Angular momentum is defined as the cross product of the radius vector and the (linear)momentum vector. Its magnitude is given by the formula: r * m * v sinθ .
Angular Momentum comes into picture only in rotational motion. So, if we have an object of mass 'm' rotating in a circle of radius 'r' and moving with tangential velocity 'v', then the angular momentum would simply be m * v * r [since sin90(degrees) = 1].
I have the following doubts:
1) Since angular momentum comes into play only during rotational motion, and since the tangential velocity vector is always perpendicular to the radius vector, there cannot be any situation where θ can take values other than 90(degrees), right? If it does so, the motion cannot be rotational, correct?
2) Then, why is angular momentum not defined as simply "m * v(tangential) * r" but defined as the cross product of 2 vectors (since even the direction of angular momentum has no physical significance) ?