Circular Motion

Centripetal Force

Apparent Weight

Newtons’ Universal Gravitation Law

Centripetal accel. & Force

v = 2r/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 fleeingForce exerted by orbiting body on the central bodyNewton’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 = 2r/T

So 2r/T = GMe/r

thus 42r2/T2 = GMe/r

and 42r3/T2 = Gme so 42r3 = GMeT2

T2 = 42r3/ Gme

T = 2r3/ 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.

42r3/T2 = Gme

Since 42 & 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.