In words, you divide by 60 to convert to revolutions per second, then you multiply by 2π to turn this into a value in radians per second, which is the angular velocity you're looking for. For example, with the wheel in the previous section traveling at 40 RPM, you convert to angular velocity as follows:

H = 1 2 tan ⁡ θ ⋅ P = 3 2 ⋅ P ≈ 0.866025 ⋅ P {\displaystyle H={\frac {1}{2\tan \theta }}\cdot P={\frac {\sqrt {3}}{2}}\cdot P\approx 0.866025\cdot P}

Johnson, Lee. "How To Convert RPM To Linear Speed" sciencing.com, https://www.sciencing.com/convert-rpm-linear-speed-8232280/. 14 February 2020.

StandardThreadSizeChartPDF

Using this, it's easy to see how to convert between RPM and angular velocity: First, convert from per minute to per second, then convert the number of revolutions to a value in radians. The formula you need is:

ISO metricthread chart

A screw thread gauging system comprises a list of screw thread characteristics that must be inspected to establish the dimensional acceptability of the screw threads on a threaded product and the gauge(s) which shall be used when inspecting those characteristics.

Most situations in physics will use angular velocity (ω) instead of RPM, which is essentially the angular change in position of an object per second, measured in radians per second.

The relationship between the height H and the pitch P is found using the following equation where θ {\displaystyle \theta } is half the included angle of the thread, in this case 30 degrees:[1]

This number pair is optionally followed by the letters UNC, UNF or UNEF (Unified) if the diameter-pitch combination is from the coarse, fine, or extra fine series, and may also be followed by a tolerance class.

The number series of machine screws once included more odd numbers and went up to #16 or more. Standardization efforts in the late 19th and the early part of the 20th century reduced the range of sizes considerably. Now, it is less common to see machine screws larger than #14, or odd number sizes other than #1, #3 and #5. Even though #14 and #16 screws are still available, they are not as common as sizes #0 through #12.[citation needed]

The calculation itself is fairly straightforward, but it's complicated if the angular velocity (i.e. the change in angular position per unit time) is expressed in a non-standard form like revolutions per minute (RPM). However, converting RPM to speed is still easy enough after you convert the RPM to a more standard measure of angular velocity.

Metricthread formula chart

\(\begin{aligned}\) \(ω &= \frac{40 \text{ RPM}}{60 \text{ second/minute}} × 2π \text{ rad/rev}\) \(&= 4.19 \text{ rad/s}\) \(\end{aligned}\)

Metricthread ChartPDF

The letter suffix "A" or "B" denotes whether the threads are external or internal, respectively. Classes 1A, 2A, 3A apply to external threads; Classes 1B, 2B, 3B apply to internal threads.[9]

The number series of machine screws has been extended downward to include #00-90 (0.047 in = 0.060 in − 0.013 in) and #000-120 (0.034 in = 0.060 in − 2 × 0.013 in) screws;[3] however, the main standard for screws smaller than #0 is ANSI/ASME standard B1.10 Unified Miniature Screw Threads. This defines a series of metric screws named after their major diameters in millimetres, from 0.30 UNM to 1.40 UNM. Preferred sizes are 0.3, 0.4, 0.5, 0.6, 0.8, 1.0 and 1.2 mm, with additional defined sizes halfway between.[2]: 1861  The standard thread pitch is approximately ⁠1/4⁠ of the major diameter. The thread form is slightly modified to increase the minor diameter, and thus the strength of screws and taps. The major diameter still extends to within ⁠1/8⁠H of the theoretical sharp V, but the total depth of the thread is reduced 4% from ⁠5/8⁠H = ⁠5/8⁠ cos(30°) P ≈ 0.541P to 0.52P.[2]: 1858–1859  This increases the amount of the theoretical sharp V which is cut off at the minor diameter by 10% from 0.25H to ⁠7/8⁠ − ⁠0.52/cos 30°⁠ ≈ 0.27456H.

Metric externalthreaddimensions

The Unified Thread Standard (UTS) defines a standard thread form and series—along with allowances, tolerances, and designations—for screw threads commonly used in the United States and Canada. It is the main standard for bolts, nuts, and a wide variety of other threaded fasteners used in these countries. It has the same 60° profile as the ISO metric screw thread, but the characteristic dimensions of each UTS thread (outer diameter and pitch) were chosen as an inch fraction rather than a millimeter value. The UTS is currently controlled by ASME/ANSI in the United States.

ISO standard metricthread ChartPDF

Where ω is the angular velocity you calculated in the previous step, and r is the radius of the circular path for the motion, and you multiply these together to find the linear speed. For example, with the wheel rotating at 40 RPM, i.e. 4.19 rad/s, assuming a radius of 15 cm = 0.15 m, the velocity is:

Rotational motion is one of the most important things to understand when you're learning classical physics, and converting a rotational velocity to a linear speed is a key task in many problems.

RPM is a measure of the number of complete revolutions in a minute. For example, if a wheel is rolling so it completes one full revolution per second, in 60 seconds it will have completed 60 revolutions, and so it would be rotating at 60 RPM. An RPM formula that you can use to find the RPM in any situation is:

This is a much more useful format when you're converting RPM to linear speed, because there is a simple relation between angular velocity and linear speed, which doesn't exist in explicit form for RPM. Given that there are 2π radians in a complete revolution, RPM is really telling you "the number of 2π radian rotations per minute."

Thread class refers to the acceptable range of pitch diameter for any given thread. The pitch diameter is indicated as Dp in the figure shown above. There are several methods that are used to measure the pitch diameter. The most common method used in production is by way of a go/no-go gauge.

ThreadsizeChartmm

The major diameter Dmaj is the diameter of the screw measured from the outer edge of the threads. The minor diameter Dmin (also known as the root diameter) is the diameter of the screw measured from the inner edge of the threads. The major diameter may be slightly different from the shank diameter, which is the diameter of the unthreaded part of the screw. The diameters are sometimes given approximately in fractions of an inch (e.g. the major diameter of a #6 screw is 0.1380 in, approximately 9⁄64 in = 0.140625 in).

Sometimes "special" diameter and pitch combinations (UNS) are used, for example a 0.619 in (15.7 mm) major diameter with 20 threads per inch. UNS threads are rarely used for bolts, but rather on nuts, tapped holes, and threaded ODs. Because of this UNS taps are readily available.[4][5] Most UNS threads have more threads per inch than the correlating UNF or UNEF standard; therefore they are often the strongest thread available.[6] Because of this they are often used in applications where high stresses are encountered, such as machine tool spindles[7] or automotive spindles.[8]

Johnson, Lee. (2020, February 14). How To Convert RPM To Linear Speed. sciencing.com. Retrieved from https://www.sciencing.com/convert-rpm-linear-speed-8232280/

The pitch P is the distance between thread peaks. For UTS threads, which are single-start threads, it is equal to the lead, the axial distance that the screw advances during a 360° rotation. UTS threads do not usually use the pitch parameter; instead a parameter known as threads per inch (TPI) is used, which is the reciprocal of the pitch.

P = 2 tan ⁡ θ ⋅ H = 2 3 ⋅ H ≈ 1.154701 ⋅ H . {\displaystyle P=2\tan \theta \cdot H={\frac {2}{\sqrt {3}}}\cdot H\approx 1.154701\cdot H.}

In an external (male) thread (e.g., on a bolt), the major diameter Dmaj and the minor diameter Dmin define maximum dimensions of the thread. This means that the external thread must end flat at Dmaj, but can be rounded out below the minor diameter Dmin. Conversely, in an internal (female) thread (e.g., in a nut), the major and minor diameters are minimum dimensions, therefore the thread profile must end flat at Dmin but may be rounded out beyond Dmaj. These provisions are to prevent any interferences.

The standard designation for a UTS thread is a number indicating the nominal (major) diameter of the thread, followed by the pitch measured in threads per inch. For diameters smaller than ⁠1/4⁠ inch, the diameter is indicated by an integer number defined in the standard; for all other diameters, the inch figure is given.

Each thread in the series is characterized by its major diameter Dmaj and its pitch, P. UTS threads consist of a symmetric V-shaped thread. In any plane containing the thread axis, the flanks of the V have an angle of 60° to each other. The outermost 1⁄8 and the innermost 1⁄4 of the height H of the V-shape are cut off from the profile.

Inchthread chart

There are a couple of additional points it's worth keeping in mind when you perform these calculations. First, the direction of the linear speed you calculate is always tangential to the point on the circle you're calculating for.

D min = D maj − 2 ⋅ 5 8 ⋅ H = D maj − 5 3 8 ⋅ P ≈ D maj − 1.082532 ⋅ P D p = D maj − 2 ⋅ 3 8 ⋅ H = D maj − 3 3 8 ⋅ P ≈ D maj − 0.649519 ⋅ P . {\displaystyle {\begin{aligned}D_{\text{min}}&=D_{\text{maj}}-2\cdot {\frac {5}{8}}\cdot H=D_{\text{maj}}-{\frac {5{\sqrt {3}}}{8}}\cdot P\approx D_{\text{maj}}-1.082532\cdot P\\D_{\text{p}}&=D_{\text{maj}}-2\cdot {\frac {3}{8}}\cdot H=D_{\text{maj}}-{\frac {3{\sqrt {3}}}{8}}\cdot P\approx D_{\text{maj}}-0.649519\cdot P.\end{aligned}}}

Johnson, Lee. How To Convert RPM To Linear Speed last modified March 24, 2022. https://www.sciencing.com/convert-rpm-linear-speed-8232280/

From this formula, you can calculate RPM in any situation and even if you've been recording the number of revolutions for less than (or more than) a minute. For example, if a wheel completes 30 revolutions in 45 seconds (i.e. 0.75 minutes), the result is: 30 ÷ 0.75 = 40 RPM.

A classification system exists for ease of manufacture and interchangeability of fabricated threaded items. Most (but certainly not all) threaded items are made to a classification standard called the Unified Screw Thread Standard Series. This system is analogous to the fits used with assembled parts.

For example, if you were swinging a yo-yo in a giant circle, but the string broke, the yo-yo would fly off in whatever direction it was traveling in at the instant the string broke. Second, it's crucial that you think about units when you're calculating rpm. The units of distance you use for the radius will be the same as the units of distance in your final speed, and so it's better to stick with meters or feet even if the number for the radius ends up being very small.

These standards provide essential specifications and dimensions for the gauges used on Unified inch screw threads (UN, UNR, UNJ thread form) on externally and internally threaded products. It also covers the specifications and dimensions for the thread gauges and measuring equipment. The basic purpose and use of each gauge are also described. It also establishes the criteria for screw thread acceptance when a gauging system is used.

The following formula is used to calculate the major diameter of a numbered screw greater than or equal to 0: Major diameter = Screw # × 0.013 in + 0.060 in. For example, the major diameter of a #10 screw is 10 × 0.013 in + 0.060 in = 0.190 in. To calculate the major diameter of "aught" size screws count the number of extra zeroes and multiply this number by 0.013 in and subtract from 0.060 in. For example, the major diameter of a #0000 screw is 0.060 in − (3 × 0.013 in) = 0.060 in − 0.039 in = 0.021 in.