Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

Static equilibrium is a special case in mechanics that is very important in everyday life. It occurs when the net force and the net torque on an object or system are both zero. This means that both the linear and angular accelerations are zero. Thus, the object is at rest, or its center of mass is moving at a constant velocity. However, this does not mean that no forces are acting on the object within the system. In fact, there are very few scenarios on Earth in which no forces are acting upon...

A rigid body is said to be in dynamic equilibrium when both its linear and angular acceleration are zero, relative to an inertial frame of reference. This means that a body in equilibrium can be moving, but only when its linear and angular velocities are constant. A rigid body is said to be in static equilibrium when it is at rest in the selected frame of reference. The distinction between static equilibrium (e.g., a state of rest) and dynamic equilibrium (e.g, a state of uniform motion) is...

In an NMR sample, precise measurement of the absolute absorption frequencies of nuclei is difficult. A standard internal reference compound is added, and the frequency difference between the reference signal and sample signals is measured.
The internal reference compound generally used in NMR spectroscopy is tetramethylsilane (TMS). TMS is preferred because it is chemically inert, soluble in NMR solvents, and easily removable. Also, the highly shielded methyl protons in TMS yield an intense...

A simple pendulum consists of a small diameter ball suspended from a string, which has negligible mass but is strong enough to not stretch. In our daily life, pendulums have many uses, such as in clocks, on a swing set, and on a sinker on a fishing line. 
The period of a simple pendulum depends on two factors: its length and the acceleration due to gravity. The period is completely independent of any other factors, such as mass or maximum displacement. For small displacements, a pendulum...