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...

Change in atmospheric pressure with height is particularly interesting. The decrease in atmospheric pressure with increasing altitude is due to the decreasing gravitational force per unit area as we move away from the surface of the earth.
Assuming the air temperature is constant at a given altitude and that the ideal gas law of thermodynamics describes the atmosphere to a good approximation, one can find the variation of atmospheric pressure with height.
Let p(y) be the atmospheric pressure at...

To escape the Earth's gravity, an object near the top of the atmosphere at an altitude of 100 km must travel away from Earth at 11.1 km/s. This speed is called the escape velocity. The temperature at which gas molecules attain the rms speed, which is equal to the escape velocity, can be estimated by using the equation for the average kinetic energy of the gas molecules. According to the kinetic theory of gas, the average kinetic energy of the gas molecules is proportional to its...

When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...

The study of external flow is essential for creating structures and objects that interact efficiently and safely with moving fluids, such as air or water. When a body is immersed in a flowing fluid, it experiences two primary forces: drag, which opposes motion along the flow direction, and lift, which acts perpendicular to the flow. The shape, size, and orientation of the object influence these forces.Streamlined and Blunt Bodies in External FlowObjects in fluid flow are classified as...

The gravitational acceleration of an object near the Earth's surface is called the acceleration due to gravity. It can be measured by conducting simple experiments on Earth. However, such an experiment is impossible to conduct on the surface of other planets.
Astronomical observations are thus used to measure the acceleration due to gravity on other planets. This can be determined by observing the effect of a planet's gravity on objects close to it. The crucial factor that helps in this...