Answered

Find the approximate kinetic energy of a circular wheel of radius r and mass M that is rotating about its center at 2 cycles/s. Assume the wheel’s mass is concentrated at the rim and the mass of the wheel’s spokes is negligible.

Answer :

MechEngineer

Answer:

[tex]8M(r\pi)^2[/tex]

Explanation:

First we convert 2 cycles/s to angular velocity knowing that each circle has an angle of 2π

[tex]\omega = 2 * 2\pi = 4\pi rad/s[/tex]

Then we calculate the moment of inertia of the cylindrical shell, assuming there's no mass inside the wheel (only at the rim):

[tex]I = mr^2 = Mr^2[/tex]

So the kinetic energy of this is

[tex]E_k = I\omega^2/2 = Mr^2*(4\pi)^2/2 = 8M(r\pi)^2[/tex]

Other Questions