About this video

• Video Title: Uniform Circular Motion and Centripetal Acceleration - Grade 12
• Channel: Rob Ackerman
• Speakers: Rob Ackerman
• Duration: 00:27:33

Overview

This video introduces the concept of uniform circular motion (UCM) and centripetal acceleration. It explains what UCM is, provides real-world examples, and derives the formula for centripetal acceleration, demonstrating its calculation with the example of Earth's orbit around the Sun.

Key takeaways

• Uniform Circular Motion (UCM): Defined as motion in a circle with constant speed and constant radius.
• Acceleration in UCM: Despite constant speed, an object in UCM experiences acceleration because its velocity vector (which includes direction) is constantly changing.
• Centripetal Acceleration: This acceleration is directed towards the center of the circle, hence the term "centripetal" meaning "center-seeking." The change in velocity vector points inward.
• Formulas for Centripetal Acceleration:
  • $a_c = v^2 / r$ (when speed and radius are known)
  • $a_c = 4\pi^2 r / T^2$ (when radius and period are known)
  • $a_c = 4\pi^2 r f^2$ (when radius and frequency are known)
• Example Calculation: The video calculates the centripetal acceleration of Earth orbiting the Sun, finding it to be approximately $0.006 , m/s^2$, which is negligible compared to Earth's gravitational acceleration ($9.8 , m/s^2$).