A ball of 0.145 is tied to a 50 cm rope and begins to spin in a horizontal circle. Determine (a) the centripetal acceleration if the velocity of the ball is 7.0 m/s and (b) find the centripetal force that keeps the ball in the circular path.

A child is twirling a 0.0103-kg ball on a string in a horizontal circle whose radius is 0.0907 m. The ball travels once around the circle in 0.474 s. (a) Determine the centripetal force acting on the ball. (b) If the speed is doubled, by what factor does the centripetal force increase?

A puck is sliding around a circular track that is banked at an angle ϕ with respect to the horizontal such that no friction between the puck and the track is required to keep the puck from slipping up or down the track. If the puck is moving at a speed 34.1 m/s and the radius of the track is 401 m, determine ϕ in degrees.

A motorcycle has a constant speed of 24.5 m/s as it passes over the top of a hill whose radius of curvature is 174 m. The mass of the motorcycle and driver is 309 kg. Find the magnitude of (a) the centripetal force and (b) the normal force that acts on the cycle.

A rotating space station is said to create artificial gravity—a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. An example of such a setup are Space Station V and the Discovery from the movie 2001: A Space Odyssey as shown below. If the space station is 1800 m in diameter, what angular velocity (in radians per second) would produce an artificial gravity similar to that on Earth inside the outer wall of the station?