups" title="Calconic_ Calculator" name="Calconic_ Calculator" height="1742px" scrolling="no" style="width: 100%; border: 0; outline: none;"></iframe>