Rotational kinetic energy
The instantaneous rotational kinetic energy of a rotating rigid body is written

(8.14) 
Making use of Equation (8.4), and some vector identities (see Section A.4),
the kinetic energy takes the form
Hence, it follows from Equation (8.5) that
Making use of Equation (8.13), we can also
write
Here,
is the row vector of the Cartesian components
, , , which is, of course, the transpose
(denoted ) of the column vector
.
When written in component form, Equation (8.17) yields

(8.18) 