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 = (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 = (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((2\pi rad)/(1rev))`

`\omega = 1.42rad/s`

Replacing at our previous equation we have,

`KE = (1)/(2) I\omega^2`

`KE = (1)/(2) (0.039)(1.42)^2`

`KE = 0.03993J`

Therefore the kinetic energy is equal to
`3.9*10^(-2)J`