Question

If an object’s rotational kinetic energy is 50 J and it rotates with an angular speed of 12 rad/s, what is the moment of inertia?

Short answer

The moment of inertia is,$0.69\mathrm{kg}.{\mathrm{m}}^2$ .

Step-by-step solution

Identification of the given data

The given data can be listed below as,

• The kinetic energy of the object is,$K_{\mathit{r}\mathit{o}\mathit{t}}=50\mathrm{J}$.
• The angular speed of object is, $\omega =12\mathrm{rad}/\mathrm{s}$

Significance of rotational kinetic energy

The rotational kinetic energy of a rotating object can be expressed as half the product of the object's angular velocity and its moment of inertia about its axis of rotation.

Determination of the moment of inertia

The relation of rotational kinetic energy is expressed as,

$K_{rot}=\frac{1}{2}I{\omega }^2$ ...(i)

Here $K_{rot}$is the rotational kinetic energy, $\omega$is the angular speed and$I$is the moment of inertia.

Substitute 50 J for $K_{rot}$, and 12 rad/s for $\omega$in the equation (i).

role="math" localid="1657850631785" $$\begin{gathered} 50\mathrm{J}=\frac{1}{2}\times \mathrm{I}\times {\left(12\mathrm{rad}/\mathrm{s}\right)}^2 \\ \mathit{}\mathit{}I=0.69\mathrm{kg}.{\mathrm{m}}^2 \end{gathered}$$

Hence the moment of inertia is, $0.69\mathrm{kg}.{\mathrm{m}}^2$.