Question

The turntable in a microwave oven has a moment of inertia of 0.039 kg⋅m2 and is rotating once every 4.4 s . Part A What is its kinetic energy? Express your answer with the appropriate units.

Answer 1

To solve this problem it is necessary to apply the concepts related to Kinetic Energy, specifically, since it is a body with angular movement, the kinetic rotational energy. Recall that kinetic energy is defined as the work necessary to accelerate a body of a given mass from rest to the indicated speed.

Mathematically it can be expressed as,

$KE = \frac{1}{2} I\omega^2$

Where

I = Moment of Inertia

$\omega =$Angular velocity

Our values are given as

$I = 0.039kg\cdot m^2$

A revolution is made every 4.4 seconds.

$\theta = 1 rev \rightarrow 4.4s$

$\Rightarrow \omega = \frac{1rev}{4.4s}$

If the angular velocity is equivalent to the displacement over the time it takes to perform it then

$\omega = 0.2272rev/s(\frac{2\pi rad}{1rev})$

$\omega = 1.42rad/s$

Replacing at our previous equation we have,

$KE = \frac{1}{2} I\omega^2$

$KE = \frac{1}{2} (0.039)(1.42)^2$

$KE = 0.03993J$

Therefore the kinetic energy is equal to $3.9*10^{-2}J$