Uniform Circular Motion

Table Of Contents

UCM

An object undergoing uniform circular motion means it is moving in a circular motion with a constant velocity.

Assumptions

• $\overrightarrow{v}$ is constant
• ${\overrightarrow{a}}_c\ne 0$
  • Acceleration is moving towards the center, so instantaneous velocity is not changing

Formulas

Acceleration

$a=\frac{v^2}{r}$ $a=4{\pi }^{2}r{f}^2$ $a=\frac{4{\pi }^{2}r}{T^2}$

Proof

UCM Acceleration Proof

Types of UCM

1. Horizontal UCM
2. Vertical UCM

Concepts

• Centripetal Force
• Centrifugal Force
• Banked Curve

Questions

• Mass on a String Problems