1. It has been suggested that rotating cylinders about 11 mi long and 5.2 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

Question

2. If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 52.0 N·m, what minimum force must be exerted by the mechanic at the end of a 37.0 cm lug wrench to accomplish the task?

I honestly don't know where to start

Answer 1

I seem to recall answering both of these questions two days ago. That would be a good place to start.

1. Write an equation for the accleration as a function of R (cylinder radius) and w, and set it equal to g (the acceleration of gravity). Then solve for the angular speed w. R = D/2; the length of the cylinders doesn't matter. I suggest using metric units for R and g.

2. Torque = force * (wrench length)

Make sure you express the wrench length in meters when you do the calculation