A 12-g coin that has a diameter equal to 1.9 cm is spinning at 15 rev/s about a
ID: 1411985 • Letter: A
Question
A 12-g coin that has a diameter equal to 1.9 cm is spinning at 15 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.
(a) What is the angular momentum of the coin about its center of mass?
kg · m2/s ---Select--- toward you away from you
(b) What is the coin's angular momentum (including direction) about a point on the tabletop 10 cm from the axis?
kg · m2/s ---Select--- toward you away from you
For the following questions, assume the coin spins about a vertical diameter at 15 rev/s while its center of mass travels in a straight line across the tabletop at 5.0 cm/s.
(c) What is the angular momentum of the coin about a point on the line of motion of the center of mass?
kg · m2/s ---Select--- toward you away from you
(d) When it is both spinning and sliding, what is the angular momentum of the coin about a point 10 cm north of the line of motion of the center of mass?
kg · m2/s ---Select--- toward you away from you
Explanation / Answer
a) I = 0.25 MR^2 + 1/12 ML^2
= 0.25*0.012*0.0095^2 +0
= 2.7075e-7
Angular momentum = Iw = 2.7075e-7*15*2pi = 0.00002552 kgm^2/s away from you.
b) Angular momentum about a point 10 cm from com = angular momentum of com about that point + angular momentum about com
= 0 + 0.00002552 kgm^2/s away from you.
= 0.00002552 kgm^2/s away from you.
c) Angular momentum about a point on the line of motion of com = angular momentum of com about that point + angular momentum about com
= 0 + 0.00002552 kgm^2/s away from you.
= 0.00002552 kgm^2/s away from you.
d)
Angular momentum about the point = angular momentum of com about that point + angular momentum about com
= 0.012*0.05*0.10 + 0.00002552 kgm^2/s towards you.
=0.00008552 kgm^2/s towards you.
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