I understand that an object with linear momentum could have angular momentum. However, can the same be in reverse? For example, will a wheel spinning in place be considered to have both angular and linear momenta? It will have tangential velocity, but the wheel itself is not moving in a straight line. Could you use its tangential velocity and say it has linear momentum?
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$\begingroup$ Linear momentum of a massive body is given by $m v_{cm}$. So a wheel rotating in place should not have linear momentum as a whole as it's center of mass is not moving. $\endgroup$ – Harshit Joshi May 4 at 14:27
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Each particle that the object consists of can carry momentum. And they all except for the particle at the very centre do carry some momentum.
$$p_\text{ non-centre-particle}\neq 0$$
The total momentum (the sum of all particles' momentum) will be zero if the object is spinning about its centre-of-mass (CoM), since all particles on one side of the spinning object (on one side of the CoM) cancel out the effect of those on the other side.
$$\sum p_\text{ particle}=p_\text{ total}=0 \qquad \text{ if centre-of-rotation is CoM}$$
