Question

Two uniform solid cylinders, each rotating about its central(longitudinal) axis, have the same mass of 1.25 kg, and rotate withthe same angular speed of 235 rad/s,but they differ in radius.

(a) What is the rotational kinetic energy ofthe smaller cylinder, of radius 0.32m?
J

(b) What is the rotational kinetic energy of the larger cylinder,of radius 0.7 m?

Answer 1

Step-by-step explanation:

mass, m = 1.25 kg

angular speed, ω = 235 rad/s

The moment of inertia of the cylinder is given by

I = 1/2 mr²

(a) the kinetic energy of rotation is given by

K = 1/2 Iω²

K = 1/4 mr²ω²

where, m is the mass of cylinder and r be the radius of cylinder

K = 0.25 x 1.25 x 0.32 x 0.32 x 235 x 235

K = 1767.2 J

(b) the kinetic energy of rotation is given by

K = 1/2 Iω²

K = 1/4 mr²ω²

where, m is the mass of cylinder and r be the radius of cylinder

K = 0.25 x 1.25 x 0.7 x 0.7 x 235 x 235

K = 8456.33 J