1. PHY221 Ch4: Newton’s Laws
Newton’s Laws NII: a=F/m, NI: Inertial frames, NIII
Examples

2. PHY221 Ch4: Newton’s Laws Main Points N2: a = F/m Vector equation
From observation to theory :
1- Force (Push pull) seems to generate acceleration
2- Systematize: We define force as a vector measured from a standard and experiment measuring force and acceleration on an object: slope of F vs a observed as constant-> define m intrinsic to object

3. PHY221 Ch4: Newton’s Laws Main Points
3- Since m intrinsic to object we switch standards and use a mass standard to define force -> kg
4- Physics raison d’etre becomes to give expression for forces:

4. PHY221 Ch4: Newton’s Laws Main Points
Assumed properties of mass (to be verified experimentally):
Scalar
independent of force
Additive: m1 and m2 attached together=>m=m1+m2

5. PHY221 Ch4: Newton’s Laws Main Points
N2 is valid in inertial (non-accelerated) frames.
N1: (F=0  a=0) defines inertial frames
Consider a reference frame attached to the room. In that frame a mass m sitting on the table will have F=0 and a=0 Thus Newton’s 2nd law is valid! Now consider a 2nd frame( the red frame) rotating w/ respect to the First one (the black frame at velocity w. In the red frame the mass m still has no force on it (F=0) but now it has an acceleration 𝑎=𝑅 𝜔 2 . Thus we have a problem since 𝑎≠0 and 𝐹=0
The problem is resolved by making all frames, like the red one, invalid for applying N2. Thus we require that N2 be applied only in frames where 𝐹=0𝑎=0. Such Frames are called INERTIAL FRAMES m

6. PHY221 Ch4: Newton’s Laws Main Points N3: No free Lunch!
This is a ”No free Lunch” Law because if action-reaction did not cancel out, we could use the property to generate energy for free!
Example: You sitting on a chair:

7. PHY221 Ch4: Newton NII in terms of momentum:
In NII F is the net force:
𝐹 = 𝐹 1 − 𝐹 or 𝐹 = 𝐹 𝐹 2

8. PHY221 Ch4: Newton Action reaction examples: Bodies in contact:
Bodies NOT in contact:
3 boxes linked by strings: