tangental velocity and artificial gravity question, please help?

Question

my phy proff forgot to post the class lectures online (we dont do lectures in class... long story) so i dont kno how to do any of the problems given on his online quiz... please help

Simulate artificial gravity in a tube shaped space station with a 192.9 m radius far from earth (earth's gravitational pull is negligible) . Choose the tangential velocity of a point on the tube such that artificial gravity of 0.9013 g results ( g is the gravitational acceleration close to the surface of the earth)

the answer is 41.29859747860695, but i dont kno how to get it, please help

Answer 1

You need a centripetal force equal to the required 0.9013g, where g = 9.8 m/s^2 is the force of gravity at the surface of the Earth. The centripetal force Fc is calculated as Fc = (v^2)/r, where v is tangential velocity and r is radius. You've been given the radius, so this problem becomes 0.9013g = v^2/(192.9 m) ==> v^2 = (192.9 m)*0.9013g ==> v = sqrt((192.9 m)*0.9013*(9.8 m/s^2)), which you can see will work out to have units of m/s.

Answer 2

The apparent centrifugal acceleration at a point in a rotating object is v²/r where v is the speed the point is moving and r is the distance of the point from the centre of rotation.

You should be able to work it out from that.