Question

A solid uniform-density sphere is tied to a rope and moves (without spinning) in a circle with speed 7 m/s. The distance from the center of the circle to the center of the sphere is 1.8 m, the mass of the sphere is 6 kg, and the radius of the sphere is 0.89 m. The angular speed, w=5.62. What is the rotational kinetic energy of the sphere?,

Answer 1

Speed of the sphere = 7 m/s Distance between center of the circle to the center of the sphere = 1.8 m Mass of the sphere = 6kg Radius of the sphere = 0.89 m Angular speed w = 5.62 Rotational kinetic energy of the sphere = 1/2 I x w^2 I being the moment of inertia, w being the angular speed I = (2/5) x M x R^2 = (2/5) x 6 x 0.89^2 = 1.90 Rotational kinetic energy = 1/2 x 1.9 x 5.62^2 = 30 J