Motion under a central force
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Motion under a central force
An object performs motion under a central force when the only significant force acting on that object is a force directed radically towards or away from a fixed object. [Diagram goes here - download the original to see it.] Since the only force acting on the object is the central force, the object must more in a plane. [Diagram goes here - download the original to see it.] There is no other force to lift it out of the plane We will also show that for an object subject to only a central force: [Equation goes here - download the original to see it.] constant. Now the transverse acceleration is [Equation goes here - download the original to see it.] But [Equation goes here - download the original to see it.] So the transverse acceleration can also be written [Equation goes here - download the original to see it.] Since the transverse acceleration for an object under only a central force is 0 [Equation goes here - download the original to see it.] Therefore:[Equation goes here - download the original to see it.] Hence, by direct integration [Equation goes here - download the original to see it.] Where is a constant.
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Contents of
Motion under a central force
1 Motion under a central force
2 Transverse Velocity
3 Kepler's Second Law
4 Motion under gravity
5 Energy and central force systems
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