Is the Bottom Velocity of a Ferris Wheel Really Twice That of the Top?

In summary, the conversation discusses the description of non-uniform circular motion in a textbook, specifically in regards to a ferris wheel. It is mentioned that the velocity at the bottom must be twice the velocity at the top, but no mathematical proof is provided and it may not be immediately obvious. The other person questions if this is accurate and provides a simple mathematical demonstration, stating that the point on top has velocity v and the point on the bottom has velocity -v, resulting in a difference of 2v between the two velocities. However, it is clarified that one is not necessarily "twice" the other.
  • #1
silvanet
2
0
I see in the description of non-uniform circular motion in a textbook, referring to a ferris wheel, that the velocity of an object at the bottom must be twice the velocity at the top, but it is not mathematically shown and it is not immediately obvious to me. Can someone show a simple mathematical demonstration of that?
 
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  • #2
Are you sure that is what is said? If the point on top has velocity v, the point on the bottom must have the same speed but opposite direction so velocity -v. The difference in velocities is v- (-v)= 2v but it is NOT true that one is "twice" the other.
 

1. What is non uniform circular motion?

Non uniform circular motion is a type of motion in which an object moves along a circular path at varying speeds. This means that the object's velocity is constantly changing as it moves around the circle.

2. How is non uniform circular motion different from uniform circular motion?

Uniform circular motion is a type of motion in which an object moves along a circular path at a constant speed. This means that the object's velocity remains the same as it moves around the circle. Non uniform circular motion, on the other hand, involves changes in velocity.

3. What causes an object to experience non uniform circular motion?

There are a few different factors that can cause an object to experience non uniform circular motion. These include changes in speed, changes in direction, and the presence of external forces such as friction or gravity.

4. How is non uniform circular motion calculated?

To calculate non uniform circular motion, you will need to know the object's initial velocity, its acceleration, and the radius of the circular path it is traveling on. These values can be plugged into equations such as Newton's second law of motion or the centripetal acceleration equation.

5. What are some real-life examples of non uniform circular motion?

Non uniform circular motion can be seen in many everyday situations, such as a car turning around a curved road, a rollercoaster moving through loops, and a satellite orbiting around a planet. Any object moving in a circular path at varying speeds is experiencing non uniform circular motion.

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