Work and power in rotational motion are completely analogous to work and power in translational motion. The total work done to rotate a rigid body through an angle 'θ' about a fixed axis is the sum of the torques integrated over the angular displacement. Hence, torque and angular displacement in rotational motion are analogous to force and linear displacement in translational motion, respectively.
Similarly, the power delivered to a system that is rotating about a fixed axis...

In 1653, the French philosopher and scientist Blaise Pascal published "Treatise on the Equilibrium of Liquids," which discussed the principles of static fluids. A static fluid is a fluid that is not in motion. When a fluid is not flowing, we say that the fluid is in static equilibrium. If the fluid is water, we say it is in hydrostatic equilibrium. For a fluid in static equilibrium, the net force on any part of the fluid must be zero; otherwise, the fluid will start to flow. Pascal...

The work-energy theorem for rotational motion is analogous to the work-energy theorem in translational motion. It states that the net work done by an external force to rotate a rigid body equals the change in the object's rotational kinetic energy. The power delivered is simply the time derivative of the work done; therefore, power is the dot product of torque and angular velocity. This relation is analogous to power in translational motion, which is given by the dot product of force and...

The total work done on an object acted upon by multiple forces can be computed using two methods that give the same result. In one method, the work done by each force is first calculated. Then, those values are summed algebraically to calculate the total work done by all the forces. In the second method, the net force is first calculated by a vector sum of all the forces. Then, the work done by this force is obtained.
Since forces perpendicular to the displacement do no work, they do not...

A weir is a hydraulic structure designed to partially obstruct an open channel, enabling precise control and measurement of water flow. By forcing water to flow over or through it, a weir allows for accurate determination of discharge rates, making it an essential tool in water resource management. These structures are extensively used in regulating river flows, irrigation systems, and flood control channels.Types of Weirs and Their FeaturesWeirs are categorized primarily into sharp-crested and...

Gravitation is one of the four fundamental forces in nature. The force between objects on Earth and Earth itself is called gravity.
Like other forces, gravity does work on an object if it displaces it toward the Earth's center. In this case, the work done by gravity is said to be positive. If an external force acts on the object against the pull of gravity and manages to lift it away from the Earth's center, work is done against gravity. In this case, the net work done is said to be...