**9.1 Moments in Statics**

The moment of a force is

Moment = Force x r (positive is anticlockwise)

The moment of \(\vec{F}\) about the point O is M=\(\vec{F}\) * d = F* rsinθ

The resultant moment is the difference between the sum of the anticlockwise moments and the sum of the clockwise moments.

**Uniform Lamina :** Usually Rectangular of uniform density, the center of mass is the center of the rectangle.

For uniform triangular lamina, the center of mass is the centroid of the triangle.

**Uniform rod :** The center of mass is at the mid-point of the rod

**Equilibrium :** If an object is in equilibrium, the resultant force is zero and the sum of the moments is zero.

\(\sum{\vec{F}}\) = \(\vec{0}\)

\(\sum{M}\) = \({0}\)

**To solve problems :**

– Draw a diagram showing all the forces

– Take moments about any point O. The moment of the Force passing through O is zero

– Resolve the forces along the x-axis and along the y-axis

**Types of problems in statics :**

Ladder against a wall

– Inclined plane

– A door

– An object in equilibrium held by 2 strings of unequal length