Tangential speed[edit]
Linear speed is the distance traveled per unit of time, while tangential speed (or tangential velocity) is the linear speed of something moving along a circular path.[4] A point on the outside edge of a merry-go-round or turntable travels a greater distance in one complete rotation than a point nearer the center. Travelling a greater distance in the same time means a greater speed, and so linear speed is greater on the outer edge of a rotating object than it is closer to the axis. This speed along a circular path is known astangential speed because the direction of motion is tangent to the circumference of the circle. For circular motion, the terms linear speed and tangential speed are used interchangeably, and both use units of m/s, km/h, and others.
Rotational speed (or angular speed) involves the number of revolutions per unit of time. All parts of a rigid merry-go-round or turntable turn about the axis of rotation in the same amount of time. Thus, all parts share the same rate of rotation, or the same number of rotations or revolutions per unit of time. It is common to express rotational rates in revolutions per minute (RPM) or in terms of the number of "radians" turned in a unit of time. There are little more than 6 radians in a full rotation (2π radians exactly). When a direction is assigned to rotational speed, it is known as rotational velocity or angular velocity. Rotational velocity is a vector whose magnitude is the rotational speed.
Tangential speed and rotational speed are related: the greater the RPMs, the larger the speed in metres per second. Tangential speed is directly proportional to rotational speed at any fixed distance from the axis of rotation.[4] However, tangential speed, unlike rotational speed, depends on radial distance (the distance from the axis). For a platform rotating with a fixed rotational speed, the tangential speed in the centre is zero. Towards the edge of the platform the tangential speed increases proportional to the distance from the axis.[5] In equation form:
where v is tangential speed and ω (Greek letter omega) is rotational speed. One moves faster if the rate of rotation increases (a larger value for ω), and one also moves faster if movement farther from the axis occurs (a larger value for r). Move twice as far from the rotational axis at the centre and you move twice as fast. Move out three times as far and you have three times as much tangential speed. In any kind of rotating system, tangential speed depends on how far you are from the axis of rotation.
When proper units are used for tangential speed v, rotational speed ω, and radial distance r, the direct proportion of v to both r and ω becomes the exact equation
Thus, tangential speed will be directly proportional to r when all parts of a system simultaneously have the same ω, as for a wheel, disk, or rigid wand. (The direct proportionality of v to r is not valid for planets, because planets have different rotational speeds).
Units[edit]
Main article: Conversion of units § Speed or velocity
Units of speed include:
- metres per second (symbol m s−1 or m/s), the SI derived unit;
- kilometres per hour (symbol km/h);
- miles per hour (symbol mi/h or mph);
- knots (nautical miles per hour, symbol kn or kt);
- feet per second (symbol fps or ft/s);
- Mach number (dimensionless), speed divided by the speed of sound;
- in natural units (dimensionless), speed divided by the speed of light in vacuum (symbol c = 299792458 m/s).
| m/s | km/h | mph | knot | ft/s | |
|---|---|---|---|---|---|
| 1 m/s = | 1 | 3.6 | 2.236936 | 1.943844 | 3.280840 |
| 1 km/h = | 0.277778 | 1 | 0.621371 | 0.539957 | 0.911344 |
| 1 mph = | 0.44704 | 1.609344 | 1 | 0.868976 | 1.466667 |
| 1 knot = | 0.514444 | 1.852 | 1.150779 | 1 | 1.687810 |
| 1 ft/s = | 0.3048 | 1.09728 | 0.681818 | 0.592484 | 1 |
(Values in bold face are exact.)
Examples of different speeds[edit]
 | This section needs additional citations for verification. (May 2013) |
 | This section may contain excessive, poor, or irrelevant examples. (May 2014) |
Main article: Orders of magnitude (speed)
| Speed | m/s | ft/s | km/h | mph | Notes |
|---|---|---|---|---|---|
| Approximate rate of continental drift | 0.00000001 | 0.00000003 | 0.00000004 | 0.00000002 | 4 cm/year. Varies depending on location. |
| Speed of a common snail | 0.001 | 0.003 | 0.004 | 0.002 | 1 millimetre per second |
| A brisk walk | 1.7 | 5.5 | 6.1 | 3.8 | |
| A typical road cyclist | 4.4 | 14.4 | 16 | 10 | Varies widely by person, terrain, bicycle, effort, weather |
| A fast martial arts kick | 7.7 | 25.2 | 27.7 | 17.2 | Fastest kick recorded at 130 milliseconds from floor to target at 1 meter distance. Average velocity speed across kick duration[6] |
| Sprint runners | 12.2 | 40 | 43.92 | 27 | Usain Bolt's 100 metre record. |
| Approximate average speed of road cyclists | 12.5 | 41.0 | 45 | 28 | On flat terrain, will vary |
| Typical suburban speed limit in most of the world | 13.8 | 45.3 | 50 | 30 | |
| Taipei 101 observatory elevator | 16.7 | 54.8 | 60.6 | 37.6 | 1010 m/min |
| Typical rural speed limit | 24.6 | 80.66 | 88.5 | 56 | |
| British National Speed Limit (single carriageway) | 26.8 | 88 | 96.56 | 60 | |
| Category 1 hurricane | 33 | 108 | 119 | 74 | Minimum sustained speed over 1 minute |
| Speed limit on a French autoroute | 36.1 | 118 | 130 | 81 | |
| Highest recorded human-powered speed | 37.02 | 121.5 | 133.2 | 82.8 | Sam Whittingham in a recumbent bicycle[7] |
| Muzzle velocity of a paintball marker | 90 | 295 | 320 | 200 | |
| Cruising speed of a Boeing 747-8passenger jet | 255 | 836 | 917 | 570 | Mach 0.85 at 35000 ft (10668 m) altitude |
| The official land speed record | 341.1 | 1119.1 | 1227.98 | 763 | |
| The speed of sound in dry air at sea-level pressure and 20 °C | 343 | 1125 | 1235 | 768 | Mach 1 by definition. 20 °C = 293.15 kelvins. |
| Muzzle velocity of an AK47 assault riflebullet | 710 | 2330 | 2600 | 1600 | |
| Official flight airspeed record for jet engined aircraft | 980 | 3215 | 3530 | 2194 | Lockheed SR-71 Blackbird |
| Space shuttle on re-entry | 7800 | 25600 | 28000 | 17,500 | |
| Escape velocity on Earth | 11200 | 36700 | 40000 | 25000 | 11.2 km·s-1 |
| Voyager 1 relative velocity to the Sun in 2013 | 17000 | 55800 | 61200 | 38000 | Fastest heliocentric recession speed of any humanmade object.[8] (11 mi/s) |
| Average orbital speed of planet Eartharound the Sun | 29783 | 97713 | 107218 | 66623 | |
| Speed of light in vacuum (symbol c) | 299792458 | 983571056 | 1079252848 | 670616629 | Exactly 299792458 m/s, by definition of the metre |
Vehicles often have a speedometer to measure the speed they are moving.
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