Problem 1.185

The angular momentum of a particle relative to a certain point \(O\) varies with time as \(\mathbf{M}=\mathbf{a}+\mathbf{b} t^{2},\) where \(\mathbf{a}\) and \(\mathbf{b}\) are constant vectors, with \(a \perp b\). Find the force moment \(N\) relative to the point \(O\) acting on the particle when the angle between the vectors \(\mathbf{N}\) and M equals \(45^{\circ}\).