Question

PLEASE USE THE NUMBERS!

A 16-g coin that has a diameter equal to 1.7 cm is spinning at 12 rev/s about a fixed vertical axis. The coin is spinning on edge with its center directly above the point of contact with the tabletop. As you look down on the tabletop, the coin spins clock-wise. Its moment of inertia about an axis through its diameter is given in the figure below. Model the coin as a cylinder of length L and radius R and take the limit as L approaches zero.

What is the angular momentum of the coin about its center of mass? Select--- toward you away from you

What is the coin's angular momentum (including direction) about a point on the tabletop 10 cm from the axis?
kg

Answer 1

(a)

$L=L_{spin}=I_{cm\omega spin}$

$L=(0.016\times 0.0085^{2}/4)\times 24\pi \; \; kgm^{2}/s$

$\boldsymbol{L=2.178\times 10^{-5} \; \; kgm^{2}/s}$

(b)

$L=L_{spin}+L_{orbit}$

$L_{orbit}=0$

$\boldsymbol{L=2.178\times 10^{-5} \; \; kgm^{2}/s}$

(c)

$L_{orbit}=0$

$\boldsymbol{L=2.178\times 10^{-5} \; \; kgm^{2}/s}$

(d)

$L_{orbit}=\pm mvr=\pm 9.6\times 10^{-5}$

$\boldsymbol{L=11.778\times 10^{-5} \; \; kgm^{2}/s}$