A 1.0 kg stone is attached to one end of a rope, which has negligible mass. The stone moves in a uniform circular motion in a vertical circle of radius 2.0 m. Calculate the tension at the bottom point, if the tension in the rope is zero at the topmost point.

A 55 kg skateboarder is moving down a ramp with a 5.0 m radius of curvature. If at the bottom of the ramp he reaches a speed of 8.0 m/s, what is the upward force acting on him when he is at the bottom of the ramp?

In an amusement park, a design of the carousel has two wires, one of which is horizontal, and the seat is attached to them. A horizontal circle of radius 7.50 m is formed by the seat as it swings at a speed of 20.0 rpm (rev/min). Determine the tension in each cable if the seat weighs 200 N and a person weighing 850 N is seated in it.

On a smooth floor, a ballet dancer weighing 50 kg is spinning at 3.0 rotations per second while holding outstretched arms. 1.80 meters is the distance from one hand to the other. The average hand weighs about 1.50 percent of the body, per biometric studies. How much force must be applied horizontally by her wrist on her hand?

A musical toy consists of a wooden ball that rotates in a horizontal circle around a central axis. The mass of the ball is 0.3 kg and is supported by two wires as shown in the figure. Determine the speed at which the tension in both wires is the same if the ball revolves at a constant speed.

A toy is made using a frictionless spherical shell with an inner radius of 35 cm and a tiny pearl of mass 8.0 g. The pearl lies on the inner shell, as shown in the figure. The shell can rotate about a fixed vertical axis at various angular speeds. When playing, a child remarks that the pearl moves from the bottom of the shell to a higher position only when the shell rotates at an angular speed greater than ω_a. The line that connects the center of the shell to the pearl forms an angle α with the vertical. Find ω_a in revolutions per minute.

Two equally weighted dancers clasp their hands in a dance hall and rotate around a shared axis once every 2.6 s. Assume each dancer's arm length is 0.90 m and each weight is 56.0 kg. Find the force with which they hold each other.