Mechanics> angular-velocity...

A straight, smooth tunnel is dug through a uniform spherical planet of mass density ? P. The tunnel passes through the center of the planet and is perpendicular to the planet''s axis of rotation, which is fixed in space. The planet rotates with a constant angular speed w so that objects in the tunnel have no apparent weight. Find the required angular speed of the planet ?.

Shuvam Shukla , 12 Years ago

Grade 12

1 Answers

SOURAV MISHRA

Last Activity: 12 Years ago

when you are in a rotating reference frame then you experience the radially outward centrifugal force.

in this case the centrifugal force balances the gravitational force of attraction.

that is G*(4/3)*πr³Pm/r² = mrw².

here m = mass of the particle, r = distance of the particle from the center of the planet along the tunnel that is the radial distance of the particle.

this gives w = {(4/3)*πGP}^(1/2)

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Mechanics> angular-velocity...

Shuvam Shukla , 12 Years ago

SOURAV MISHRA

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