Linear velocity (v) is related to angular velocity (ω) by the equation v = ωr.

The average kinetic energy of gas molecules is directly proportional to the absolute temperature (KE ∝ T).

For an ideal gas, the RMS speed is always greater than the average speed due to the squaring of velocities in the RMS calculation.

For an ideal gas, the RMS speed is always greater than the average speed due to the nature of the distribution of molecular speeds.

The relationship is K = C + 273.15, where K is the temperature in Kelvin and C is the temperature in Celsius.

When two parallel lines are cut by a transversal, the corresponding angles are equal.

Critical damping occurs at a specific value of the damping coefficient, which separates under-damping from over-damping.

A damping ratio of 1 indicates critical damping, while less than 1 indicates underdamping and greater than 1 indicates overdamping.

A damping ratio less than 1 indicates underdamping, equal to 1 indicates critical damping, and greater than 1 indicates overdamping.

At constant temperature and pressure, density is directly proportional to molar mass according to the ideal gas law.

In polarized light, the electric field and magnetic field are always perpendicular to each other.

In linearly polarized light, the electric field vector is perpendicular to the direction of propagation.

The relationship is given by the equation ΔG = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.

At equilibrium, the reaction quotient Q is equal to the equilibrium constant K.

The relationship between Kp and Kc is given by Kp = Kc(RT)^(Δn), where Δn is the change in the number of moles of gas.

The relationship is given by Frequency = 1/Period.

The frequency (f) is the reciprocal of the period (T), so f = 1/T.

The period T is the reciprocal of frequency f, given by T = 1/f.

The relationship is given by the equation Speed = Frequency × Wavelength, which can be rearranged to show the other relationships.

The number of emitted electrons is related to the intensity of light, not the frequency, as long as the frequency is above the threshold.

The relationship is given by the equation ΔG = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.

ΔG = -RT ln K relates Gibbs free energy change to the equilibrium constant.

The orbital period T of a satellite is related to its height h by T ∝ h^(3/2), which indicates that the period is inversely proportional to the square root of the gravitational force acting on it.

The energy of individual photons is dependent on frequency (E = hν) and not on intensity.

The magnetic field around a long straight wire is inversely proportional to the distance from the wire, as given by B = μ₀I/2πr.

According to Ampere's Law, the magnetic field B is directly proportional to the enclosed current.

The mean free path (λ) is inversely proportional to the diameter (d) of the gas molecules, meaning λ ∝ 1/d.

The mean free path is inversely proportional to the density of gas molecules. As density increases, the mean free path decreases due to more frequent collisions.

The mean free path is inversely proportional to the diameter of gas molecules; as the diameter increases, the mean free path decreases.

Boiling point elevation is directly proportional to the molality of the solution.