physics

Goniometer

Goniometer is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Goniometer rather than just read about it. In short: A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, γωνία (gōnía) 'angle' and μέτρον (métron) 'measure'.

Key takeaways

Goniometer belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Goniometer to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Goniometer from memory before moving on to harder problems.

Reference excerpt

A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, γωνία (gōnía) 'angle' and μέτρον (métron) 'measure'. The protractor is a commonly used type in the fields of mechanics, engineering, and geometry. The first known description of a goniometer, based on the astrolabe, was by Gemma Frisius in 1538.

Protractor

A protractor is a measuring instrument, typically made of transparent plastic, for measuring angles. Some protractors are simple half-discs or full circles. More advanced protractors, such as the bevel protractor, have one or two swinging arms, which can be used to help measure the angle. Most protractors measure angles in degrees (°). Radian-scale protractors measure angles in radians. Some precision protractors further divide degrees into arcminutes. A protractor divided in centiturns is normally called a "percentage protractor".

Bevel

A bevel protractor is a graduated circular protractor with one pivoted arm used for measuring or marking off angles. Sometimes Vernier scales are attached to give more precise readings. It has wide application in architectural and mechanical drawing, although its use is decreasing with the availability of modern drawing software or CAD. Universal bevel protractors are also used by toolmakers; as they measure angles by mechanical contact they are classed as mechanical protractors. The bevel protractor is used to establish and test angles to very close tolerances. It reads to 5 arcminutes (5′ or ⁠1/12⁠°) and can measure angles from 0° to 450°. The bevel protractor consists of a beam, a graduated dial, and a blade which is connected to a swivel plate (with Vernier scale) by a thumb nut and clamp. When the edges of the beam and blade are parallel, a small mark on the swivel plate coincides with the zero line on the graduated dial. To measure an angle between the beam and the blade of 90° or less, the reading may be obtained directly from the graduation number on the dial indicated by the mark on the swivel plate. To measure an angle of over 90°, subtract the number of degrees as indicated on the dial from 180°, as the dial is graduated from opposite zero marks to 90° each way. Since the spaces, both on the main scale and the Vernier scale, are numbered both to the right and the left from zero, any angle can be measured. The readings can be taken either to the right or to the left, according to the direction in which the zero on the main scale is moved.

Gallery

Applications

Surveying Prior to the invention of the theodolite, the goniometer was used in surveying. The application of triangulation to geodesy was described in the second (1533) edition of Cosmograficus liber by Petri Appiani as a 16-page appendix by Frisius entitled Libellus de locorum describendorum ratione. A simple semicircle protractor or protractor triangle with a knitted small weight attached via a piece of thread to protractor origin point (most of protractors has a thin hole at origin point) could be used as a cheap goniometer, level (optical instrument), inclinometer, or quadrant for a wide range of tasks.

In military topography There are various tools designed for use together with topographic maps, often a combination of protractor, scale ruler, and grid scale for measuring azimuth, distance, and coordinates (in MGRS, UTM, USNG, etc.).

Most military protractors and plotters are designed to be laid on top of detailed topographic maps and therefore are made from thin flexible transluent plastic to intentionally avoid parallax and optics distortion. However, this makes tools less durable.

Royal Artillery Mils Protractor Semi circular 6in and 9in Mils protractors, produced in UK (marked R.A.), Australia (marked R.A.A.) and New Zealand (marked R.N.Z.A.) since 1960s for the Royal Artillery, the Royal Australian Artillery and the RNZA. Protractors were commonly used in the Vietnam War and other conflicts since then. Protractors stamped with the Ordnance Survey product number were sometimes additionally stamped with a NATO Stock Number. Instruction on its basic use were described in the Military Map Reading booklet (an excerpt from the Manual of Map Reading and Land Navigation, Army Code 71874. Issue 1.0: Apr 2009). Identical and modified protractors were commercially produced by various publishers. Its original design was derived from the 400 degrees semicircle protractor (Patent 11465 of 1916) produced by J.H. Steward Ltd. in 1935, since adapted by the Royal Artillery to use Milliradians.

GTA 05-02-012 Coordinate Scale and Protractor Since 1981, the GTA 05-02-012 Coordinate Scale and Protractor tool (initially GTA 5-2-12, which superseded GTA 5-2-10) is a standardized 125x125mm square-size military protractor (its official standard is a PDF file with a vector template for print, latest revision released in June, 2008). This tool was designed and produced by the Department of Army Graphic Training Aid for the needs of the U.S. Army. For its users, special guides and instructions were published: GTA 05-02-013 How To Find Your Way (old title: How To Avoid Getting Lost), TC 3-25.26 (FM 3-25.26) Map Reading and Land Navigation, STP 21-1-SMCT Soldier's Manual of Common Tasks, Warrior Skills Level 1, etc.The GTA 05-02-012 protractor is included in the backpack check lists of most military and ranger students, recruits, and first responders. It is also used by military personnel in NATO member states and its allies. Identical or modified versions of this tool, based on an officially released template, are commercially produced by various publishers.

Combat Mission Plotter For the needs of combat missions, planners designed special plotters for drafting special symbols on maps. Such tools combined protractors, rulers, and scale plotters on a single plate.

GPS Plotting Protractor The GPS Plotting Protractor is a special protractor used to define positions with an accuracy to 10 meters according to a reference grid. It can also be used to measure GPS accuracy. In 2017, in Infantry, the magazine of the U.S. Army, training notes were published under the title of Winning in a GPS-Degrade Environment, describing military actions in severe navigational conditions. The author summarized this article with the note:

It turned out that the best defense against 21st century modern warfare was to rely upon the fundamentals from the 20th century: maps with graphics, compass, and protractor.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Goniometer

Start with the simplest possible case. Write down what Goniometer claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Goniometer before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Goniometer ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Goniometer

In research: Goniometer appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Goniometer in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Goniometer is common in secondary-school and first-year university syllabi. It links to neighbouring topics Angle measuring instruments, Dimensional instruments, Laboratory equipment, so understanding it makes those chapters shorter.
In everyday life: Look for Goniometer outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Goniometer” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Goniometer in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Goniometer means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Goniometer out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Goniometer in simple terms?

Why does Goniometer matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Goniometer?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Goniometer.