A bridge on a bicycle racing track is shaped like an arc of a circle of radius 12.0 m. What should be the speed limit for a cyclist to avoid flying over the top of the bridge?

A tiny sphere of mass 125 g revolves in a vertical plane around a horizontal axis at the end of a cable of length 80 cm. What should be the minimum angular velocity of rotation in order for the sphere to complete a full revolution without the cable becoming loose at the highest position?

A motion capture system is employed to track the motion of an adult pedestrian walking over a rigid, level surface. The position of the center of gravity of the pedestrian is investigated. According to the data analysis, the pedestrian's center of gravity follows a vertically curved (circular) path when walking. Furthermore, the center of gravity is defined by an arc with a radius of 1.0 m. Determine the minimum speed at which a pedestrian starts to run.

A bird that can withstand an acceleration of 11g sees its prey during flight. It dives vertically down to catch it at a constant speed of 350 m/s. At what height above the ground the bird must begin to pull out (following a vertical circular trajectory) to avoid blacking out and crashing into the ground.

A roller coaster includes a vertical loop that provides thrilling experiences to its riders. As shown below, the loop has a radius of 15.0 meters and the coaster completes the loop in 6.0 seconds. Find the ratio of a passenger's apparent weight to their real weight at the bottom of the loop.