--- title: "Unit 6.4 | Rolling and Orbiting Satellites" description: "Learn rolling without slipping and orbiting satellites in AP Physics 1: the rolling energy split, ramp races, circular orbits and escape speed." featured_image: "https://nerd-notes.com/wp-content/uploads/2026/10/133458.jpg" url: "https://nerd-notes.com/unit-6-4-rolling-and-orbiting-satellites/" date_modified: "2026-10-31T09:35:32+00:00" --- # Unit 6.4 | Rolling and Orbiting Satellites ## 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-6-4-rolling-and-orbiting-satellites/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-6-4-rolling-and-orbiting-satellites/ A rolling ball moves and spins, and an orbiting planet keeps both its energy and its angular momentum. This lesson ends Unit 6 with both. [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### Unit 6 Breakdown You are on Lesson 4 of 4 1. [Unit 6.1 | Rotational Kinetic Energy and Work](https://nerd-notes.com/unit-6-1-rotational-kinetic-energy-and-work/) 2. [Unit 6.2 | Angular Momentum and Angular Impulse](https://nerd-notes.com/unit-6-2-angular-momentum-and-angular-impulse/) 3. [Unit 6.3 | Conservation of Angular Momentum](https://nerd-notes.com/unit-6-3-conservation-of-angular-momentum/) 4. [Unit 6.4 | Rolling and Orbiting Satellites](https://nerd-notes.com/unit-6-4-rolling-and-orbiting-satellites/) #### In this lesson:  - Rolling without slipping: [katex] v = R\omega [/katex], and kinetic energy that is part translational, part rotational - Why a solid sphere beats a hoop down a ramp, and why a sliding block beats them both - Orbits: a satellite keeps both its angular momentum and its mechanical energy; circular orbit speed and escape speed - The 4 problem types: the rolling energy split, rolling down a ramp, circular orbits, and elliptical orbits and escape [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-6-4-rolling-and-orbiting-satellites&utm_content=top) ### Introduction This lesson covers **rolling** and **orbiting satellites**, the last two topics of Unit 6. Both use everything from the unit at once: rotational kinetic energy, angular momentum and their conservation laws. A rolling ball moves and spins, so its kinetic energy has two parts ([Unit 6.1](https://nerd-notes.com/unit-6-1-rotational-kinetic-energy-and-work/)). A planet circling a star has angular momentum about the star, and nothing exerts a torque about the star to change it ([Unit 6.3](https://nerd-notes.com/unit-6-3-conservation-of-angular-momentum/)). [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### Rolling Without Slipping When a wheel or ball rolls without slipping, the point touching the ground is momentarily at rest. The center moves forward one circumference for each full turn, so the center’s speed and the spin are locked together ([Unit 5.1](https://nerd-notes.com/unit-5-1-rotational-kinematics/)): [katex] v_{cm} = R\omega [/katex] \(\omega\) \(v\) \(2v\) \(v = 0 \text{ at the contact point}\) \(R\) \(v = R\omega\) \(K = \tfrac{1}{2}Mv^2 + \tfrac{1}{2}I\omega^2\) *Rolling without slipping. The center moves at \(v\), the top at \(2v\), and the contact point not at all.* [Remove Ads](https://nerd-notes.com/pricing/?for=students) The kinetic energy is the translational energy of the center of mass plus the rotational energy about it: [katex] K = \tfrac{1}{2}Mv^2 + \tfrac{1}{2}I\omega^2 [/katex] Write the rotational inertia as [katex] I = \beta MR^2 [/katex], where [katex] \beta [/katex] is the number in front for each shape. With [katex] \omega = \frac{v}{R} [/katex] the energy becomes [katex] K = \tfrac{1}{2}(1 + \beta)Mv^2 [/katex]. The radius cancels, and the shape decides the split: | **Rolling object** | [katex] \beta [/katex] | **Rotational share of K** | **Speed after a drop h** | | --- | --- | --- | --- | | Block sliding on ice (no rolling) | 0 | 0 | [katex] \sqrt{2gh} [/katex] | | Solid sphere | [katex] \tfrac{2}{5} [/katex] | [katex] \tfrac{2}{7} [/katex] (29%) | [katex] \sqrt{\tfrac{10}{7}gh} [/katex] | | Solid cylinder or disk | [katex] \tfrac{1}{2} [/katex] | [katex] \tfrac{1}{3} [/katex] (33%) | [katex] \sqrt{\tfrac{4}{3}gh} [/katex] | | Hoop or thin-walled pipe | 1 | [katex] \tfrac{1}{2} [/katex] (50%) | [katex] \sqrt{gh} [/katex] | [Remove Ads](https://nerd-notes.com/pricing/?for=students) Static friction is what makes a ball roll instead of slide, but it does no work on a ball that rolls without slipping: the contact point does not move. So mechanical energy is conserved for rolling without slipping. Every rolling and orbit question on the AP exam is one of the four types below. | **Problem type** | **The clue** | **The setup** | | --- | --- | --- | | 1. The rolling energy split | “rolls without slipping”, “ratio of rotational to total” | [katex] K = \tfrac{1}{2}Mv^2 + \tfrac{1}{2}I\omega^2 [/katex] with [katex] v = R\omega [/katex] | | 2. Rolling down a ramp | released from rest at height [katex] h [/katex], “which reaches the bottom first” | [katex] Mgh = \tfrac{1}{2}(1 + \beta)Mv^2 [/katex] | | 3. Circular orbits | a satellite in a circular orbit of radius [katex] r [/katex] | [katex] \frac{GMm}{r^2} = \frac{mv^2}{r} [/katex], so [katex] v = \sqrt{\frac{GM}{r}} [/katex] | | 4. Elliptical orbits and escape | “closest” and “farthest” points, “minimum speed to escape” | [katex] mv_pr_p = mv_ar_a [/katex] and [katex] \tfrac{1}{2}mv^2 – \frac{GMm}{r} [/katex] constant | [Remove Ads](https://nerd-notes.com/pricing/?for=students) Rotational Kinetic Energy and Rolling Official course · step-by-step video walkthrough [Watch · 21 min](https://nerd-notes.com/courses/?utm_source=blog&utm_medium=article&utm_campaign=unit-6-4-rolling-and-orbiting-satellites&utm_content=video-mid#course=94339&module=98824&lesson=99197) ### Problem Type 1: The rolling energy split **How to spot it:** An object rolls without slipping, and the question compares its translational and rotational kinetic energy, or asks for its total kinetic energy. **Setup:** Use [katex] \omega = \frac{v}{R} [/katex] to write both parts in terms of [katex] v [/katex]: [katex] K_{trans} = \tfrac{1}{2}Mv^2 [/katex], [katex] K_{rot} = \tfrac{1}{2}\beta Mv^2 [/katex]. The ratio [katex] \frac{K_{rot}}{K_{trans}} = \beta [/katex] depends only on the shape. A [katex] 5.0\,\text{kg} [/katex] bowling ball (a solid sphere) rolls without slipping at [katex] 4.0\,\text{m/s} [/katex]. Find its translational, rotational and total kinetic energy. [katex] K_{trans} = \tfrac{1}{2}(5.0)(4.0)^2 = 40 \text{ J} [/katex]. [katex] K_{rot} = \tfrac{1}{2}\left(\tfrac{2}{5}MR^2\right)\frac{v^2}{R^2} = \tfrac{1}{5}(5.0)(4.0)^2 = 16 \text{ J} [/katex]. Total: [katex] 56\,\text{J} [/katex]. The radius was never needed. [Remove Ads](https://nerd-notes.com/pricing/?for=students) **AP trap:** Writing [katex] K = \tfrac{1}{2}Mv^2 [/katex] for a rolling object. That is only the translational part. Rolling objects always carry extra kinetic energy in the spin. [Open in UBQ](https://nerd-notes.com/ubq/29732/) Question 1 The moment of inertia of a solid cylinder about its axis is given by I = (1/2)mR². If this cylinder rolls without slipping, the ratio of its… 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/81033/) Question 2 Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic… 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/109357/) Question 3 Three objects of the same mass M are rolling without slipping across a horizontal laboratory floor with the same constant translational speed v… 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/112624/) Question 4 A uniform solid sphere of mass M and radius R rolls without slipping along a horizontal surface with a constant center-of-mass speed v. The… 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) 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-6-4-rolling-and-orbiting-satellites&utm_content=mid) ### Problem Type 2: Rolling down a ramp **How to spot it:** Objects released from rest roll down a ramp (or roll up one): “speed at the bottom”, “how high does it go”, “which reaches the bottom first”. **Setup:** Energy: [katex] Mgh = \tfrac{1}{2}(1 + \beta)Mv^2 [/katex], so [katex] v = \sqrt{\frac{2gh}{1 + \beta}} [/katex]. Mass and radius cancel. The smaller [katex] \beta [/katex] (mass closer to the center), the faster it goes and the sooner it arrives. A solid sphere, a solid cylinder and a hoop roll without slipping down a [katex] 1.5\,\text{m} [/katex] high ramp, and a block slides down an identical frictionless ramp. Find each speed at the bottom. [Remove Ads](https://nerd-notes.com/pricing/?for=students) - Block: [katex] v = \sqrt{2(9.8)(1.5)} \approx 5.4 \text{ m/s} [/katex]. All of the energy goes into moving forward. - Solid sphere: [katex] v = \sqrt{\frac{2(9.8)(1.5)}{1.4}} \approx 4.6 \text{ m/s} [/katex]. - Solid cylinder: [katex] v = \sqrt{\frac{2(9.8)(1.5)}{1.5}} \approx 4.4 \text{ m/s} [/katex]. - Hoop: [katex] v = \sqrt{\frac{2(9.8)(1.5)}{2}} \approx 3.8 \text{ m/s} [/katex]. The order of finishing is the same: block, sphere, cylinder, hoop. Each has the same [katex] Mgh [/katex] to spend. The more of it that goes into spinning, the less is left for moving down the ramp. A ball rolling up a ramp is the same problem backwards: it climbs to [katex] h = \frac{(1 + \beta)v^2}{2g} [/katex], higher than a sliding block with the same speed, because its spin energy also turns into height. But if the ramp is frictionless, nothing can slow the spin: the ball keeps its rotational energy and rises only as high as a sliding block would, [katex] \frac{v^2}{2g} [/katex]. [Remove Ads](https://nerd-notes.com/pricing/?for=students) ▶ **Watch:** a worked rolling problem, and the friction that makes an object roll (starts at 18:45). [Embedded content](https://www.youtube-nocookie.com/embed/by-ViCS_P_Y?start=1125&rel=0) **AP trap:** Thinking a heavier or bigger ball wins. For rolling without slipping, mass and radius cancel. Only the shape, [katex] \beta [/katex], matters. Two solid spheres of any size tie. [Open in UBQ](https://nerd-notes.com/ubq/110877/) Question 5 A solid disk and a thin hoop, both with mass M and radius R, are released from rest at the top of an incline of height h. Both objects roll down 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/29739/) Question 6 A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In… 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/110356/) Question 7 A block of mass M and a solid sphere of mass M are both released from rest at the same height h on two different ramps. The block slides down a… 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/122867/) Question 8 A bowling ball, modeled as a uniform solid sphere of mass M and radius R, is released from rest at the top of a rough incline of height H. The ball… 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) Rotational Energy Practice Official course · graded, with step-by-step explanations [Practice](https://nerd-notes.com/courses/?utm_source=blog&utm_medium=article&utm_campaign=unit-6-4-rolling-and-orbiting-satellites&utm_content=practice-practice#course=94339&module=98824&lesson=99201) Quiz Lab Rotational Energy and Rolling Which one wins the race down the ramp, and where the energy goes. 15 questions · Free [Take the quiz](https://nerd-notes.com/quiz/?id=184) ### Orbiting Satellites A satellite (or moon, or planet) orbiting a much more massive body feels only gravity, and gravity always points at the center of the big body. A force aimed at a point exerts no torque about that point. So for the satellite: - **Angular momentum about the central body is conserved:** [katex] L = mvr_\perp [/katex] stays constant all the way around. - **Mechanical energy is conserved**, with the gravitational potential energy [katex] U_G = -\frac{GMm}{r} [/katex] (zero far away, negative closer in): [katex] \tfrac{1}{2}mv^2 – \frac{GMm}{r} [/katex] stays constant. In a circular orbit, [katex] r [/katex] and [katex] v [/katex] never change, so both laws hold trivially. In an elliptical orbit both quantities trade back and forth, and the two conservation laws tell you how. [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### Problem Type 3: Circular orbits **How to spot it:** A satellite or moon in a circular orbit: its speed, period, kinetic energy or angular momentum, often compared between two orbits. **Setup:** Gravity provides the centripetal force ([Unit 2](https://nerd-notes.com/unit-3-4-combining-circular-motion-and-gravitation-satellites-orbits-and-more/)): [katex] \frac{GMm}{r^2} = \frac{mv^2}{r} [/katex], so [katex] v = \sqrt{\frac{GM}{r}} [/katex]. Then [katex] L = mvr [/katex], [katex] K = \frac{GMm}{2r} [/katex] and [katex] E = K + U_G = -\frac{GMm}{2r} [/katex]. A satellite orbits Earth ([katex] M = 5.97 \times 10^{24} \text{ kg} [/katex]) in a circle of radius [katex] 7.0 \times 10^{6} \text{ m} [/katex]. Find its speed and period. How does its speed change if it moves to an orbit 4 times as wide? [katex] v = \sqrt{\frac{(6.67 \times 10^{-11})(5.97 \times 10^{24})}{7.0 \times 10^{6}}} \approx 7.5 \times 10^{3} \text{ m/s} [/katex]. Period: [katex] T = \frac{2\pi r}{v} \approx 5.8 \times 10^{3} \text{ s} [/katex], about 97 minutes. Four times the radius gives [katex] \frac{1}{\sqrt{4}} [/katex], half the speed. [Remove Ads](https://nerd-notes.com/pricing/?for=students) The satellite’s own mass cancels: every object in that orbit moves at the same speed. A higher orbit is slower, but its total energy [katex] -\frac{GMm}{2r} [/katex] is less negative, so moving up takes energy. **AP trap:** Thinking a heavier satellite needs to go faster to stay up. The mass of the satellite cancels from [katex] v = \sqrt{\frac{GM}{r}} [/katex]. Only the central mass and the radius matter. [Open in UBQ](https://nerd-notes.com/ubq/21037/) Question 9 Two satellites are in circular orbits around Earth. Satellite A has speed v_A. Satellite B has an orbital radius nine times that of satellite A. What… 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/109283/) Question 10 Two satellites, Satellite A and Satellite B, are in circular orbits around the same planet of mass M. The radius of the orbit for Satellite A is R… 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/109920/) Question 11 A satellite of mass m orbits a planet of mass M and radius R in a circular path at an altitude R above the planet’s surface with speed v₁. A second… 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/109916/) Question 12 Satellite A and Satellite B are in circular orbits around Earth at the same distance R from the center of the planet. Satellite B has twice the mass… 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) ### Problem Type 4: Elliptical orbits and escape speed **How to spot it:** An orbit with a closest and a farthest point, a comet swinging past the Sun, or “the minimum launch speed to escape”. **Setup:** Angular momentum between any two points: [katex] mv_1r_{\perp 1} = mv_2r_{\perp 2} [/katex] (at the closest and farthest points, [katex] r_\perp [/katex] is just [katex] r [/katex]). Energy between any two points: [katex] \tfrac{1}{2}mv_1^2 – \frac{GMm}{r_1} = \tfrac{1}{2}mv_2^2 – \frac{GMm}{r_2} [/katex]. To escape, the object must reach [katex] r \to \infty [/katex] with [katex] v \ge 0 [/katex]. \(M\) \(r_p\) \(r_a\) \(v_p\) \(v_a\) \(m v_p r_p = m v_a r_a\) \(\tfrac{1}{2}mv^2 - \tfrac{GMm}{r} = \text{constant}\) *Drawn with \(r_a = 2r_p\), as in the example below, so \(v_a\) is half of \(v_p\). Close in, \(r\) is small and the speed large; far out, the reverse. \(mvr\) is the same at both.* [Remove Ads](https://nerd-notes.com/pricing/?for=students) A satellite moves at [katex] 8.0\,\text{km/s} [/katex] at its closest point to a planet, [katex] 8.0 \times 10^{6} \text{ m} [/katex] from the planet’s center. Its farthest point is [katex] 1.6 \times 10^{7} \text{ m} [/katex] from the center. How fast is it moving there? At both points the velocity is perpendicular to the radius, so [katex] (8.0)(8.0 \times 10^{6}) = v_a(1.6 \times 10^{7}) [/katex] and [katex] v_a = 4.0 \text{ km/s} [/katex]. Twice as far, half as fast. Energy agrees: as it climbs away it trades kinetic energy for potential energy. #### Escape speed An object escapes if it can reach infinite distance, where [katex] U_G = 0 [/katex], without running out of kinetic energy. The minimum launch speed from the surface (radius [katex] R [/katex]) makes the total energy exactly zero: [katex] \tfrac{1}{2}mv_{esc}^2 – \frac{GMm}{R} = 0 \quad\Rightarrow\quad v_{esc} = \sqrt{\frac{2GM}{R}} [/katex] [Remove Ads](https://nerd-notes.com/pricing/?for=students) For Earth, [katex] v_{esc} = \sqrt{\frac{2(6.67 \times 10^{-11})(5.97 \times 10^{24})}{6.37 \times 10^{6}}} \approx 11.2 \text{ km/s} [/katex]. Like orbit speed, it does not depend on the mass of the object being launched. **AP trap:** Using [katex] mgh [/katex] for orbits. [katex] mgh [/katex] only works near the surface, where [katex] g [/katex] is constant. Far from a planet use [katex] U_G = -\frac{GMm}{r} [/katex], which goes to zero far away and is negative everywhere else. [Open in UBQ](https://nerd-notes.com/ubq/39136/) Question 13 The elliptical orbit of a comet is shown above. Positions 1 and 2 are, respectively, the farthest and nearest positions to the Sun, and at position 1… 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/109912/) Question 14 A science probe of mass m is launched from the surface of a spherical planet of mass M and radius R. The minimum launch speed required for the probe… 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) Quiz Lab Orbiting Satellites How orbit size sets speed, period and energy, from circles to ellipses. 15 questions · Free [Take the quiz](https://nerd-notes.com/quiz/?id=180) ### Unit 6 Wrap-Up - **Spinning objects carry kinetic energy**, [katex] \tfrac{1}{2}I\omega^2 [/katex], and a torque does work [katex] \tau\Delta\theta [/katex] (6.1). - **Angular momentum** is [katex] I\omega [/katex] for a spinning object and [katex] mvr_\perp [/katex] for a moving one; an angular impulse [katex] \tau\Delta t [/katex] changes it (6.2). - **With no net external torque**, angular momentum is conserved, even when kinetic energy is not (6.3). - **Rolling** splits kinetic energy between moving and spinning, and **orbits** conserve both angular momentum and energy (6.4). Review the whole unit in the [rotational energy and angular momentum speed review](https://nerd-notes.com/rotational-motion/), or watch the rotation section of my speed review: [Embedded content](https://www.youtube-nocookie.com/embed/vyxFy63Ay9s?start=4024&rel=0) Ready for the whole unit? Take the unit review: [Remove Ads](https://nerd-notes.com/pricing/?for=students) Quiz Lab Unit 6: Rotational Dynamics and Angular Momentum Mastery A comprehensive review of rotation, covering moments of inertia, rotational kinematics, energy in rolling systems, conservation laws, and static equilibrium. 10 questions · Free [Take the quiz](https://nerd-notes.com/quiz/?id=28) 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-6-4-rolling-and-orbiting-satellites&utm_content=end) ### Unit 7 Preview Next up is [Unit 7: Oscillations](https://nerd-notes.com/unit-7-1-defining-simple-harmonic-motion/). Springs and pendulums repeat the same motion over and over, and the energy ideas from Units 3 and 6 explain how. ## 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-6-4-rolling-and-orbiting-satellites/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-6-4-rolling-and-orbiting-satellites/