Acceleration for a non-inertial reference frame

In summary: N=m.a_{rely} -2(\omega \times v_{rel})## ##m##, ##\omega## and ##v_{rel}## are a given values; ##a_{rely}=0## because the slider just moves in ##x##Almost correct. You need to multiply the second term by the mass. Also, the problem gives only magnitude of ##\omega##, but I think it is safe to assume that it is in the ##+z## direction.
  • #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?
 

Attachments

  • 20191023_000514.jpg
    20191023_000514.jpg
    21.5 KB · Views: 206
Physics news on Phys.org
  • #2
There are two non-inertial frames, one fixed on the platform and one fixed on the slider. Which one are you considering? When you say that ##a_0=0## because the "system doesn't move" which system is this? What are you going to use for ##v_{rel}##? Also, don't replace any numbers before you get an expression for ##N## in terms of symbols all of which are given. That will make it easier to check your work.
 
  • #3
kuruman said:
There are two non-inertial frames, one fixed on the platform and one fixed on the slider. Which one are you considering? When you say that ##a_0=0## because the "system doesn't move" which system is this? What are you going to use for ##v_{rel}##? Also, don't replace any numbers before you get an expression for ##N## in terms of symbols all of which are given. That will make it easier to check your work.
I'm considering a system fixed to the platform. I said that ##a_0=0## because the origin doesn't move. Then I said that ##a_i## is the acceleration measured from an inertial frame, but as I took the disk frame, I said that it was 0.

As for not replacing the numbers, yes, I'll take your advice, but I replaced them to check if the data that I plugged in was ok.
 
  • #4
So what's your symbolic answer?
 
  • #5
kuruman said:
So what's your symbolic answer?
##y)N-\Sigma F_{rely}=m.a_{rely}##
##N=\Sigma F_{rely}+m.a_{rely}##

Where ##\Sigma F_{rely}## is the sum of the pseudo-forces acting on the ##y## direction and ##a_{rely}## is the acceleration of the slider relative to the disk.
 
  • #6
Like Tony Stark said:
##y)N-\Sigma F_{rely}=m.a_{rely}##
##N=\Sigma F_{rely}+m.a_{rely}##

Where ##\Sigma F_{rely}## is the sum of the pseudo-forces acting on the ##y## direction and ##a_{rely}## is the acceleration of the slider relative to the disk.
Not what I had in mind. I am asking for an expression giving ##N## in terms of symbols for which you have numbers. You don't have numbers for any of the quantities on the right hand side except for the mass ##m##.
 
  • #7
kuruman said:
Not what I had in mind. I am asking for an expression giving ##N## in terms of symbols for which you have numbers. You don't have numbers for any of the quantities on the right hand side except for the mass ##m##.
##y)N=m.a_{rely} -2(\omega \times v_{rel})##

##m##, ##\omega## and ##v_{rel}## are a given values; ##a_{rely}=0## because the slider just moves in ##x##
 
  • #8
Almost correct. You need to multiply the second term by the mass. Also, the problem gives only magnitude of ##\omega##, but I think it is safe to assume that it is in the ##+z## direction.
 

FAQ: Acceleration for a non-inertial reference frame

1. What is acceleration for a non-inertial reference frame?

Acceleration for a non-inertial reference frame refers to the change in velocity of an object in a frame of reference that is accelerating. This means that the object's velocity is changing not only due to its own motion, but also due to the acceleration of the frame of reference it is in.

2. How is acceleration calculated for a non-inertial reference frame?

Acceleration for a non-inertial reference frame is calculated by taking into account the acceleration of the frame of reference and the acceleration of the object in the frame. This can be done using the equation a = a' + a'', where a is the total acceleration, a' is the acceleration of the frame, and a'' is the acceleration of the object in the frame.

3. What is an inertial reference frame?

An inertial reference frame is a frame of reference in which Newton's laws of motion hold true. In other words, in an inertial reference frame, an object will maintain its velocity unless acted upon by an external force and an object will continue to move in a straight line unless acted upon by an external force.

4. How does acceleration in a non-inertial reference frame differ from acceleration in an inertial reference frame?

In a non-inertial reference frame, the acceleration of an object is not solely due to the forces acting on the object, but also due to the acceleration of the frame itself. In an inertial reference frame, the acceleration of an object is only due to the forces acting on the object.

5. What are some examples of non-inertial reference frames?

Some examples of non-inertial reference frames include a rotating frame of reference (such as a merry-go-round), a frame of reference in free-fall, and a frame of reference on a accelerating train or car.

Similar threads

Back
Top