Question

uniform circular motion: a disk-shaped space station 150 m in diameter (75 m radius) spins at a uniform rate about an axis through its center and perpendicular to the plane of the disk. if the acceleration of a point on the rim of the disk is to be equal to g, what must be the speed of an astronaut standing at the rim of the space station? use g

Answer 1

Time taken to complete one revolution for disk-shaped space station spins at uniform rate is 17.381 seconds

Given diameter of the disk(d) = 150 m

Radius = d/2 = 75 m

acceleration (a) = g

Ω = sqrt(g/r)

            = sqrt(9.8/75) rad/s^2

            = 0.361 rad/s^2

Time taken to complete one revolution = 2π/Ω

= 17.381 seconds

A circular motion is a body's movement along a circle-shaped route. Uniform Circular Motion is the term used to describe a body travelling at a consistent speed along a circular route. Here, the velocity varies while the speed is constant.

If a particle is travelling in a circle, it must be experiencing some acceleration that is pushing it in that direction and causing it to rotate around the centre. The motion is uniformly circular because the acceleration, which is perpendicular to the particle's velocity at every time, only modifies the direction of the velocity, not its quantity. The force pushing in the direction of the centre is known as the centripetal force, and we refer to this acceleration as centripetal acceleration (or radial acceleration).

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