- #1

Like Tony Stark

- 179

- 6

- Homework Statement
- The disk with a slot rotates with ##\omega =20 \frac{rad}{s}## about a vertical axis that passes through its centre. There's a slider of mass ##0.73 kg## that oscilates because of the action of a spring (not shown in the picture) and it has a positive velocity ##90 \frac{cm}{s}## relative to the disk when it is in ##x=0##. Determine the normal force exerted by the slot on the slider when ##x=0##.

- Relevant Equations
- ##a_I=a_o+\dot \omega \times r+\omega \times (\omega \times r)+2(\omega \times v_{rel}) +a_{rel}##.

Well, first a wrote the equation for acceleration in non inertial systems.

##a_I=a_o+\dot \omega \times r+\omega \times (\omega \times r)+2(\omega \times v_{rel}) +a_{rel}##.

Then, ##a_o=0## (because the system doesn't move), ##a_i=0## (because it is measured from the non inertial system), ##\dot \omega =0## (because the angular velocity is constant), ##r=0## (because ##x=0##)

So we get

##-2 (\omega \times v_{rel})=a_{rel}##

Then, we write Newton's equations

##x) Fe=m.a_{rel}##

##y) N-F_{Cor}=0##

Where ##Fe## is the elastic force and ##F_{Cor}=2(\vec \omega \times v_{rel})##

So I just have to replace with the numbers that I was given and get ##N##.

Are my ideas correct?

##a_I=a_o+\dot \omega \times r+\omega \times (\omega \times r)+2(\omega \times v_{rel}) +a_{rel}##.

Then, ##a_o=0## (because the system doesn't move), ##a_i=0## (because it is measured from the non inertial system), ##\dot \omega =0## (because the angular velocity is constant), ##r=0## (because ##x=0##)

So we get

##-2 (\omega \times v_{rel})=a_{rel}##

Then, we write Newton's equations

##x) Fe=m.a_{rel}##

##y) N-F_{Cor}=0##

Where ##Fe## is the elastic force and ##F_{Cor}=2(\vec \omega \times v_{rel})##

So I just have to replace with the numbers that I was given and get ##N##.

Are my ideas correct?