Related Concept Videos

Theorems of Pappus and Guldinus01:10

Theorems of Pappus and Guldinus

The two theorems developed by Pappus and Guldinus are widely used in mathematics, engineering, and physics to find the surface area and volume of any body of revolution. This is done by revolving a plane curve around an axis that does not intersect the curve to find its surface area or revolving a plane area around a non-intersecting axis to calculate its volume.
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a cylinder...
Gravitation01:16

Gravitation

In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down the three laws of planetary motion, explaining in detail the geometrical properties of the planetary orbits around the Sun, there was no immediate idea to discern their connection with more fundamental laws. It was Isaac Newton who, in 1665–66, figured out the connection between planetary motion, the motion of the moon around the Earth, and the...
GTPases and their Regulation02:14

GTPases and their Regulation

Guanine nucleotide-binding proteins (G-proteins), also known as GTPases, are a superfamily of proteins that regulate many cellular processes, such as cell signaling, vesicular transport, and the regulation of cell shape and motility. Mutation or dysfunction of these proteins can lead to disease. There are around 40,000 known G-proteins that can broadly be classified into two groups ‒  small G-proteins consisting of a single domain and large multi-domain G-proteins.
Large G-proteins, also known...
GTPases and their Regulation02:14

GTPases and their Regulation

Guanine nucleotide-binding proteins (G-proteins), also known as GTPases, are a superfamily of proteins that regulate many cellular processes, such as cell signaling, vesicular transport, and the regulation of cell shape and motility. Mutation or dysfunction of these proteins can lead to disease. There are around 40,000 known G-proteins that can broadly be classified into two groups ‒  small G-proteins consisting of a single domain and large multi-domain G-proteins.
Large G-proteins, also known...
Excess Pressure Inside a Drop and a Bubble01:13

Excess Pressure Inside a Drop and a Bubble

The shape of a small drop of liquid can be considered spherical, neglecting the effect of gravity. This drop can further be considered as two equal hemispherical drops put together due to surface tension. The forces acting on the spherical drop are due to the pressure of the liquid inside the drop, the pressure due to air outside the drop, and the force due to the surface tension acting on the two hemispherical drops.