Answer:
e. 2ωs / √5
Explanation:
The rotational kinetic energy of any rigid body, like an extension of the translational kinetic energy, is defined as follows:
Krot = 1/2 *I * ω²
For a solid sphere of mass M and radius R, the moment of inertia regarding any axis through its center, is as follows:
I =2/5 M*R²⇒ Krot(sp) = 1/2 (2/5 M*R²)*ωs² (1)
For a solid cylinder, rotating through an axis running through the central axis of the cylinder, the moment of inertia can be calculated as follows:
I = 1/2 M*R² ⇒ Krot(c) = 1/2 (1/2*M*R²)*ωc² (2)
As both rotational kinetic energies must be equal each other, we can equate (1) and (2), as follows:
1/2 (2/5 M*R²)*ωs² = 1/2 (1/2*M*R²)*ωc²
Simplifying common terms, and solving for ωc, we have:
ωc = 2*ωs /√5
