Question

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?

Answer 1

The centripetal force will decrease by a factor of `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=(2pi)/T`, where `omega` is the angular speed, and `T` is time taken for 1 rotations. When a object has 6`Hz` for circular motion, than it means it rotates around the path 6 time per second and thus. will only take `1/6` for 1 rotation. Likewise, 4`Hz` will have a `T` value of `1/4`. Finding the angular speed for both, we get

`omega=12pi` for the 6`Hz` train

`omega=8pi` for the 4`Hz` train

Now to find centripidal force, we need the equation

`F=momega^2r`, were `m=` mass (kg) and `r=`radius of rotation.

Placing our values into this formula, we get

`F=15552piN` for the 6`Hz` train

`F=6912piN` for the 4`Hz` train

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

Hope this helps.