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Lesson 12
Newton IV - Non-Inertial Frames and More
I.
Non-Inertial (Accelerating) Reference Frames (Axis)
A.
Newton's Laws are only valid for non-accelerated reference frames (Inertial
Frames).
All forces on free body diagrams are real!
They have a cause! {WANTf}
B.
In accelerated (non-inertial) reference frames, ficticous forces (no cause - Not
WANTf) must be added to the free body diagrams to obtain the correct results
with Newton's Laws.
Demonstration: Consider a person standing in the middle of a spinning merry-go-round
holding a ball on a string as shown below. A second observer is standing stationary
watching the merry-go-round also as shown below.
Spinning Observer's Reference Frame (Non-Inertial)
Stationary Observer's (Non-Inertial) Reference Frame
Another Example: Consider a ball tied by a rope to the top of an accelerating car. What
does the person in the car see? What does an observer outside the car see?
Gravitational Example: Einstein noted in his work on General Relativity that it is
impossible for an observer to know the difference between an accelerated fram of
reference and a force. Consider a person standing in an elevator with a floating ball (ie
no gravity present). If a space ship hooks on to the elevator and accelerates the elevator
upward at g, then the observer sees the ball accelerate downward with the magnitude g!
g
C.
Problem: There is no such thing as absolute motion or acceleration. Accelerating
with respect to what? So where is the inertial frame?
Solution: Einstein modified Newton's Laws so that they work the same in both
accelerated and non-accelerated reference frames. (It is an improved system of
Newton's Laws. However, it is much harder mathematically and only used for
problems involving high speeds or large gravitational forces (ie astrophysics).
II.
Linear Momentum and Newton II
A.
According to our present statement of Newton's 2nd Law, an object can only be
accelerated if there is a net push or pull (force) by one or more external objects.
So how does a rocket in outer space speed up, slow down, or change course
without an external force?
Solution: Netwon's I and II laws as we have written them so far do not apply to
rockets. We stated the object was a particle (constant mass object). Rockets lose
mass as they expend fuel. Newton understood this difficulty and wrote his laws
in a more general form.
B.
Definition of Linear Momentum
The linear momentum of an object is the product of an object's mass times its
velocity.
Linear momentum is a __________________________________.
The units of linear momentum are __________________________.
The concept of linear momentum proceeded Isaac Newton. It was developed by
Rene' Descart who felt that the total motion of the universe must be conserved
(constant) so that God didn't have to constantly rewind the universal clock. Again,
the notion that anything made by God must be perfect.
C.
Newton's First Law (Varsity Form)
D.
Newton's 2nd Law (Varsity Form)
Newton II Problem: A person is riding in a roller coaster as shown below. At point A,
the coaster is traveling at 20 m/s through a loop whose radius of curvature is 10 m. At
point B, the coaster is on the top of the track whose radius of curvature is 15 m.
Assuming that the track is frictionless and that the total mass of the coaster/rider is 500
kg, what is
B
A
A) The normal force supplied by the track upon the coaster at point A.
B) The maximum speed that coaster can have at point B before leaving the track?
Newton II Problem: In the barrel of fun ride, the bottom of the ride is dropped out from
under the passengers. What is the expression for the minimum tangential speed required
to prevent the passengers from falling when the bottom is dropped.
R