# Spinning Chair and Wheel

## Homework Statement

The problem is Problem 2 on page 3 here: http://ocw.mit.edu/courses/physics/...ngular-momentum/MIT8_01SC_problems25_soln.pdf

## Homework Equations

3. The Attempt at a Solution [/B]
My question concerns the solution in the above link. According to the solution, the angular momentum of the wheel about the central axis is
$${\bf L}_{S,w}^{\text{total}}={\bf L}_{S,w}^{\text{rot}}+{\bf L}_{cm,w}^{\text{spin}}=((I_w+m_wd^2)\omega+I_w\omega_s){\bf \hat{k}}.$$
(See page 4.) However, isn't the angular momentum of a system of particles about a point equal to the angular momentum of the center of mass plus the angular momentum of the particles with respect to the center of mass? (See http://en.wikipedia.org/wiki/Angular_momentum#Angular_momentum_simplified_using_the_center_of_mass, for example.) This would mean the angular momentum of the wheel about the central axis is actually
$${\bf L}_{S,w}^{\text{total}}=(m_wd^2\omega+I_w\omega_s){\bf \hat{k}}.$$

Thanks to anyone who can help clear this up!