Rotational Kinetic Energy: Practice Problem & Solution
A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation ($E_{sphere} / E_{cylinder}$) will be: (2016 - II)
Solution Explained:
To solve this problem, we apply the core principles of Rotational Kinetic Energy. Understanding the underlying formula is key to arriving at the correct answer below:
Kinetic energy $E = \frac{1}{2}I\omega^2$. For sphere, $E_1 = \frac{1}{2}(\frac{2}{5}mR^2)\omega^2 = \frac{1}{5}mR^2\omega^2$. For cylinder, $E_2 = \frac{1}{2}(\frac{1}{2}mR^2)(2\omega)^2 = mR^2\omega^2$. Ratio is $\frac{1/5}{1} = 1:5$.
Leave a Reply