Marble in a Cone

A marble is spun in a cone that has a radius \({{params.R}}\ \rm{m}\) and height \({{params.H}}\ \rm{m}\) with an initial velocity of \({{params.v}}\ \rm{m/s}\) tangent to the horizontal rim of the cone. As the marble spins around the bowl, its rotational radius r shrinks. As the marble descends, where r = \({{params.r}}\ \rm{m}\), the velocity vector makes an angle \(\theta\) with the horizontal. Determine the new velocity magnitude and \(\theta\) in degrees.

Part 1

What is \(\lvert v \rvert\)?

Answer Section

Please enter in a numeric value in m/s.

Part 2

What is \(\theta\)?

Answer Section

Please enter in a numeric value in \(\circ\).

Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.