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 marble goes around a loop-the-loop track by always being in contact with the loop. The radius of the vertical loop is 12.5 cm. At the top of the loop, the magnitude of the gravitational force is 1.25 times the magnitude of the normal force. Find the magnitude of the marble's velocity at the top.

An object of mass 0.125 kg attached to a cable revolves in a vertical circular motion of radius 0.5 m. The magnitude of the velocity is 4.5 m/s at the highest vertical position and 7.8 m/s at the lowest vertical position. Find the cable's tension at the highest vertical position.

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 acceleration 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.