A 25-g coin that has a diameter equal to 1.3 cm is spinning at 18 rev/s about a

Question

A 25-g coin that has a diameter equal to 1.3 cm is spinning at 18 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 and direction of the coin about its center of mass?
kg · m2/s  

(b) What is the coin's angular momentum (including direction) about a point on the tabletop 10 cm from the axis?
kg · m2/s  

For the following questions, assume the coin spins about a vertical diameter at 18 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 and direction of the coin about a point on the line of motion of the center of mass?
kg · m2/s  

(d) When it is both spinning and sliding, what is the angular momentum and direction of the coin about a point 10 cm north of the line of motion of the center of mass?
kg · m2/s  

Explanation / Answer

a)

I = moment of inertia = ML2/12 + MR2/4 = (0.025) (0.013)2/12 + (0.025) (0.013/2)2/4 = 6.2 x 10-7 kgm2

w = angular velocity = 18 re/s = 18 x 6.28 rad/s = 113.04 rad/s

angular momentum is given as

L = I w = (6.2 x 10-7) (113.04) = 7.01 x 105

direction: upward

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