Chapter 10: Q33P (page 289)

Calculate the rotational inertia of a wheel that has a kinetic energy of 24400 Jwhen rotating at 602rev/min.

Expert verified

Rotational inertia of a wheel is, l = 12.3 kg.m².

Step by step solution

By using the concept of Rotational kinetic energy, we can find rotational inertia of thewheel.

Rotational Kinetic energy $K = \frac{1}{2} l ω^{2}$

To calculate rotational inertia of the wheel we will use rotational kinetic energy formula and rearrange it for inertia I

$\begin{array}{rcl} K & = & \frac{1}{2} l ω^{2} \\ l & = & \frac{2 K}{ω^{2}} \end{array}$ …(1)

We have K = 24000 J

$ω = 602 r e v / m i n$

Converting it into rad/sec

$\begin{array}{rcl} ω & = & 602 r e v / m i n \times \frac{2 πrad / rev}{60 s / m i n} \\ = & 63 r a d / s \end{array}$

Using $ω$ and K in equation (1), we get

$\begin{array}{rcl} l & = & \frac{2 \times 24400 J}{{(63 r a d / s)}^{2}} \\ = & 12.29 k g . m^{2} \\ \approx & 12.3 k g . m^{2} \end{array}$

Hence the rotational inertia of a wheel (I) is 12.3kg.m².

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