Question

URGENT! 50pts! Help with rotational speed questions please?

1.) You sit at the outer rim of a Ferris Wheel that rotates 2 revolutions per minute (RPM). What would your rotational speed be if you were instead clinging to a position halfway from the center to the outer rim.

2.)At the outer edge of a rotating space habitat, 130m from the center, the rotational acceleration is g. What is the rotational acceleration at a distance of 65 m from the center of the habitat?

Answer 1

1). If you want the wheel to turn as one solid piece, then all parts of it must have the same RATE of rotation. If one part was going 2 RPM and another part was going 3 RPM, then there's no way both parts could stay hooked together. Their SPEED depends on their distance from the center, but they all have to make the same RPM. 2). The CENTRIPETAL acceleration of anything that's rotating is. m-v-squared/ R. The object's speed depends on its radius, and it's acceleration varies directly with the square of the speed. So if you move in to half the radius, the acceleration becomes 1/4 of the original value.