--- title: "Unit 5.2 | Torque" description: "Learn torque for AP Physics 1: τ = rF sin θ, lever arms, signs, net torque, and torque from an object's own weight, with worked examples and practice." featured_image: "https://nerd-notes.com/wp-content/uploads/2026/10/133281.jpg" url: "https://nerd-notes.com/unit-5-2-torque/" date_modified: "2026-10-31T09:35:20+00:00" --- # Unit 5.2 | Torque ## 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-5-2-torque/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-5-2-torque/ Same force, different result: where and how you push decides how much it turns. This lesson covers torque and the four torque problem types on the AP exam. [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### Unit 5 Breakdown You are on Lesson 2 of 4 1. [Unit 5.1 | Rotational Kinematics](https://nerd-notes.com/unit-5-1-rotational-kinematics/) 2. [Unit 5.2 | Torque](https://nerd-notes.com/unit-5-2-torque/) 3. [Unit 5.3 | Rotational Equilibrium](https://nerd-notes.com/unit-5-3-rotational-equilibrium/) 4. [Unit 5.4 | Rotational Inertia and Newton’s Second Law](https://nerd-notes.com/unit-5-4-rotational-inertia-and-newtons-second-law/) #### In this lesson:  - What torque is, and why where and how you push matters as much as how hard - Torque from one force: [katex] \tau = rF\sin\theta [/katex], and the lever arm - Signs: counterclockwise positive, clockwise negative, and how to add torques - The 4 torque problem types: one force at an angle, comparing pushes, net torque, and torque from an object’s own weight [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-5-2-torque&utm_content=top) ### Introduction This lesson covers **torque**: what it is, how to calculate it, and the four kinds of torque problems you will see on the AP exam. In [Unit 5.1](https://nerd-notes.com/unit-5-1-rotational-kinematics/) you described rotation. Now: what changes it? In [Unit 2](https://nerd-notes.com/unit-2-1-the-forces-that-move-us-unpacking-dynamics-in-ap-physics-1/), a net force changes linear motion. For rotation, the job belongs to torque. Try opening a door by pushing right next to the hinge. It barely moves. Push just as hard at the handle and it swings open. Same force, different result. That difference is torque. [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### What Is Torque? **Torque** ([katex] \tau [/katex]) measures how well a force turns an object about a pivot (also called the axis). It depends on three things: how hard you push, how far from the pivot you push, and the angle you push at. [katex] \tau = rF\sin\theta [/katex] \(\theta\) \(F\sin\theta\) \(F\) \(r\) \(\tau = rF\sin\theta\) *Only the part of the force perpendicular to the rod, \(F\sin\theta\), turns it. The part along the rod just pulls on the pivot.* [Remove Ads](https://nerd-notes.com/pricing/?for=students) - [katex] r [/katex] is the distance from the pivot to the point where the force acts. - [katex] \theta [/katex] is the angle between [katex] r [/katex] (the rod) and the force. - Torque is measured in newton-meters, [katex] \text{N·m} [/katex]. #### Two ways to read the same formula Group it as [katex] r(F\sin\theta) [/katex]: the distance times the *perpendicular part of the force*. That is the picture above. Or group it as [katex] (r\sin\theta)F [/katex]: the force times the **lever arm**, the perpendicular distance from the pivot to the line the force acts along. This view is faster when a force is slanted, like a ladder or a cable: extend the force into a line and measure the shortest distance to the pivot. [Remove Ads](https://nerd-notes.com/pricing/?for=students) #### Torque has a direction A torque turns an object counterclockwise or clockwise. Use counterclockwise as positive and clockwise as negative. To find the direction, imagine that force acting alone: put a pencil on the pivot, push it with your finger in the direction of the force, and watch which way it turns. A force makes zero torque if it acts at the pivot ([katex] r = 0 [/katex]) or points straight toward or away from the pivot ([katex] \theta = 0^\circ [/katex] or [katex] 180^\circ [/katex]). Every torque question on the AP exam is one of the four types below. | **Problem type** | **The clue** | **The setup** | | --- | --- | --- | | 1. One force at an angle | a wrench, a door, a cable “at an angle” | [katex] \tau = rF\sin\theta [/katex], with [katex] \theta [/katex] between [katex] r [/katex] and [katex] F [/katex] | | 2. Comparing pushes | “greatest torque”, “rank”, “ratio” | Compare [katex] rF\sin\theta [/katex] factor by factor | | 3. Net torque from several forces | several forces on one rod or disk | Sign each torque (+ counterclockwise, − clockwise), then add | | 4. Torque from an object’s own weight | a beam, rod or meter stick “of mass M” | The weight acts at the center of mass | [Remove Ads](https://nerd-notes.com/pricing/?for=students) All About Rotational Forces (Torque) Official course · step-by-step video walkthrough [Watch · 15 min](https://nerd-notes.com/courses/?utm_source=blog&utm_medium=article&utm_campaign=unit-5-2-torque&utm_content=video-mid#course=94339&module=97778&lesson=104029) ### Problem Type 1: One force at an angle **How to spot it:** One force pulls or pushes on a wrench, door, rod or beam at an angle, and the question asks for its torque. **Setup:** Find [katex] r [/katex] from the pivot to where the force acts. Find the angle between the rod and the force. Then [katex] \tau = rF\sin\theta [/katex]. A mechanic pulls on the end of a [katex] 0.25\,\text{m} [/katex] wrench with an [katex] 80\,\text{N} [/katex] force, at [katex] 60^\circ [/katex] to the handle. What torque does she apply to the bolt? [katex] \tau = rF\sin\theta = (0.25)(80)\sin 60^\circ \approx 17 \text{ N·m} [/katex]. Pulling perpendicular to the handle would give [katex] (0.25)(80) = 20 \text{ N·m} [/katex], the most this force can do. [Remove Ads](https://nerd-notes.com/pricing/?for=students) **AP trap:** Using the wrong angle. [katex] \theta [/katex] is between the force and the rod, not between the force and the horizontal or the vertical. If a problem gives the angle from the other line, the angle you need is [katex] 90^\circ [/katex] minus it. [Open in UBQ](https://nerd-notes.com/ubq/29758/) Question 1 A force of 17 N is applied to the end of a 0.63 m long torque wrench at an angle 45° from a line joining the pivot point to the handle. What is 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/111528/) Question 2 A uniform horizontal rod of length L is attached to a vertical wall by a hinge at its left end. A force of magnitude F is applied to the rod at 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/92031/) Question 3 You try to open a door, but you are unable to push at a right angle to the door. So, you push the door at an angle of 35° from the horizontal. How… 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-5-2-torque&utm_content=mid) ### Problem Type 2: Comparing pushes **How to spot it:** Several doors, wrenches or forces are compared: “which exerts the greatest torque”, “rank the torques”, “what is the ratio”. **Setup:** Write [katex] \tau = rF\sin\theta [/katex] for each case and compare factor by factor. For a ratio, write [katex] \frac{\tau_2}{\tau_1} [/katex] and cancel what the two cases share. \(F\) \(\tau = wF\) \(F\) \(\tau = \tfrac{1}{2}wF\) \(F\) \(\tau = wF\sin 30^\circ = \tfrac{1}{2}wF\) \(F\) \(\tau = 0\) *A door of width \(w\) seen from above, hinge on the left. Pushing at the middle, or at a slant, halves the torque. Pushing along the door toward the hinge does nothing.* [Remove Ads](https://nerd-notes.com/pricing/?for=students) Push 1 is a force [katex] F [/katex] at the doorknob, perpendicular to the door. Push 2 is [katex] 2F [/katex] at the middle of the door, also perpendicular. Push 3 is [katex] 2F [/katex] at the doorknob, at [katex] 45^\circ [/katex] to the door. Rank the torques. Call the door width [katex] w [/katex]. [katex] \tau_1 = wF [/katex]. [katex] \tau_2 = \tfrac{w}{2}(2F) = wF [/katex]. [katex] \tau_3 = w(2F)\sin 45^\circ \approx 1.4\,wF [/katex]. So [katex] \tau_3 > \tau_1 = \tau_2 [/katex]. **AP trap:** Thinking the bigger force always wins. Push 2 is twice as strong as push 1 but makes the same torque, because it acts half as far from the hinge. [Open in UBQ](https://nerd-notes.com/ubq/109356/) Question 4 A mechanic uses a wrench to loosen a bolt. The mechanic applies a force at different positions and angles relative to the wrench handle. Consider 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/122899/) Question 5 A rigid lever is mounted on a fixed horizontal axle at its left end. Four separate forces, labeled W, X, Y, and Z, can each be applied individually… 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/111618/) Question 6 A technician uses a wrench to loosen a bolt. In the first attempt, the technician applies a force of magnitude F at a distance r from the center of… 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/29875/) Question 7 Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied… 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 3: Net torque from several forces **How to spot it:** Several forces act on one rod, beam or disk. The question asks for the net torque, the way it will turn, or the torque needed to stop it from turning. **Setup:** Pick the pivot. For each force find [katex] rF\sin\theta [/katex] and give it a sign: + counterclockwise, − clockwise. Then add: [katex] \sum\tau [/katex]. \(10\,\text{N}\) \(8\,\text{N}\) \(6\,\text{N}\) \(0.50\,\text{m}\) \(0.30\,\text{m}\) \(0.50\,\text{m}\) \(\textcolor{#0072FF}{+}\ \text{counterclockwise}\) \(\textcolor{#0072FF}{-}\ \text{clockwise}\) *Three forces on a 1.0 m rod pivoted at its center.* A [katex] 1.0\,\text{m} [/katex] rod is pivoted at its center. A [katex] 10\,\text{N} [/katex] force pushes down on the left end, an [katex] 8\,\text{N} [/katex] force pushes down [katex] 0.30\,\text{m} [/katex] to the right of the pivot, and a [katex] 6\,\text{N} [/katex] force pushes up on the right end. Find the net torque. [Remove Ads](https://nerd-notes.com/pricing/?for=students) - Left end pushed down: the rod turns counterclockwise, [katex] +(0.50)(10) = +5.0 \text{ N·m} [/katex]. - Pushed down right of the pivot: clockwise, [katex] -(0.30)(8) = -2.4 \text{ N·m} [/katex]. - Right end pushed up: counterclockwise, [katex] +(0.50)(6) = +3.0 \text{ N·m} [/katex]. [katex] \sum\tau = 5.0 – 2.4 + 3.0 = +5.6 \text{ N·m} [/katex], so the rod starts to turn counterclockwise. **AP trap:** Adding the sizes and forgetting the signs. Decide each force’s direction on its own, as if it were the only force on the rod. [Open in UBQ](https://nerd-notes.com/ubq/28484/) Question 8 A rod may freely rotate about an axis that is perpendicular to the plane of the page. The rod is divided into four sections of equal length of 0.2 m… 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/109831/) Question 9 A uniform rod of length L is pivoted at its center. Two forces, each of magnitude F, are applied to the rod as shown. Force 1 is applied at 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/28505/) Question 10 A rod is initially at rest on a rough horizontal surface. Three forces are exerted on the rod with the magnitudes and directions shown in the figure… 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: Torque from an object’s own weight **How to spot it:** The rod, beam, board or meter stick has mass: “a uniform beam of mass M”, “a 200 g meter stick”. **Setup:** Treat the whole weight [katex] Mg [/katex] as one force at the center of mass. For a uniform object that is the middle, so its lever arm is the distance from the pivot to the middle. \(Mg\) \(mg\) \(\tfrac{L}{2}\) \(L\) \(\tau = Mg\,\tfrac{L}{2} + mgL\) *The beam’s weight acts at its middle, \(\tfrac{L}{2}\) from the wall. The sign’s weight acts at the end.* A uniform [katex] 4.0\,\text{m} [/katex] beam of mass [katex] 30\,\text{kg} [/katex] sticks straight out from a wall, bolted at one end. A [katex] 20\,\text{kg} [/katex] sign hangs from its far end. Find the torque about the bolt. [Remove Ads](https://nerd-notes.com/pricing/?for=students) Beam: [katex] (30)(9.8)(2.0) = 588 \text{ N·m} [/katex]. Sign: [katex] (20)(9.8)(4.0) = 784 \text{ N·m} [/katex]. Both turn the beam the same way (clockwise, downward), so the total is about [katex] 1370 \text{ N·m} [/katex] clockwise. **AP trap:** Putting the weight of a uniform beam at its end. It acts at the middle, [katex] \tfrac{L}{2} [/katex] from either end. [Open in UBQ](https://nerd-notes.com/ubq/22894/) Question 11 A meter stick of mass.2 kg is pivoted at one end and supported horizontally. A force of 3 N downwards is applied to the free end, perpendicular to… 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/47224/) Question 12 A 6.00 m long, 500 kg steel uniform beam extends horizontally from the point where it has been bolted to the framework of a new building under… 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/39475/) Question 13 What is the net torque acting on the pivot supporting a 10 kilogram beam 2 meters long as shown above? Assume that the positive direction is… 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) Practice Set: Torque Basics Official course · graded, with step-by-step explanations [Practice](https://nerd-notes.com/courses/?utm_source=blog&utm_medium=article&utm_campaign=unit-5-2-torque&utm_content=practice-practice#course=94339&module=97778&lesson=104028) Quiz Lab Torque and Static Equilibrium Seesaws, beams, signs and ladders that stay put. Balance the torques and the forces. 15 questions · Free [Take the quiz](https://nerd-notes.com/quiz/?id=178) 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-5-2-torque&utm_content=end) ### Lesson 5.3 Preview In the [next lesson](https://nerd-notes.com/unit-5-3-rotational-equilibrium/) we look at what happens when the torques cancel: rotational equilibrium, the idea behind seesaws, shelves, cranes and ladders. ## 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-5-2-torque/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-5-2-torque/