Question

In a large hollow cylinder, roller-coaster rider

can drive the car along the wall of the cylinder.

What minimum speed must be the car

without sliding downward?

Answer 1

The minimum speed must provide enough potential energy to reach the top and remain upside down:

$$mg=ma_c,\\\space\\ mg=m\frac{v^2}R,\\\space\\ v=\sqrt{gR}.$$