Circular Marble
Angular Speed- physics?
The entrance of a science museum features a funnel into which marbles are rolled one at a time. The marbles circle around the wall of the funnel, eventually spiraling down into the neck of the funnel. The internal radius of the funnel at the top is 1.50 m. At the bottom, the funnel’s neck narrows to an internal radius of 0.025 m. A 5.0 * 10^-3 kg marble begins rolling a large circular orbit around the funnel’s rim at 0.65 rev/s. If it continues moving in a roughly circular path, what will the marble’s angular speed be as it passes throught the neck of the funnel? (consider only the effects of the conservation of angular momentum).
This question is tremendously simplified by ignoring several effects:
1) The loss of PE as the marble moves down the funnel, which increases both the translational speed as well as the angular speed.
2) The Corriolis effect depending on the hemisphere and direction of rotation.
3) The centripetal force that will retard the motion of the marble down the funnel much the same as a sattelite in orbit around the Earth.
4) Friction as the marble rolls
The simplest solution is to just consider the change in radius of rotation and assume the energies are constant and there is no loss to friction
in this case
I1*ω1=I2*ω2
treating the marble as a point mass
I=m*r^2
since the mass doesn’t change, the equation is
r1^2*ω1=r2^2*ω2
ω1=0.65
r1=1.5
r2=0.025
solve for ω2
ω2=1.5^2*0.65/0.025^2
ω2=2340 rev/s
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Crown Paradise Club Cancun by CheapCaribbean
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