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Discussion Question 1D
P212, Week 1
P211 Review: Uniform Circular Motion
page 1
2
1
ˆ
r
12
r
12
,
F
1
→
2
=−
G
m
1
m
2
r
12
2
ˆ
r
12
In P112 you will encounter problems where charged particles move in uniform
circular motion.
The forces involved may be electric or magnetic in nature.
The
answer to part(e) contains the secret of the cyclotron.
Kepler’s Third Law (KIII) for planetary motion about the sun for circular orbits is
T
2
=
CR
3
where
T
is the period, R is the radius of the planet’s orbit and
C
is a constant.
(a)
Derive KIII
for a circular orbit and in the process find an algebraic expression for
C
in terms the mass of the sun
M
S
, the universal gravitational constant
G
, and numerical
factors.
F = G m M
S
/ R
2
F = ma = m v
2
/ R
Set equal to each other and substitute period for velocity.
T
2
= 4
π
2
R
3
/ (G M
S
)
(b)
Using your answer from part (b),
reexpress KIII as a
relationship
between the
angular frequency
ω
of the motion and the radius
R
of the form:
2
= f(
R
,
G
,
M
S
).
ω
2
= G M
S
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 Spring '08
 Kim
 Charge, Magnetism, Circular Motion, Force

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