A Technical Tour de Force, but Not for the Faint of Heart!

Consider water flowing from a nozzle to a turbine vane. As the water hits the turbine vane, it exerts a force that causes it to move along the flow of direction. Force is an impact that changes an object's motion, shape, or orientation. Forces can be caused by physical contact, such as a push or pull, or through non-contact interactions, such as magnetic or gravitational forces. Force is a vector quantity with both magnitude and direction, and is measured in newtons (N) in the SI unit...

Pseudo forces, or fictitious forces, appear to act on an object in motion in a rotating frame of reference with respect to an inertial reference frame. These forces are not real forces but rather mathematical constructs and are introduced to simplify calculations in a non-inertial frame while using Newton's laws of motion. Common examples of pseudo forces include centrifugal, Coriolis, and Euler forces. These forces are essential in fields such as mechanics, astrophysics, and fluid...

The kinetic energy of a particle is one-half of the product of the particle’s mass and the square of its speed. Note that just as Newton’s second law can be expressed as either the rate of change of momentum or mass multiplied by the rate of change of velocity, so too can the kinetic energy of a particle be expressed in terms of its mass and momentum, instead of its mass and velocity. 

The torque-free motion refers to the movement of a rigid body in space when no external torques are acting upon it. This type of motion can be observed in environments where there are no external forces or frictions, like in outer space. For example, a rotation of Mars in space is a torque-free motion. Mars is an axisymmetric object, meaning it has an axis of symmetry along which it rotates, designated as the z-axis. The rotating frame of reference is defined such that the center of mass of...

ATP-driven pumps, also known as transport ATPases, are integral membrane proteins. They have binding sites for ATP located on the membrane's cytosolic side and the ion-conducting domain in the transmembrane region. These pumps use the free energy released from ATP hydrolysis to move the solutes across cell membranes against an electrochemical gradient.
There are four main types of ATP-driven pumps - P-type, V-type, F-type, and ABC transporter. All these pumps are of varying complexities and...

Torque is an important quantity for describing the dynamics of a rotating rigid body. We see the application of torque in many ways in the world, such as when pressing the accelerator in a car, which causes the engine to apply additional torque on the drivetrain. Here, we define torque and provide a framework to create an equation to calculate torque for a rigid body with fixed-axis rotation.
Torque can be considered as the rotational counterpart to force. Since forces change the translational...