Question

A spinning rigid body has a rotational kinetic energy of 10 j and an angular speed of 10 s−1 . what is its rotational inertia?

Answer 1

Rotational kinetic energy = Iω²/2 = 10
I = rotational inertia(moment of inertia)
ω= angular speed = 10 s⁻¹

∴ 10 = I(10²)/2
∴ I = 20/10² = 0.2 kg-m²

Answer 2

Answer:

$I=0.2kg\cdot m^{2}$

Explanation:

The moment of inertia (or rotational inertia) is the rotational analog of mass for linear motion, this means it is the property of bodies that makes them oppose to rotate. For this particular problem we need to recall the rotational kinetic energy formula:

$K_{r}=\frac{1}{2}I\omega^{2}$,

where $I$ is the rotational inertia and $\omega$ is the angular speed.

Since we already know the value for the angular speed, the only thing left is to solve for the rotational inertia and compute:

$K_{r}=\frac{1}{2}I\omega^{2}$,

$2K_{r}=I\omega^{2}$,

$\frac{2K_{r}}{\omega^{2}}=I$,

$I=\frac{2*10}{10^{2}}$,

$I=0.2kg\cdot m^{2}$.