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?

1 Answer
Joseph W.
Aug 8, 2017

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.

Related questions
See all questions in Circular Motion
Impact of this question
1203 views around the world
You can reuse this answer
Creative Commons License