  We derive the expressions for the full angular distributions of $\bar B\to
D\ell\bar \nu_\ell$ and $\bar B\to D^{\ast }\ell\bar \nu_\ell$ decays and
discuss the spectra on each angle separately. The coefficient functions,
depending on helicity amplitudes, can then be combined in an ensemble of
observables which can then be used to check for the presence of New Physics. We
examine the sensitivity of each of these observables on the presence of
non-Standard Model interaction terms at low energies. The expressions presented
here are general and can be used for studying any other semileptonic
pseudoscalar to pseudoscalar/vector meson decay. We also examine the problem of
pollution of the $\bar B\to D^{\ast}(\to D\pi)_S\ell\bar \nu_\ell$ decay sample
by the $\bar B\to D_0^{\ast}(\to D\pi)\ell\bar \nu_\ell$ events, and point out
that a measurement of two particular quantities could clarify whether or not
the $(D\pi)_{S-\rm wave}$ in the vicinity of $D^\ast$-peak is (approximately)
described by the Breit-Wigner formula.
