Answer to Question #97425 in Mechanics | Relativity for Mimo

Question #97425
Define what is a central force and describe 3 main characteristics of the motion dynamics resulting from such type of force. List 5 distinctive examples of central forces with their origin and characteristics.
1
Expert's answer
2019-10-28T11:37:00-0400

Central force is a force whose line of action for any position of the body to which it is applied passes through a point called the center of force.

Characteristics:

1) for any central force M=r×F=0,\vec{M}=\vec{r}\times\vec{F}=0, where MM is the force moment.

2) The work of the central force along a closed circuit is 0.

3) For any central force

F=gradU\vec{F}=- \text{grad}\,U

Examples:

1) Coulomb's force: F=kq1q2rr3\vec{F} = k\frac{q_1q_2 \vec{r}}{r^3}

2) the gravitational force: F=Gm1m2rr3\vec{F} = G\frac{m_1m_2 \vec{r}}{r^3}

3) Harmonic oscillator: F=kx\vec{F} = -k\vec{x}

4) Uniform circular motion: F=mω2r\vec{F} = m\omega^2 \vec{r}

5) uniformly accelerated motion: F=ma\vec{F} = m\vec{a}


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