# A model train, with a mass of 4 kg, is moving on a circular track with a radius of 5 m. If the train's rate of revolution changes from 1/9 Hz to 1/4 Hz, by how much will the centripetal force applied by the tracks change by?

Change in centripetal force$= m {w}_{2}^{2} r - m {w}_{1}^{2} r$
$= 4 {\pi}^{2} m r \left({n}_{2}^{2} - {n}_{1}^{2}\right) = 4 \times {\pi}^{2} \times 4 \times 5 \times \left(\frac{1}{4} ^ 2 - \frac{1}{9} ^ 2\right)$
$\approx 39.6 N$