In physics, circular motion is rotation along a circle: a circular path or a circular orbit. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. We can talk about circular motion of an object if we ignore its size, so that we have the motion of a point mass in a plane. This is a discussion of a present category of science. ... A sphere rotating around its axis. ... Circle illustration This article is about the shape and mathematical concept of circle. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... The simplest three-dimensional case of rotation is rotation of a body about a fixed axis of rotation: each point of the body moves in a plane perpendicular to the axis, carrying out a circular motion, with the circle centered at the intersection of the plane and the axis. ...

Examples of circular motion are: an artificial satellite orbiting the Earth in geosynchronous orbit, a stone which is tied to a rope and is being swung in circles (cf. hammer throw), a racecar turning through a curve in a racetrack, an electron moving perpendicular to a uniform magnetic field, a gear turning inside a mechanism. It has been suggested that this article or section be merged with geostationary orbit. ... The modern or Olympic hammer throw is an athletic throwing event where the object to be thrown is a heavy steel ball attached with wire (maximum 4 ft (1. ... Alternative use: Race track Racetrack is a pencil and paper game, nominally for two players. ... Magnetic field lines shown by iron filings In physics, the space surrounding moving electric charges, changing electric fields and magnetic dipoles contains a magnetic field. ... Spur gears found on a piece of farm equipment A gear is a wheel with teeth around its circumference, the purpose of the teeth being to mesh with similar teeth on another mechanical device -- possibly another gear wheel -- so that force can be transmitted between the two devices in a...

Circular motion involves acceleration of the moving object by a centripetal force which pulls the moving object towards the center of the circular orbit. Without this acceleration, the object would move inertially in a straight line, according to Newton's first law of motion. Circular motion is accelerated even if the speed is constant, because the object's velocity vector is constantly changing direction. Acceleration is the time rate of change of velocity and/or direction, and at any point on a velocity-time graph, it is given by the slope of the tangent to the curve at that point. ... The centripetal force is the external force required to make a body follow a circular path at constant speed. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ...

Constant speed

In the simplest case the speed, mass and radius are constant.

Consider a body of one kilogram, moving in a circle of radius one metre, with an angular velocity of one radian per second. “Kg” redirects here. ... Remote Authentication Dial In User Service (RADIUS) is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ... This article is about the unit of length. ... Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ... Some common angles, measured in radians. ... Look up second in Wiktionary, the free dictionary. ...

• The speed is one metre per second
• The inward acceleration is one metre per second per second.
• It is subject to a centripetal force of one kilogram metre per second per second, which is one newton.
• The momentum of the body is one kg·m·s⁻¹.
• The moment of inertia is one kg·m².
• The angular momentum is one kg·m²·s⁻¹.
• The kinetic energy is 1/2 joule.
• The circumference of the orbit is 2π (~ 6.283) metres.
• The period of the motion is 2π seconds per turn.
• The frequency is (2π)⁻¹ hertz.
• From the point of view of quantum mechanics, the system is in an excited state having quantum number ~ 9.48×10³⁵.

Then consider a body of mass m, moving in a circle of radius r, with an angular velocity of ω. This article does not cite any references or sources. ... Acceleration is the time rate of change of velocity and/or direction, and at any point on a velocity-time graph, it is given by the slope of the tangent to the curve at that point. ... The centripetal force is the external force required to make a body follow a circular path at constant speed. ... For other uses, see Newton (disambiguation). ... In classical mechanics, momentum (pl. ... Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, (SI units kg m², Former British units slug ft2), is the rotational analog of mass. ... This gyroscope remains upright while spinning due to its angular momentum. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... The joule (IPA: or ) (symbol: J) is the SI unit of energy. ... The circumference is the distance around a closed curve. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... Look up period in Wiktionary, the free dictionary. ... ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... This article is about the SI unit of frequency. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... This article or section is in need of attention from an expert on the subject. ... Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ... Look up Ω, ω in Wiktionary, the free dictionary. ...

• The speed is v = r·ω.
• The centripetal (inward) acceleration is a = r·ω ² = r ⁻¹·v ².
• The centripetal force is F = m·a = r·m·ω ² = r⁻¹·m·v ².
• The momentum of the body is p = m·v = r·m·ω.
• The moment of inertia is I = r ²·m.
• The angular momentum is L = r·m·v = r ²·m·ω = I·ω.
• The kinetic energy is E = 2⁻¹·m·v ² = 2⁻¹·r ²·m·ω ² = (2·m)⁻¹·p ² = 2⁻¹·I·ω ² = (2·I)⁻¹·L ² .
• The circumference of the orbit is 2·π·r.
• The period of the motion is T = 2·π·ω ⁻¹.
• The frequency is f = T ⁻¹ . (Instead of letter f, the frequency is often denoted by the Greek letter ν, which however is almost indistinguishable from the letter v used here for velocity).
• The quantum number is J = 2·π·L h⁻¹.

.. Two bodies with a slight difference in mass orbiting around a common barycenter. ... For other uses, see Nu. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ...

Variable speed

In the general case, circular motion requires that the total force can be decomposed into the centripetal force required to keep the orbit circular, and a force tangent to the circle, causing a change of speed.

The magnitude of the centripetal force depends on the instantaneous speed.

In the case of an object at the end of a rope, subjected to a force, we can decompose the force into a radial and a lateral component. The radial component is either outward or inward.

See also

• Angular momentum
• Rotational equations of motion
• Pendulum (mathematics)
• Uniform circular motion
• Simple harmonic motion

This gyroscope remains upright while spinning due to its angular momentum. ... It has been suggested that SUVAT equations be merged into this article or section. ... The mathematics of pendulums can be quite complex, but some formula and proofs are given below. ... The realm of physics consists of two types of circular motion: uniform circular motion and non-uniform circular motion. ... Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. ...

External links

• Circular Motion - a chapter from an online textbook
• Circular Motion: Kinematics on Project PHYSNET.