Energy and power calculations are fundamental in engineering and physics. These equations are used to analyse work, motion, forces and rotating systems in mechanical applications.
This page provides key formulae for work, power, rotational motion, kinetic energy and potential energy used in engineering calculations.
The standard acceleration due to gravity is used in many engineering and physics calculations involving forces, energy and motion near the Earth's surface.
The mass moment of inertia of a body about an axis has been defined as the sum of the products of mass-elements and the square of their distance from the axis
The mass moment of inertia describes how mass is distributed about an axis and is essential for analysing rotational motion and angular acceleration.
The Work Done W (= Joules = N.m ) by constant Force F_x (N) applied for a distance x (m)
W = F_x . x
Power is the rate of doing Work P (= Watts = N.m / s ) by constant Force F_x (N) applied for a distance x (m) over t(seconds)
P = F_x . x / t
also Power = Force F_x at a set velocity v ( N / s)
P = F_x . v
Work is defined as the force applied over a distance, while power represents the rate at which work is done. These relationships are fundamental in mechanical systems and energy transfer calculations.
The power transmitted by a rotating shaft = the torque T x the angular velocity.
P = T * ω =
T * 2 * π * n
P (kW) = T(Nm).n (rev/min) / 9 549
In rotating systems, power is related to torque and angular velocity. These equations are widely used in engines, motors and rotating machinery.
Energy exists in different forms including potential and kinetic energy. These equations are used to analyse motion, lifting systems and energy transfer in mechanical engineering.
The energy gained by a body during a displacement is equal to the work done by external forces acting upon the body. This includes frictional and non friction forces.
The potential energy is the energy possessed by a body by virtue of its position relative to some datum level.
The change in potential energy (Joules) gained by a mass of M (kg) lifted through a height of h (metres)
ep = M . g n. h
The kinetic energy of a a body by virtue of its motion at uniform linear velocity
ek = 1/2 . m . v 2
The kinetic energy of a a rotating body
ek = 1/2 . I . p 2
Conservation of Energy..
In the absence of any dissipative forces i.e.friction , the sum of the potential energy and kinetic energy remains constant.
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or converted between forms. This is a key concept in all engineering systems.
These energy and power equations are often used alongside dynamics formulae and stress and strain equations in engineering analysis and design.