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

Work and Power

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

Rotation

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

Energy

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)

e_{p} = M . g _{n}. h

The kinetic energy of a a body by virtue of its motion at uniform linear velocity

e_{k} = 1/2 . m . v ^{2}

The kinetic energy of a a rotating body

e_{k} = 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.