Rolling without slipping on curved surfaces
SuperFly Physics
by Andy Rundquist
1M ago
I’ve been trying to see if I can model balls rolling on curved surfaces and I think I’ve cracked it. Here’s a teaser to get you interested: What you see is a sphere rolling on a curved surface. The blue line is the path of the contact point and the orange line is the path of the center of the ball. What that ball is doing is called “rolling without slipping” which just means that the contact point doesn’t slide at all. In fact, the part of the ball in contact with the surface is (momentarily) at rest! Rolling without slipping is something that happens in nature a lot. If something isn’t doing ..read more
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Situations that share equations of motion
SuperFly Physics
by Andy Rundquist
1M ago
Recently my friend Rhett Allain has been making some awesome videos showing how to solve complex problems with a Lagrangian approach. I love it when he posts a new video because it usually motivates me to try to model something similar. Here’s the video he posted that inspired this post: Rhett’s vid about two masses tied together through a hole in a table I love this particular problem so I decided to dig in and see what I could learn from building my own model of it. One thing I was curious about was whether using a Lagrange multiplier technique could save me time. Basically I wondered if I ..read more
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Rigid bodies, formulation and examples
SuperFly Physics
by Andy Rundquist
2M ago
My friend Rhett Allain gave me a good challenge recently with this tweet: What about a bead on a freely rotating hoop that can rotate in three dimensions? — Rhett Allain (@rjallain) November 23, 2022 I had been working on a problem that he posted about regarding a bead sliding freely on a hoop that is spinning about an axis in its plane that goes through the center. That’s a pretty typical Lagrangian Dynamics-type problem and I wondered what would happen if the hoop wasn’t driven to constantly go with a particular angular frequency but rather was set spinning on that axis with that initial ..read more
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Creating bike routes with python
SuperFly Physics
by Andy Rundquist
3M ago
This weekend my goal was to ride 50 miles to and from my house. In my last post I showed four ways to find where I could get to for a certain distance, but I really hate “there and back” rides, so I wanted to find loop-based routes that would have my target distance and not have any doubling back. I used basically the same tools and I’m decently happy with the results. tl;dr here’s the route How’d I do it? Here’s the basic gist of what I did: Get the lat/long of my house to have a starting point Do some geo-based math to find points on a regular polygon that includes my house. I set the polyg ..read more
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What’s my 30 mile cycle limit?
SuperFly Physics
by Andy Rundquist
4M ago
UPDATED WITH 4th APPROXIMATION! Last weekend I went hammock camping by towing all my gear behind my bike. I loved it and now I’m interested in finding other adventures that won’t tax me too much. I really think that, for now, 30 miles in one day towing the trailer is a good limit for me. It leaves me enough energy to make camp and I’m able to relax and enjoy myself. 1st approximation My first thought was to just look at a map with a 30-mile radius circle centered on my house. I figured if I could find any campgrounds in that circle I’d be good to go. 30 mile radius circle around my house The p ..read more
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Classroom photo sharing app
SuperFly Physics
by Andy Rundquist
6M ago
For a long time I’ve wanted an app that could Allow my students to take a picture of their work and share it with the class Certainly my computer should be able to display it, but with thumbnails for all the images Bonus if all the images are on everyone’s device This post is about my attempt to make just such an app in Google Apps Script. It includes detailed instructions for how you can make your own copy. If you want to see it in action, see this vid. Before jumping in, I want to say thanks to some great twitter friends who had thoughts about other ways to do this. I haven’t tried them al ..read more
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Audience ranking questions
SuperFly Physics
by Andy Rundquist
6M ago
I’m helping to run a workshop this week and we realized that instead of using post-it notes through the day to capture “burning questions” we could use a tool that both collects questions and allows the audience to vote on them. After the first day of post-it notes I volunteered to get us set up with one of the many systems that exist that do this. I went back to my hotel room and did the usual google searching, finding tools I had used (including the one that the Physics Education Research Conference organizers used earlier this month at their opening session) and others I hadn’t heard of. Un ..read more
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Brachistochrone for rolling things
SuperFly Physics
by Andy Rundquist
11M ago
The Brachistochrone curve is the shape of a wire for beads to slide down (friction free) to get from point A to point B the fastest. Note that since I used the word “down” there I’m implying this happens in gravity. Here’s an old post of mine describing how I go about teaching it. This post is all about scratching an itch I’ve had for a while: What if instead of sliding beads we want to roll balls. Is the shape the same? Spoiler: Nope, not the same. My first thoughts had to do with how you’d factor rolling into the typical analysis. Normally you determine the integral formula for the time to g ..read more
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License plate math game
SuperFly Physics
by Andy Rundquist
1y ago
I do lots of things while I ride my bike to work to pass the time. Recently I’ve invented this game (surely others have too): Pick a target integer (I start at zero and move up by one in each iteration) Find a license plate (defined to be one with 3 integers on it like MN has) Find a way to insert mathematical operations before and between the numbers so that the result is your target Here’s an example: Let’s say your target is 15. Here are a bunch of potential plates: 135 (1*3*5) 453 (45/3) note that just lumping 2 (or 3) numbers together is allowed 771 (7+7+1) 241 (2^4-1) You get the gis ..read more
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Book editor in Google Apps Script
SuperFly Physics
by Andy Rundquist
1y ago
I’m teaching a class in the fall called “Web App Development with Google Apps Script” that I think I want to write my own book for. I started doing some of that using wikibooks, but I was frustrated at some of the limitations that platform has, namely that you have to click around a lot as you’re going back and forth among sections and it’s really hard to add images, as most are considered to be copyrighted unless you jump through a bunch of hoops. So I thought it might be fun to see if I could make a book editor in Google Apps Script. That’s pretty meta, huh? tl;dr? I made a ton of progress ..read more
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