--- title: "Unit 3.2 | Solving Circular Motion Problems using FBDs" description: "Solve circular motion problems using Free Body Diagrams (FBDs). Gain a deep understanding centripetal forces." featured_image: "https://nerd-notes.com/wp-content/uploads/2023/06/motorbike-ciruclar-motion-unit-3.2-nerdnotes.webp" url: "https://nerd-notes.com/unit-3-2-solving-circular-motion-problems-using-fbds/" date_modified: "2024-06-21T17:45:59+00:00" --- # Unit 3.2 | Solving Circular Motion Problems using FBDs ## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/unit-3-2-solving-circular-motion-problems-using-fbds/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-3-2-solving-circular-motion-problems-using-fbds/ ### Unit 3 Breakdown You are on Lesson 2 of 4 1. **[Unit 3.1 | Understanding circular motion and centripetal forces](https://nerd-notes.com/unit-3-1-understanding-circular-motion-centripetal-forces/)** 2. **Unit 3.2 | Solving circular motion problems using FBDs** (Current Lesson) 3. **[Unit 3.3 | The gravitational force](https://nerd-notes.com/unit-3-3-the-gravitational-force/)** 4. **[Unit 3.4 | Combining circular motion and gravitation (satellites, orbits, and more)](https://nerd-notes.com/unit-3-4-combining-circular-motion-and-gravitation-satellites-orbits-and-more/)** #### In this lesson:  - You will draw FBDs for circular motion scenarios - Use the FBDs to solve circular motion problems - Cover a problem solving framework to help solve circular motion problems ### FBDs for circular motion  Just like we did for [linear motion](https://nerd-notes.com/unit-2-3-drawing-fbds-right/), we also draw FBDs for circular motion.  The only difference is that there should always be a net force pointing into the circular path. Why? Without this inwards net force, the object would just move along a straight path ([as in covered 3.1)](https://nerd-notes.com/unit-3-1-understanding-circular-motion-centripetal-forces/). More pointers for FBDs: - Do NOT draw/label “centripetal force” as a vector. Instead draw the force *causing* the centripetal acceleration. For example, for a a yo-yo moving in a circle, tension force would be the centripetal force. - Draw only forces! You do NOT need to show the tangential velocity. - If needed, you can also lightly sketch out the “circular path” to give yourself a reference - Don’t forget to draw weight, normal, and other *linear* forces in the scenario. Still confused? Let’s practice drawing FBD. ### Common circular motion scenarios and their FBDs Try drawing an FBD for the following situations. Then watch the video explanation to check your answers. 1. Spinning a yo-yo in a circle 2. A car traveling around a horizontal bend 3. A car going over a hill 4. Person on the bottom of a roller coaster loop 5. A spacecraft orbiting earth (bonus) Locked Video Content ### Solving circular motion questions using a familiar framework In the last unit we covered a problem solving framework for linear forces. You can [read it here](https://nerd-notes.com/how-to-solving-any-force-problem-framework/), but in short: 1. Draw an FBD 2. Find [katex] F_{net} [/katex] in either direction and set it equal to [katex] ma [/katex] 3. Substitute missing variables and solve Just remember to change the type of acceleration to centripetal: [katex] F_{net} = ma_c = m\frac{v^2}{r} [/katex] #### One more formula Period, [katex] T [/katex], is the time is takes for an object to make one complete revolution. In the content of circular motion: Period is the time it takes to go once around the circular path. So becuase, objects move at constant speed during uniform circular motion, we use the [katex] d = vt [/katex] formula to find the period. The distance, [katex] d [/katex] is simply the circumference (aka one revolution) of the circle. The velocity [katex]v [/katex] is the tangential velocity of the object. Solving for t we get: [katex] T = \frac{2\pi r}{v} [/katex] Note: [katex] T [/katex] (capital T) is period, whereas [katex] t [/katex] is a general amount of time. ### Practice Question 1: A spinning yo-yo A child spins a toy .1 kg yo-yo in a vertical circle at a speed of 5 m/s. The circular path has a radius of .5 meters. Find the tension in the string, when the toy is at the bottom of the circular path. 1st step: Draw an FBD 2nd step: Sum forces 3rd step: Re-arrange and solve for [katex]T[/katex] (tension) Answer: [katex] \approx 6 \, N [/katex]. ### PS 2 and 3 Locked Video Content ### Your turn – 4 Practice Problems If you can solve these questions, you can move on to the next section or use [UBQ](https://nerd-notes.com/ubq/) to find more questions. [Open in UBQ](https://nerd-notes.com/ubq/19592/) Question 1 Intermediate Mathematical A car travels at a constant speed around a circular track whose radius is \(2.6 \, \text{km}\). The car goes once around the track in \(360 \, \text{s}\). What is the magnitude of the centripetal acceleration of the car? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/28542/) Question 2 Beginner Mathematical A 2.0 kg ball on the end of a 0.65 m long string is moving in a vertical circle. At the bottom of the circle, its speed is 4.0 m/s. Find the tension in the string. Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/29568/) Question 3 Intermediate Mathematical Friction provides the force needed for a car to travel around a flat, circular race track. Answer the following: Part (a)2 pts What is the maximum speed at which a car can safely travel if the radius of the track is 80 m and the coefficient of static friction is 0.4? Part (b)2 pts How much time does it take the car to go around the circle 3 times? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/29560/) Question 4 Intermediate Mathematical A \(2 \, \text{kg}\) ball is swung in a vertical circle. The length of the string the ball is attached to is \(0.7 \, \text{m}\). It takes \(0.4 \, \text{s}\) for the ball to travel one revolution (assume the ball travels at constant speed). Part (a)3 pts What is the period of the ball? Part (b)3 pts What is the speed of the ball? Part (c)3 pts What is the tension in the string when the ball reaches the top? Part (d)3 pts What is the tension in the string when the ball reaches the bottom? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) ### Lesson 3.3 Preview In the [next lesson](https://nerd-notes.com/unit-3-3-the-gravitational-force/) we will cover the gravitational force. While this might seem unrelated to circular motion, the gravitational force plays a large role for objects orbiting earth — like satellites. ## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/unit-3-2-solving-circular-motion-problems-using-fbds/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-3-2-solving-circular-motion-problems-using-fbds/