# Does an object rotating in place have linear momentum?

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?

• 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. May 4, 2020 at 14:27

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.

$$\sum p_\text{ particle}=p_\text{ total}=0 \qquad \text{ if centre-of-rotation is CoM}$$