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mkphysics
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1. The two components of a double star are observed to move in circles of radii r_1 and r_2. What is the ratio of their masses? (Hint: Write down their accelerations in terms of the angular velocity of rotation, w)
The answer is m1/m2 = r2/r1.
How does one cancel the velocity from the problem to get this result?
For an isolated two body system
m1.a1=-m2.a2
where m are the body masses and a are the accelerations
w=v/r
angular velocity equals velocity divided by radius
a=dw/dt
angular acceleration
m1.dw1/dt = m2.dw2/dt
therefore m1.w1=-m2.w2
m1/m2 = -w2/w1
m1/m2 = -(v2/r2)/(v1/r1)
m1/m2 = -v2r1/v1r2
The answer is m1/m2 = r2/r1.
How does one cancel the velocity from the problem to get this result?
Homework Equations
For an isolated two body system
m1.a1=-m2.a2
where m are the body masses and a are the accelerations
w=v/r
angular velocity equals velocity divided by radius
a=dw/dt
angular acceleration
The Attempt at a Solution
m1.dw1/dt = m2.dw2/dt
therefore m1.w1=-m2.w2
m1/m2 = -w2/w1
m1/m2 = -(v2/r2)/(v1/r1)
m1/m2 = -v2r1/v1r2
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