Research Lab for Interactive 3D Education

Uniform circular motion occurs when a material point travels along a circular trajectory with constant velocity magnitude. The velocity vector continuously changes direction, always being tangent to the circumference.

Main characteristics

• Circular trajectory with constant radius $R$
• Constant angular velocity $\omega$
• Centripetal acceleration $a_c = \omega^2 R$

Parametric equations

The equations describing the position of a point in circular motion are:

• $x(t) = R\cdot\cos(\omega t)$
• $z(t) = R\cdot\sin(\omega t)$

Where:

• $R$ is the radius of the circle
• $\omega$ is the angular velocity
• $t$ is time

The period $T$ of motion is given by $T = \frac{2\pi}{\omega}$ and represents the time needed to complete one full revolution.

Energy in circular motion

In uniform circular motion, kinetic energy is constant:

Where $m$ is the mass of the material point.