Question

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.

Answer 1

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 $\vec{M}=\vec{r}\times\vec{F}=0,$ where $M$ is the force moment.

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

3) For any central force

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

Examples:

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

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

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

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

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