Physics · University
Central forces, angular momentum and effective potential · revision notes
A central force is directed along the line joining the particle to a fixed centre and has magnitude depending only on radial distance in the usual model.
Key ideas and conditions
Central force
A central force is directed along the line joining the particle to a fixed centre and has magnitude depending only on radial distance in the usual model.
Conservation
Its torque about the centre vanishes, so angular momentum about that centre is conserved. The trajectory lies in a plane when angular momentum is nonzero.
Radial energy
For conserved angular momentum L, the effective radial potential is V(r)+L²/(2mr²). The second term describes the angular contribution.
Stability
A circular orbit corresponds to a stationary point of effective potential. A local minimum gives stability against small radial displacements in this model.
Explain without looking
- If angular momentum is constant and radius halves, by what factor does tangential speed change?
- Why must one specify the centre when asserting angular-momentum conservation?
Further reading and review references
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