# Is force independent of reference frame?

1. Nov 20, 2015

### sandyforever

1. The problem statement, all variables and given/known data
Recently, I have been wondering whether forces are independent of reference frames(inertial and non inertial). From Newton's law we know that the second law is valid only for inertial frames. But what about the non inertial frames. Let ∑F be the net force on an object in an inertial reference frame k. Let 'm' be it's mass and 'a' be it's acceleration in the frame k.

2. Relevant equations

By Newton's second law in the frame k, ∑F = m×a

3. The attempt at a solution
Acceleration can have different meaning for different reference frames but certainly we can't conclude about the net force using the second law for both the inertial and non inertial reference frames as it's valid for only one of the cases. So do we then take into consideration the fictitious forces for the non inertial cases for the purpose of calculating the net force. How does it explains then? Please help!

2. Nov 20, 2015

### PeroK

In terms of fictitious forces and non-inertial (accelerating) reference frames, there must be lots online (assuming you don't have a mechanics text that explains it). The way I look at it is:

If you are accelerating to the right at $a_0$, and you want to explain things from your accelerating reference frame, where everything is accelerating to the left at $-a_0$. You have to imagine a fictitious force, proportional to the mass, on everything. For a body of mass $m$ the force is $F_f = -ma_0$.

If there is a real force $F$ on that body, then the net force (in your reference frame) is $F_{net} = F + F_f = F - ma_0$.

And, if you observe an acceleration of $a_{net}$ then you know that the real force on the object is $F = F_{net} + ma_0 = m(a_{net} + a_0)$

3. Nov 20, 2015

### sandyforever

Thanks, but can you please tell me what are the types of forces that Newton's second law takes into consideration?

4. Nov 20, 2015

### PeroK

I'm not sure I understand. All forces. But, the second law doesn't apply in a non-inertial reference frame unless you add in the fictitious forces.