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I have mind boggling problem, trying to distinguish between Dynamic reaction versus Coriolis acceleration of thin hoop.

Problem: A thin, hoop of mass m and radius r spins at the constant rate ω 1 about an axle held by a fork-ended vertical rod, which rotates at the constant rate ω 2. The mass of spokes and spindle are negligible.

1. Determine Coriolis acceleration of point P at the edge of the hoop, when point P is aligned with vertical axis of the rod.

2. Determine acceleration produced by gyroscopic couple of the hoop on axle held by a fork-ended vertical rod, where support of the axle by the rod equals to radius of point P on each side of the hoop.

To solve Coriolis I am using equation ac = 2 omega1 omega2 *r.

To solve acceleration of gyroscopic couple I am using C = I omega1 omega2 / r, where mass to compute inertia = 1kg.

The question is:

Why is Coriolis acceleration doubled in comparison with gyroscopic acceleration? Both are causing the same effect of force and torque consequentially.

Where do i have problem in my calculations?

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