--- title: "Unit 2.A | Understanding Circular Motion and Centripetal Forces" description: "Understand circular motion and centripetal forces from scratch, quickly. Learn how to solve circular motion problems and more." featured_image: "https://nerd-notes.com/wp-content/uploads/2023/06/unit-3.1-roller-coaster-circular-motion-nerdnotes.jpg" url: "https://nerd-notes.com/unit-3-1-understanding-circular-motion-centripetal-forces/" date_modified: "2026-10-31T09:32:20+00:00" --- # Unit 2.A | Understanding Circular Motion and Centripetal Forces ## Attribution Guidelines 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, summarizing, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/unit-3-1-understanding-circular-motion-centripetal-forces/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-3-1-understanding-circular-motion-centripetal-forces/ This lesson covers the fundamental and nuanced concepts involved in circular motion. Without these laws it would be impossible for an object to move in a circular path. [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### Unit 2.A–2.D Breakdown You are on Lesson 1 of 4 1. [Unit 2.A | Understanding Circular Motion and Centripetal Forces](https://nerd-notes.com/unit-3-1-understanding-circular-motion-centripetal-forces/) 2. [Unit 2.B | Solving Circular Motion Problems using FBDs](https://nerd-notes.com/unit-3-2-solving-circular-motion-problems-using-fbds/) 3. [Unit 2.C | The Gravitational Force](https://nerd-notes.com/unit-3-3-the-gravitational-force/) 4. [Unit 2.D | Combining circular motion and gravitation (satellites, orbits, & more)](https://nerd-notes.com/unit-3-4-combining-circular-motion-and-gravitation-satellites-orbits-and-more/) #### In this lesson:  - You will learn about centripetal forces and acceleration - The similarities and difference between linear and centripetal forces - Equations for circular motion - Common situations involving centripetal forces [Remove Ads](https://nerd-notes.com/pricing/?for=students) Learn Physics from Scratch The only course that teaches you to solve problems with dead-simple frameworks that make physics look easy. - Self-paced - About 12 weeks - ★ 4.9 · 12,000+ students [Enroll here](https://nerd-notes.com/physics/ap-physics-1-from-scratch-course/?utm_source=blog&utm_medium=article&utm_campaign=unit-3-1-understanding-circular-motion-centripetal-forces&utm_content=top) ### Introduction So far you’ve covered forces such as weight, friction, and normal force. These are all *linear* forces, because they accelerate objects along a straight, linear, path. *Circular* forces, on the other hand, move objects in circular paths. Yet, you’ll learn that these *circular* forces are much like *linear* forces…with a caveat. [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### How Can a Force Be Circular? In [Unit 1 Kinematics](https://nerd-notes.com/unit-1-1-understanding-vectors-and-the-standard-units-used-in-physics/), we defined acceleration as a change in speed or direction. Imagine a car going around a racetrack at a constant speed of 60 mph. In this scenario, the driver turns the steering wheel to change the direction of the car. The continuous change of direction, as the car travels around the track, is why we say the car is accelerating. And we call this type of acceleration “**centripetal acceleration**.” So despite traveling at constant speed, the change in *direction* of the car causes a centripetal acceleration. [Remove Ads](https://nerd-notes.com/pricing/?for=students) #### Relation to Linear Forces Let’s connect this to linear forces. Recall Newton’s 2nd law: a **net force** acting on a mass will cause an acceleration [katex] F_{net} = ma [/katex]. In circular motion, it is the net “centripetal” force that causes a centripetal acceleration. Furthermore, both centripetal force and acceleration point INTO the circle at any given point. We’ll discuss *why* in a moment. So just like in linear forces let’s use Newton’s 2nd law again, but this time use subscripts to indicate a centripetal acceleration: [katex] F_{net} = ma_c [/katex] Note – [katex] a_c [/katex] means centripetal acceleration. #### Inwards! So why do centripetal forces (and acceleration) point into the circle? [Remove Ads](https://nerd-notes.com/pricing/?for=students) Well it turns out that objects **don’t** naturally want to move in a circle. Remember Newton’s 1st law? An object in motion will want to resist any changes in its motion. This means that an object is fine traveling in a straight line without resistance. However, the moment something tries to “bend” the path, the object will try to resist that change in motion. Thus we need an inwards force, to “force” the object to bend into a circular path. We call this the “centripetal force.” Without the centripetal force an object will just continue to move in a straight line. \(\vec{v}\) \(F_{net}\) *With no inward force the object keeps its velocity and moves in a straight line (Newton’s 1st law). An inward net force bends the path into a circle.* [Remove Ads](https://nerd-notes.com/pricing/?for=students) All About Circular Motion Official course · step-by-step video walkthrough [Watch · 28 min](https://nerd-notes.com/courses/?utm_source=blog&utm_medium=article&utm_campaign=unit-3-1-understanding-circular-motion-centripetal-forces&utm_content=video-mid#course=94339&module=94418&lesson=98737) ### Uniform Circular Motion Quick note: The title of unit is “**Uniform** circular motion.” The word “uniform” refers to the object’s constant speed as it moves in a circular path. **If** the speed were to change, the object would also experience a ***tangential*** acceleration (in addition to its centripetal acceleration). \(a_c\) \(\text{only } a_c \text{: the direction changes}\) \(a_c\) \(a_t\) \(a\) \(a_c \text{ and } a_t \text{: the speed changes too}\) *At constant speed the only acceleration is \(a_c\), toward the center. If the object speeds up, a tangential \(a_t\) is added along the motion.* [Remove Ads](https://nerd-notes.com/pricing/?for=students) #### Recap To summarize everything so far: 1. Centripetal forces and centripetal accelerations are similar to linear forces and linear accelerations. The *only* difference is centripetal forces and accelerations point into the circular path. 2. Without a centripetal force pointing into the circular path, the object would just move in a straight path (according to Newton’s 1st law). 3. Uniform circular motion typically involves a “uniform” (aka constant) speed. The centripetal acceleration comes from a change in the direction of the object. 4. If the object were to speed up or slow down as it moved in a circle then that would cause a linear (tangential) acceleration. Learn Physics from Scratch The only course that teaches you to solve problems with dead-simple frameworks that make physics look easy. - Self-paced - About 12 weeks - ★ 4.9 · 12,000+ students [Enroll here](https://nerd-notes.com/physics/ap-physics-1-from-scratch-course/?utm_source=blog&utm_medium=article&utm_campaign=unit-3-1-understanding-circular-motion-centripetal-forces&utm_content=mid) ### Centripetal forces are normal linear forces With your understanding of ***why*** centripetal forces point inwards, let’s learn ***what*** forces are actually pointing inwards. [Remove Ads](https://nerd-notes.com/pricing/?for=students) The first point to note: The “centripetal force” isn’t a separate force but a term for the net force directed towards the center of the circle. To understand this better, take a look at the example below. A car drives around a circular, ice-covered track. What happens to the car if it goes too fast? It would skid off the track! This indicates the **force of friction**, between the tires and the road, are responsible for “pulling us in.” Therefore, in this example the force of friction is the centripetal force, and it points toward the center of the circular path. To recap: The “centripetal force” is sort of a placeholder for the actual inwards force. [Remove Ads](https://nerd-notes.com/pricing/?for=students) Another example: Imagine spinning a yo-yo toy in a vertical circle. What is the centripetal force that moves the yo-yo in a circle? If you said the force of tension, you would be right! The tension in string of the yo-yo pulls it into a circular path. ### Direction  ![](https://nerd-notes.com/wp-content/uploads/2024/06/2000px-Circular_motion_velocity_and_acceleration2.svg_-300x300-1.png) *Figure 1: Centripetal acceleration always points into the circle, while velocity is always tangential to the circular path.* As you just learned, centripetal acceleration (and centripetal force), ALWAYS points into the circular path.  But what direction does velocity point at any given point? Velocity always acts **tangent** to the circular path. In other words the velocity vector just touches the circle at one point. For example, imagine Figure 1 is someone spinning a yo-yo in a vertical circle. When the yo-yo reaches the bottom most point, the yo-yo string snaps. There’s no force of tension to create a circular force. Which direction would the yo-yo go flying the instant the string breaks? Up, down, left, right, or somewhere in between? [Remove Ads](https://nerd-notes.com/pricing/?for=students) Answer: The yo-yo will fly straight to the right, following its tangential velocity at that moment. According to Newton’s 1st law, in the absence of forces, the object will continue moving in its original direction, which is tangential in this case. ### Conceptual Practice Answer these four conceptual questions. Thoroughly understand the explanations before moving on. [Open in UBQ](https://nerd-notes.com/ubq/22703/) Question 5 Which of the following do not affect the maximum speed that a car can drive in a circle? Choose all correct answers. 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/29600/) Question 6 A compressed spring mounted on a disk can project a small ball. When the disk is not rotating, as shown in the top view above, the ball moves… 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/21859/) Question 7 A delivery truck is traveling north. It then turns along a leftward circular curve. The packages in the truck to slide to the RIGHT. Which of the… 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/21863/) Question 8 Suppose you are a passenger traveling in a car along a road that bends to the left. Why will you feel like you are being thrown against the door?… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### Planetary Orbits – Quick Note Planets move around in *elliptical orbits*, **not** circular orbits. Therefore, we must use Kepler’s laws to analyze planetary motion. Although we do NOT cover Kepler’s laws in this course, there is a clever work-around.  In many Physics courses we **approximate** the orbits of planets to be circular. Hence, we can apply the principles of circular motion to planets. So if you see questions involving planets, you can use equations from circular motion! ### Equations for circular motion Since centripetal forces are still just regular forces, the only new formula you need to know for **centripetal acceleration**: [katex] a_c = \frac{v^2}{r} [/katex] In this formula, [katex] v [/katex] is the tangential velocity of the object, and [katex] r [/katex] is the radius of the circular path. [Remove Ads](https://nerd-notes.com/pricing/?for=students) Now let’s use Newton’s 2nd law to derive an equation for **centripetal force**: 1. Start with Newton’s second law: [katex] F_{net} = ma [/katex] 2. Replace linear acceleration with centripetal acceleration: [katex] F_{net} = ma_c [/katex] 3. Replace ac with the already made equation for centripetal acceleration: [katex] F_{net} = \frac{mv^2}{r} [/katex] Remember, when it comes time to solve a problem it is your job to determine [katex] F_{net} [/katex] and plug in relevant values. 20 Centripetal Motion Practice Questions Official course · graded, with step-by-step explanations [Practice](https://nerd-notes.com/courses/?utm_source=blog&utm_medium=article&utm_campaign=unit-3-1-understanding-circular-motion-centripetal-forces&utm_content=practice-practice#course=94339&module=94418&lesson=98739) Learn Physics from Scratch The only course that teaches you to solve problems with dead-simple frameworks that make physics look easy. - Self-paced - About 12 weeks - ★ 4.9 · 12,000+ students [Enroll here](https://nerd-notes.com/physics/ap-physics-1-from-scratch-course/?utm_source=blog&utm_medium=article&utm_campaign=unit-3-1-understanding-circular-motion-centripetal-forces&utm_content=end) ### Lesson 2.B Preview In the [next lesson](https://nerd-notes.com/unit-3-2-solving-circular-motion-problems-using-fbds/) we will use FBDs to start solving real world circular motion problems. [Remove Ads](https://nerd-notes.com/pricing/?for=students) This typically involves problems with rollercoaster, cars, spinning objects, and much more. ## Attribution Guidelines 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, summarizing, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/unit-3-1-understanding-circular-motion-centripetal-forces/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-3-1-understanding-circular-motion-centripetal-forces/