## Physics equations and formulas – dummies gas smoker recipes

Equations of angular motion are relevant wherever you have rotational motions around an axis. When the object has rotated through an angle of θ with an angular velocity of ω and an __angular acceleration__ of α, then you can use these equations to tie these values together.

You must use radians to measure the angle. Also, if you know that the distance from the axis is r, then you can work out the linear distance traveled, s, velocity, v, centripetal acceleration, a c, and force, F c. When an object with moment of inertia, I (the angular equivalent of mass), has an *angular acceleration*, α, then there is a net torque Στ.

A heat engine takes heat, Q h, from a high temperature source at temperature T h and moves it to a low temperature sink (temperature T c) at a rate Q c and, in the process, does mechanical work, W. (This process can be reversed such that work can be performed to move the heat in the opposite direction — a heat pump.) The amount of work performed in proportion to the amount of heat extracted from the heat source is the efficiency of the engine. A Carnot engine is reversible and has the maximum possible efficiency, given by the following equations. The equivalent of efficiency for a heat pump is the coefficient of performance.

A volume, V , of fluid with mass, m , has density, ρ. A force, F , over an area, A , gives rise to a pressure, P. The pressure of a fluid at a depth of h depends on the density and the gravitational constant, g. Objects immersed in a fluid causing a mass of weight, W water displaced, give rise to an upward directed buoyancy force, F buoyancy. Because of the conservation of mass, the volume flow rate of a fluid moving with velocity, v , through a cross-sectional area, A, is constant. Bernoulli’s equation relates the pressure and speed of a fluid.

A mass, m , accelerates at a rate, a, due to a force, F , acting. Frictional forces, F F, are in proportion to the normal force between the materials, F N, with a coefficient of friction, μ. Two masses, m 1 and m 2, separated by a distance, r , attract each other with a gravitational force, given by the following equations, in proportion to the gravitational constant G :

Particular kinds of force result in periodic motion, where the object repeats its motion with a period, T, having an angular frequency, ω, and amplitude, A. One example of such a force is provided by a spring with spring constant, k. The position, x, velocity, v, and acceleration, a, of an object undergoing simple harmonic motion can be expressed as sines and cosines.

The random vibrational and rotational motions of the molecules that make up an object of substance have energy; this energy is called thermal energy. When thermal energy moves from one place to another, it’s called heat, Q. When an object receives an amount of heat, its temperature, T , rises.

The heat required to cause a change in temperature of a mass, m , increases with a constant of proportionality, c , called the specific heat capacity. In a bar of material with a cross-sectional area A, length L, and a temperature difference across the ends of ΔT, there is a heat flow over a time, t , given by these formulas: