Centroids and Center of Gravity Examples

A rectangular wall panel is $3.00\ \text{m}$ wide and $2.40\ \text{m}$ high. Locate its area centroid from the lower-left corner.

A triangular plate has a base of $6.00\ \text{m}$ and altitude of $3.00\ \text{m}$. Determine the centroid height above the base.

A T-section consists of a $100\times20\ \text{mm}$ flange above a centered $20\times80\ \text{mm}$ web. Locate $\bar{y}$ from the bottom.

A $200\times100\ \text{mm}$ rectangle has a circular hole of radius $20.0\ \text{mm}$ centered at $x=150\ \text{mm}$ and $y=50.0\ \text{mm}$. Locate $\bar{x}$ from the left edge.

An area $A=0.240\ \text{m}^2$ has centroid coordinate $\bar{y}=1.50\ \text{m}$. Determine its first moment $Q_x$.

A load rises linearly from zero to $18.0\ \text{kN/m}$ over $6.00\ \text{m}$. Determine its equivalent force and line of action from the zero-intensity end.

A circular area of radius $a=0.500\ \text{m}$ is revolved about an external coplanar axis located $R=2.00\ \text{m}$ from the circle center. Determine the generated torus volume.

A geometrically symmetric rectangular panel is made from two equal-volume halves, but the left material has twice the density of the right. Will its geometric centroid and center of mass coincide?

An L-shaped area is formed from a $200\times200\ \text{mm}$ square by removing a $120\times120\ \text{mm}$ square from the upper-right corner. Locate the centroid from the lower-left corner.

A load varies linearly from $4.00\ \text{kN/m}$ to $12.0\ \text{kN/m}$ over $5.00\ \text{m}$. Determine the equivalent force and its line of action from the $4.00\ \text{kN/m}$ end.

A circular curve of radius $a=0.400\ \text{m}$ is revolved about an external coplanar axis located $R=1.50\ \text{m}$ from the circle center. Determine the torus surface area.