Uniform circular motion
Encyclopedia
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, uniform circular motion describes the motion of a body traversing a circular
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
path at constant speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...
. The distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...
of the body from the axis of rotation remains constant at all times. Though the body's speed is constant, its velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
is not constant: velocity, a vector quantity, depends on both the body's speed and its direction of travel. This changing velocity indicates the presence of an acceleration; this centripetal acceleration is of constant magnitude and directed at all times towards the axis of rotation. This acceleration is, in turn, produced by a centripetal force
Centripetal force
Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...
which is also constant in magnitude and directed towards the axis of rotation.
In the case of rotation around a fixed axis
Rotation around a fixed axis
Rotation around a fixed axis is a special case of rotational motion. The fixed axis hypothesis exclude the possibility of a moving axis, and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation around more than one axis at the same...
of a rigid body
Rigid body
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it...
that is not negligibly small compared to the radius of the path, each particle of the body describes a uniform circular motion with the same angular velocity, but with velocity and acceleration varying with the position with respect to the axis.
Velocity
Figure 1 illustrates velocity and acceleration vectors for uniform motion at four different points in the orbit. Because the velocity v is tangent to the circular path, no two velocities point in the same direction. Although the object has a constant speed, its direction is always changing. This change in velocity is caused by an acceleration a, whose magnitude is (like that of the velocity) held constant, but whose direction also is always changing. The accelerationAcceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
points radially inwards (centripetally) and is perpendicular to the velocity. This acceleration is known as centripetal acceleration.
For a path of radius r, when an angle θ is swept out, the distance traveled on the periphery of the orbit is s = rθ. Therefore, the speed of travel around the orbit is
,where the angular rate of rotation is ω. (By rearrangement, ω = v/r.) Thus, v is a constant, and the velocity vector v also rotates with constant magnitude v, at the same angular rate ω.
Acceleration
The left-hand circle in Figure 2 is the orbit showing the velocity vectors at two adjacent times. On the right, these two velocities are moved so their tails coincide. Because speed is constant, the velocity vectors on the right sweep out a circle as time advances. For a swept angle dθ = ω dt the change in v is a vector at right angles to v and of magnitude v dθ, which in turn means that the magnitude of the acceleration is given by
| 1 m/s 3.6 km/h 2.2 mph |
2 m/s 7.2 km/h 4.5 mph |
5 m/s 18 km/h 11 mph |
10 m/s 36 km/h 22 mph |
20 m/s 72 km/h 45 mph |
50 m/s 180 km/h 110 mph |
100 m/s 360 km/h 220 mph |
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| Slow walk WALK WALK may refer to:*WALK , a radio station licensed to East Patchogue, New York, United States*WALK-FM, a radio station licensed to Patchogue, New York, United States... |
Bicycle Bicycle A bicycle, also known as a bike, pushbike or cycle, is a human-powered, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A person who rides a bicycle is called a cyclist, or bicyclist.... |
City car City car A city car is a small car intended for use primarily in an urban area.City cars are sold worldwide and most automotive industry manufacturers have one or two in their line-up. In North-America city cars are often referred to simply as "subcompacts" alongside the superminis. These kind of cars... |
Aerobatics Aerobatics Aerobatics is the practice of flying maneuvers involving aircraft attitudes that are not used in normal flight. Aerobatics are performed in airplanes and gliders for training, recreation, entertainment and sport... |
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| 10 cm 3.9 in |
Laboratory centrifuge Laboratory centrifuge A laboratory centrifuge is a piece of laboratory equipment, driven by a motor, which spins liquid samples at high speed.There are various types of centrifuges, depending on the size and the sample capacity.... |
10 m/s² 1.0 g |
40 m/s² 4.1 g |
250 m/s² 25 g |
1.0 km/s² 100 g |
4.0 km/s² 410 g |
25 km/s² 2500 g |
100 km/s² 10000 g |
| 20 cm 7.9 in |
5.0 m/s² 0.51 g |
20 m/s² 2.0 g |
130 m/s² 13 g |
500 m/s² 51 g |
2.0 km/s² 200 g |
13 km/s² 1300 g |
50 km/s² 5100 g |
|
| 50 cm 1.6 ft |
2.0 m/s² 0.20 g |
8.0 m/s² 0.82 g |
50 m/s² 5.1 g |
200 m/s² 20 g |
800 m/s² 82 g |
5.0 km/s² 510 g |
20 km/s² 2000 g |
|
| 1 m 3.3 ft |
Playground Playground A playground or play area is a place with a specific design for children be able to play there. It may be indoors but is typically outdoors... carousel Carousel A carousel , or merry-go-round, is an amusement ride consisting of a rotating circular platform with seats for riders... |
1.0 m/s² 0.10 g |
4.0 m/s² 0.41 g |
25 m/s² 2.5 g |
100 m/s² 10 g |
400 m/s² 41 g |
2.5 km/s² 250 g |
10 km/s² 1000 g |
| 2 m 6.6 ft |
500 mm/s² 0.051 g |
2.0 m/s² 0.20 g |
13 m/s² 1.3 g |
50 m/s² 5.1 g |
200 m/s² 20 g |
1.3 km/s² 130 g |
5.0 km/s² 510 g |
|
| 5 m 16 ft |
200 mm/s² 0.020 g |
800 mm/s² 0.082 g |
5.0 m/s² 0.51 g |
20 m/s² 2.0 g |
80 m/s² 8.2 g |
500 m/s² 51 g |
2.0 km/s² 200 g |
|
| 10 m 33 ft |
Roller-coaster vertical loop |
100 mm/s² 0.010 g |
400 mm/s² 0.041 g |
2.5 m/s² 0.25 g |
10 m/s² 1.0 g |
40 m/s² 4.1 g |
250 m/s² 25 g |
1.0 km/s² 100 g |
| 20 m 66 ft |
50 mm/s² 0.0051 g |
200 mm/s² 0.020 g |
1.3 m/s² 0.13 g |
5.0 m/s² 0.51 g |
20 m/s² 2 g |
130 m/s² 13 g |
500 m/s² 51 g |
|
| 50 m 160 ft |
20 mm/s² 0.0020 g |
80 mm/s² 0.0082 g |
500 mm/s² 0.051 g |
2.0 m/s² 0.20 g |
8.0 m/s² 0.82 g |
50 m/s² 5.1 g |
200 m/s² 20 g |
|
| 100 m 330 ft |
Freeway on-ramp |
10 mm/s² 0.0010 g |
40 mm/s² 0.0041 g |
250 mm/s² 0.025 g |
1.0 m/s² 0.10 g |
4.0 m/s² 0.41 g |
25 m/s² 2.5 g |
100 m/s² 10 g |
| 200 m 660 ft |
5.0 mm/s² 0.00051 g |
20 mm/s² 0.0020 g |
130 m/s² 0.013 g |
500 mm/s² 0.051 g |
2.0 m/s² 0.20 g |
13 m/s² 1.3 g |
50 m/s² 5.1 g |
|
| 500 m 1600 ft |
2.0 mm/s² 0.00020 g |
8.0 mm/s² 0.00082 g |
50 mm/s² 0.0051 g |
200 mm/s² 0.020 g |
800 mm/s² 0.082 g |
5.0 m/s² 0.51 g |
20 m/s² 2.0 g |
|
| 1 km 3300 ft |
High-speed railway High-speed rail High-speed rail is a type of passenger rail transport that operates significantly faster than the normal speed of rail traffic. Specific definitions by the European Union include for upgraded track and or faster for new track, whilst in the United States, the U.S... |
1.0 mm/s² 0.00010 g |
4.0 mm/s² 0.00041 g |
25 mm/s² 0.0025 g |
100 mm/s² 0.010 g |
400 mm/s² 0.041 g |
2.5 m/s² 0.25 g |
10 m/s² 1.0 g |
See also
- Example: Circular motion
- Circular motionCircular motionIn physics, circular motion is rotation along a circular path or a circular orbit. It can be uniform, that is, with constant angular rate of rotation , or non-uniform, that is, with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of...
- Centripetal forceCentripetal forceCentripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...
- Non-uniform circular motionNon-uniform circular motionNon-uniform circular motion is any case in which an object moving in a circular path has a varying speed. Some examples of non-uniform circular motion include a roller coaster, a vertical pendulum, and a car riding over a hill. All of these situations include an object traveling at different...
- Fictitious forceFictitious forceA fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame....
- Reactive centrifugal forceReactive centrifugal forceIn classical mechanics, reactive centrifugal force is the reaction paired with centripetal force. A mass undergoing circular motion constantly accelerates toward the axis of rotation. This centripetal acceleration is caused by a force exerted on the mass by some other object. In accordance with...
- Sling (weapon)Sling (weapon)A sling is a projectile weapon typically used to throw a blunt projectile such as a stone or lead "sling-bullet". It is also known as the shepherd's sling....
External links
- Physclips: Mechanics with animations and video clips from the University of New South Wales