For example, a pendulum rotates about its pivot point, but does the pendulum also have translational motion? I ask this because in the following link, the author assumed in his first equation that a tennis racket has only rotational motion as it is swinging freely about a pivot point, so I was confused whether the racket also included translational motion or not: Physics of a Tennis Racquet
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The author you mentioned is right.
A rigid body is in pure translation if and only if all points of the body have the same velocity vector. The body is in pure rotation about a fixed axis if and only if all points follow concentric circles about the axis.
Therefore the tennis racket and the pendulum swinging about a fixed pivot have only rotational motion.
answered Mar 20, 2018 at 23:27
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$\begingroup$ One more thing, how does the author derive the equations "from the kinematics of the problem"? $V^{'}_{B}=w^{'}_{B}d$ and $V_{B}=-w_{B}d$ $\endgroup$ Commented Mar 21, 2018 at 12:52