Applications of Uniform Circular Motion
In 1851, a French physicist named Jean-Bernard-Leon Foucault suspended an iron ball with a radius of approximately 0. 5 feet from the ceiling of the Pantheon in Paris with a wire that was over 200 feet long. The ball was used as a pendulum, and it could swing more than 12 feet back and forth. Beneath the ball he placed a circular ring with sand on top of it. Attached to the bottom of the ball was a pin, which scraped away the sand in its path each time the ball went by.
To get the ball started on a perfect plane, the ball was held to the side by a cord until it was motionless. At that point, the cord was burned, which started the ball swinging. As the ball continued to swing as a pendulum, the path the pin carved into the sand changed, as the floor itself, as well as the rest of the Earth, was moving beneath it. Essentially, the Foucault pendulum demonstrates the rotation of the Earth.
The Foucault pendulum is not forced to stay in a fixed plane like Newton’s pendulum, also known as Newton’s cradle, which means it can move freely in response to the Coriolis force. The Coriolis force, also known as the Coriolis effect, occurs when masses above the Earth’s surface, such as a bullet or rocket, appear to be deflected from their trajectory, meaning they don’t reach their intended location straight ahead of them. In fact it is our frame of reference, the Earth, which is changing.
Our frame of reference changes due to our uniform circular motion around the Earth. As the Earth is not a perfect circle (elliptical), the closer to the equator you are, the further away you are from the Earth’s centre and the less force of gravity you experience. The Earth’s radius is 6378 km. As a result of your increased distance from the centre of the Earth at the maximum point at the Earth’s radius on the equator, you have a lower centripetal force at that location.
This is shown by the formula for centripetal acceleration, which is: pic] Where centripetal acceleration (m/s2) is equal to the velocity (m/s) squared divided by the radius (m). As the formula shows, as the radius between you and the centre of the Earth increases, your centripetal acceleration decreases. At the equator, your centripetal acceleration is around 0. 03 m/s2 . Therefore, Foucault’s pendulum in Paris has a higher centripetal acceleration than 0. 03 m/s2, as it is located closer to the poles than the equator.