UCM and acceleration (11 min)

Mechanics of UCM (6 min)

Example: Car on flat curve(4min)

Example: loop-the-loop (5 min)

Summary

The goal is to study systems where the net force is perpendicular to the velocity such as the case in uniform circular motion (UCM), where objects travel around a circle at a constant speed. UCM is also an excellent place to study the effects of reference frames that have fictitious forces arise.

Atomistic Goals

Students will be able to...

1. Identify systems that exhibit uniform circular motion. 
2. Draw physical representations from multiple directions and choose the perspective that helps the analysis the most.
3. Draw a FBD that only includes real forces. 
4. Identify which forces are responsible for keeping the object traveling in a circle.
5. Define centripetal force.
6. Show that the direction of the net force, and thus acceleration, are perpendicular to the direction of velocity during UCM.
7. Show that the direction of the net force and acceleration point towards the center of the circle during UCM.    
8. Identify the radially inward direction and align the coordinate system with it.
9. Identify the tangential direction.
10. Realize that UCM is a situation where the speed of the object affects the magnitude of the acceleration (v2/r) and thus net force.
11. (UPMF) Explain the nature of fictitious forces that arise in UCM and inertia's role in the effect. 
12. Show how period, frequency, speed, and distance are related.

Lo-fi UCM demo to chill/study to:

https://www.youtube.com/watch?v=ID0R43My4Co

The Ladybug Revolution!

The Return of the Ladybug Revolution: part II

For additional simulations on this subject, visit the simulations repository.

 For additional demos involving this subject, visit the demo repository

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The Circular Motion page by PhysClips, an Australia physics education project has excellent clips with animation that describe most of UCM including the directions of some very important vectors. Make sure to watch the Uniform Circular Motion clip and the Centripetal Acceleration clip under Circular Motion in the module. Don't forget to take notes! *Aside: remember that a differential or dv implies a very small change in velocity in this case and the a is just the average acceleration, which is still a vector.

The Physics Classroom UCM page offers a concise short description worth reading in addition to the textbook above.

Centrifugal force explained! The Physics Classroom does a good job of explaining this pseudo force. 

Resource Repository

This link will take you to the repository of other content on this topic.

A pretty good video showing how to solve UCM problems with insights into why certain assumptions/conclusions are made. Beware, there are no vector symbols and the units are "sloppy."

https://www.youtube.com/watch?v=Xu3licsSU5Y

• If an object is moving in a circle, the misconception that since the speed is constant the net force must be zero. There must always be a net force towards the center.
• The net force in the radial direction is always equal to m v²/r.
• Many people believe that if an object is accelerating then its speed must be changing. This is not true. Speed is merely the magnitude of a vector. The direction of a vector can change without changing its magnitude. This means I can change my velocity, i.e. accelerate, but I don't have to change my speed.
• The misconception that you must always choose the tangential direction when choosing your axis.
• Warning: careful consideration must be made whenever using the term centripetal force, as it implies an actual force, separate from others, in the radial direction. The term centripetal is referring to the net effect of all the real forces when an object is in UCM. In the case of UCM, the net force is in the radial direction and that net force (from real forces) is called the centripetal force.
• Another issue people have is that they believe that since, in uniform circular motion, the speed of the object stays constant then the object must be in equilibrium. They then assume that another force is balancing out the inward forces. This is not true. For an object to change its direction, it must have a non-zero net force.
• The difference between Centripetal and Centrifugal

https://www.youtube.com/watch?v=yAfg_8OLjvs

• Often times circular motion can be tricky to visualize. Drawing the snapshot in time of the scenario for different viewing angles can help clarify the directions of forces.
• Any object that travels in uniform circular motion always takes the same amount of time to move completely around the circle so you can use the period and the circumference to find the tangential velocity.
• Labeling the radial direction of your FBD with $\hat{r}$ will help avoid making the mistake of thinking that the acceleration in that direction is linear when translating the FBD to Newton's 2^nd law.

Multiple Representations is the concept that a physical phenomena can be expressed in different ways. 

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