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S5.5 Kinetic energy of a rotating body: moment of inertia

Worked example

Worked example

A solid cylinder of mass 500kg and radius 1.0m is used as a flywheel to power a lorry. If the flywheel is initially ‘charged’ by bringing it up to a speed of ω=200π rad s-1, what is its kinetic energy? If the lorry uses 8.0 kW of power, for how many minutes can it operate before the flywheel comes to rest.

Solution

\[ K = \frac{1}{2} I \omega^2 \]

For the cylindrical flywheel

I=MR2/2=500kg×1.0/2=250kgm2

Hence

K=250×(200π)2/2=4.93×107 J

Since P=W/Δt, the lorry can operate for

\[ \Delta t=\frac{K}{8.0 \times 10 ^3}=6.17\times 10^3\; s = 1.7\;{\rm hours} \]

 

Demo

Demo

(Demonstration of rolling three cylinders with different moments of inertia down a slope)
 
TIncreasing Rotational Inertia

Learning Resources

Textbook: HRW Chapter 10.6 and 10.10. Ignore section 10.7 on calculating moments of inertia by integration.
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