# A model train, with a mass of 12 kg, is moving on a circular track with a radius of 9 m. If the train's rate of revolution changes from 6 Hz to 4 Hz, by how much will the centripetal force applied by the tracks change by?

Aug 8, 2017

The centripetal force will decrease by a factor of $\frac{9}{4}$ or more exactly, by 8640N

#### Explanation:

Just learnt circular motion today so . . . umm, answer might not be 100% correct. Anyhow, we first need to find the angular speed to find centripetal force. Angular speed is found using

$\omega = \frac{2 \pi}{T}$, where $\omega$ is the angular speed, and $T$ is time taken for 1 rotations. When a object has 6$H z$ for circular motion, than it means it rotates around the path 6 time per second and thus. will only take $\frac{1}{6}$ for 1 rotation. Likewise, 4$H z$ will have a $T$ value of $\frac{1}{4}$. Finding the angular speed for both, we get

$\omega = 12 \pi$ for the 6$H z$ train

$\omega = 8 \pi$ for the 4$H z$ train

Now to find centripidal force, we need the equation

$F = m {\omega}^{2} r$, were $m =$ mass (kg) and $r =$radius of rotation.

Placing our values into this formula, we get

$F = 15552 \pi N$ for the 6$H z$ train

$F = 6912 \pi N$ for the 4$H z$ train

Thus, we can now find the difference between the centripetal force applied by the tracks.

Hope this helps.