Transcript Circular Motion

Circular Motion
Centripetal Force
Apparent Weight
Newtons’ Universal Gravitation Law
Centripetal accel. & Force
 v = 2pr/T
 acp = v2/r
 Fcp = mv2/r
 Centripetal = center seeking.
acp & Fcp are both toward the
central body.
 Fcp is the force exerted by the
central body on the orbiting body.
(Recall Newton’s 3rd)
 acp is the accel. of the orbiting body
caused by that force.
 Direction of v?
Centrifugal
p. 156 text - “A
Nonexistent Force”
This is not really
true - just misused.
Centrifugal =
center fleeing
Force exerted by
orbiting body on
the central body
Newton’s 3rd axn/rxn forces
Apparent Weight
What the weight of an object
appears to be as a result of the
acceleration of a supporting.
Faw = m(g-a)
Ex. of supporting bodies elevators & space stations &
rockets - oh my!
When an orbiting body is accel.
@ a rate of g weightlessness
occurs.
Newton’s Universal Law of
Gravitation
Fg = Gm1m2/r2
For earth: Fg = GMem/r2
Fg is also wt. therefore, mg = GMem/r2
mg = GMem/r2
g = GMe/r2
What does this tell us?
Usefulness of Newt’s Univ.
Grav. Law.
Observation Fcp ≠ one of the fundamental forces
Sometimes Fcp = Fg
Knowing when is the key!
If mass is the cause of the force then Fcp = Fg
Therefore, mv2/r = GMem/r2
mv2/r = GMem/r2
v2/r = GMe/r2 & v2 = GMe/r thus v = GMe/r
Usefulness of Newt’s Univ.
Grav. Law.
But v = 2pr/T
So 2pr/T = GMe/r
thus 4p2r2/T2 = GMe/r
and 4p2r3/T2 = Gme so 4p2r3 = GMeT2
T2 = 4p2r3/ Gme
T = 2p r3/ Gme
Usefulness of Newt’s Univ.
Grav. Law.
Therefore, we can determine all sorts of
information about central & orbiting
bodies if we know other information.
This is how they know the mass of the
sun & planets & moons etc.
Kepler’s 3rd Law
T2/R3 = k
Applies to any given orbited or central
body.
Newt’s Univ. Gav. Law &
Kepler’s 3rd Law.
4p2r3/T2 = Gme
Since 4p2 & Gme are all constant
r3/T2 or T2/r3 = k which is Kepler’s 3rd law.
Although Kepler (1571-1630) preceded
Newton (1643-1727). Kepler’s 3rd Law
follows from Newton’s Universal Law of
Gravitation.