A sphere of uniform density with mass 15 kg and radius 0.6 m is spinning, making one complete revolution every 0.3 s. The center of mass of the sphere has a speed of 3 m/s. (a) What is the rotational kinetic energy of the sphere

Answer :

boffeemadrid

Answer:

[tex]473.56\ \text{J}[/tex]

Explanation:

T = Time taken to complete one revolution = 0.3 s

m = Mass of sphere = 15 kg

r = Radius of sphere = 0.6 m

I = Moment of inertia of sphere = [tex]\dfrac{2}{5}mr^2[/tex]

Angular speed of the sphere is

[tex]\omega=\dfrac{2\pi}{T}=\dfrac{2\pi}{0.3}\\\Rightarrow \omega=20.94\ \text{rad/s}[/tex]

Rotational kinetic energy is given by

[tex]K_r=\dfrac{1}{2}I\omega^2=\dfrac{1}{2}\times \dfrac{2}{5}mr^2\omega^2\\\Rightarrow K_r=\dfrac{1}{2}\times \dfrac{2}{5}\times 15\times 0.6^2\times 20.94^2\\\Rightarrow K_r=473.56\ \text{J}[/tex]

The rotational kinetic energy of the sphere is [tex]473.56\ \text{J}[/tex].

Other Questions