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In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
, circular motion is a movement of an object along the
circumference In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out ...
of a
circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is cons ...
or
rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The
rotation around a fixed axis Rotation around a fixed axis is a special case of rotational motion. The fixed- axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's ...
of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the
center of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...
of a body. In circular motion, the distance between the body and a fixed point on the surface remains the same. Examples of circular motion include: an artificial satellite orbiting the Earth at a constant height, a
ceiling fan A ceiling fan is a fan mounted on the ceiling of a room or space, usually electrically powered, that uses hub-mounted rotating blades to circulate air. They cool people effectively by increasing air speed. Fans do not reduce air temperature ...
's blades rotating around a hub, a stone which is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
, and a
gear A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called ''cogs''), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic ...
turning inside a mechanism. Since the object's velocity vector is constantly changing direction, the moving object is undergoing
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
by a centripetal force in the direction of the center of rotation. Without this acceleration, the object would move in a straight line, according to
Newton's laws of motion Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in mo ...
.


Uniform circular motion

In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
, uniform circular motion describes the motion of a body traversing a circular path at constant
speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quant ...
. Since the body describes circular motion, its
distance Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
from the axis of rotation remains constant at all times. Though the body's speed is constant, its
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
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 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 is a special case of rotational motion. The fixed- axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's ...
of a rigid body 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.


Formulas

For motion in a circle of
radius In classical geometry, a radius (plural, : radii) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', ...
, the circumference of the circle is . If the period for one rotation is , the angular rate of rotation, also known as
angular velocity In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object ...
, is: \omega = \frac = 2\pi f = \frac and the units are radians/second. The speed of the object traveling the circle is: v = \frac = \omega r The angle swept out in a time is: \theta = 2 \pi \frac = \omega t The
angular acceleration In physics, angular acceleration refers to the time rate of change of angular velocity. As there are two types of angular velocity, namely spin angular velocity and orbital angular velocity, there are naturally also two types of angular accelera ...
, , of the particle is: \alpha = \frac In the case of uniform circular motion, will be zero. The acceleration due to change in the direction is: a_c = \frac = \omega^2 r The centripetal and
centrifugal Centrifugal (a key concept in rotating systems) may refer to: *Centrifugal casting (industrial), Centrifugal casting (silversmithing), and Spin casting (centrifugal rubber mold casting), forms of centrifigual casting *Centrifugal clutch *Centrifu ...
force can also be found out using acceleration: F_c = \dot \mathrel\overset ma_c = \frac The vector relationships are shown in Figure 1. The axis of rotation is shown as a vector perpendicular to the plane of the orbit and with a magnitude . The direction of is chosen using the
right-hand rule In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation of axes in three-dimensional space. It is also a convenient method for quickly finding the direction of a cross-product of 2 vectors. Most of ...
. With this convention for depicting rotation, the velocity is given by a vector
cross product In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and ...
as \mathbf = \boldsymbol \omega \times \mathbf r , which is a vector perpendicular to both and , tangential to the orbit, and of magnitude . Likewise, the acceleration is given by \mathbf = \boldsymbol \omega \times \mathbf v = \boldsymbol \omega \times \left( \boldsymbol \omega \times \mathbf r \right) , which is a vector perpendicular to both and of magnitude and directed exactly opposite to . In the simplest case the speed, mass and radius are constant. Consider a body of one kilogram, moving in a circle of
radius In classical geometry, a radius (plural, : radii) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', ...
one metre, with an
angular velocity In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object ...
of one
radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that ...
per
second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ea ...
. * The
speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quant ...
is 1 metre per second. * The inward
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
is 1 metre per square second, . * It is subject to a centripetal force of 1 kilogram metre per square second, which is 1 newton. * The
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...
of the body is 1 kg·m·s−1. * The
moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular accele ...
is 1 kg·m2. * The
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
is 1 kg·m2·s−1. * The
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acce ...
is 1
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force appli ...
. * The
circumference In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out ...
of the
orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
is 2 (~6.283) metres. * The period of the motion is 2 seconds per turn. * The
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
is (2)−1
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that o ...
.


In polar coordinates

During circular motion the body moves on a curve that can be described in
polar coordinate system In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to th ...
as a fixed distance from the center of the orbit taken as origin, oriented at an angle from some reference direction. See Figure 4. The displacement ''vector'' \mathbf is the radial vector from the origin to the particle location: \mathbf(t) = R \hat\mathbf_R(t)\,, where \hat\mathbf_R(t) is the
unit vector In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat"). The term ''direction v ...
parallel to the radius vector at time and pointing away from the origin. It is convenient to introduce the unit vector
orthogonal In mathematics, orthogonality is the generalization of the geometric notion of '' perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
to \hat\mathbf_R(t) as well, namely \hat\mathbf_\theta(t). It is customary to orient \hat\mathbf_\theta(t) to point in the direction of travel along the orbit. The velocity is the time derivative of the displacement: \mathbf(t) = \frac \mathbf(t) = \frac \hat\mathbf_R(t) + R \frac \, . Because the radius of the circle is constant, the radial component of the velocity is zero. The unit vector \hat\mathbf_R(t) has a time-invariant magnitude of unity, so as time varies its tip always lies on a circle of unit radius, with an angle the same as the angle of \mathbf(t). If the particle displacement rotates through an angle in time , so does \hat\mathbf_R(t), describing an arc on the unit circle of magnitude . See the unit circle at the left of Figure 4. Hence: \frac = \frac \hat\mathbf_\theta(t) \, , where the direction of the change must be perpendicular to \hat\mathbf_R(t) (or, in other words, along \hat\mathbf_\theta(t)) because any change d\hat\mathbf_R(t) in the direction of \hat\mathbf_R(t) would change the size of \hat\mathbf_R(t). The sign is positive, because an increase in implies the object and \hat\mathbf_R(t) have moved in the direction of \hat\mathbf_\theta(t). Hence the velocity becomes: \mathbf(t) = \frac \mathbf(t) = R\frac = R \frac \hat\mathbf_\theta(t) = R \omega \hat\mathbf_\theta(t) \, . The acceleration of the body can also be broken into radial and tangential components. The acceleration is the time derivative of the velocity: \begin \mathbf(t) &= \frac \mathbf(t) = \frac \left(R \omega \hat\mathbf_\theta(t) \right) \\ &= R \left( \frac \hat\mathbf_\theta(t) + \omega \frac \right) \, . \end The time derivative of \hat\mathbf_\theta(t) is found the same way as for \hat\mathbf_R(t). Again, \hat\mathbf_\theta(t) is a unit vector and its tip traces a unit circle with an angle that is . Hence, an increase in angle by \mathbf(t) implies \hat\mathbf_\theta(t) traces an arc of magnitude , and as \hat\mathbf_\theta(t) is orthogonal to \hat\mathbf_R(t), we have: \frac = -\frac \hat\mathbf_R(t) = -\omega \hat\mathbf_R(t) \, , where a negative sign is necessary to keep \hat\mathbf_\theta(t) orthogonal to \hat\mathbf_R(t). (Otherwise, the angle between \hat\mathbf_\theta(t) and \hat\mathbf_R(t) would ''decrease'' with increase in .) See the unit circle at the left of Figure 4. Consequently, the acceleration is: \begin \mathbf(t) &= R \left( \frac \hat\mathbf_\theta(t) + \omega \frac \right) \\ &= R \frac \hat\mathbf_\theta(t) - \omega^2 R \hat\mathbf_R(t) \,. \end The centripetal acceleration is the radial component, which is directed radially inward: \mathbf_R(t) = -\omega^2 R \hat\mathbf_R(t) \, , while the tangential component changes the magnitude of the velocity: \mathbf_\theta(t) = R \frac \hat\mathbf_\theta(t) = \frac \hat\mathbf_\theta(t) = \frac \hat\mathbf_\theta(t) \, .


Using complex numbers

Circular motion can be described using
complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the fo ...
s. Let the axis be the real axis and the y axis be the imaginary axis. The position of the body can then be given as z, a complex "vector": z = x + iy = R\left(\cos
theta(t) Theta (, ; uppercase: Θ or ; lowercase: θ or ; grc, ''thē̂ta'' ; Modern: ''thī́ta'' ) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth . In the system of Greek numerals, it has a value of 9. G ...
+ i \sin
theta(t) Theta (, ; uppercase: Θ or ; lowercase: θ or ; grc, ''thē̂ta'' ; Modern: ''thī́ta'' ) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth . In the system of Greek numerals, it has a value of 9. G ...
right) = Re^\,, where is the
imaginary unit The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition an ...
, and \theta(t) is the argument of the complex number as a function of time, . Since the radius is constant: \dot = \ddot R = 0 \, , where a ''dot'' indicates differentiation in respect of time. With this notation the velocity becomes: v = \dot = \frac\left(R e^\right) = R \frac\left(e^\right) = R e^ \frac \left(i \theta \right) = iR\dot(t) e^ = i\omega R e^ = i\omega z and the acceleration becomes: \begin a &= \dot = i\dot z + i\omega\dot = \left(i\dot - \omega^2\right)z \\ &= \left(i\dot - \omega^2 \right) R e^ \\ &= -\omega^2 R e^ + \dot e^ R e^ \, . \end The first term is opposite in direction to the displacement vector and the second is perpendicular to it, just like the earlier results shown before.


Velocity

Figure 1 illustrates velocity and acceleration vectors for uniform motion at four different points in the orbit. Because the velocity 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 , whose magnitude is (like that of the velocity) held constant, but whose direction also is always changing. The
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
points radially inwards ( centripetally) and is perpendicular to the velocity. This acceleration is known as centripetal acceleration. For a path of radius , when an angle is swept out, the distance traveled on the periphery of the orbit is . Therefore, the speed of travel around the orbit is v = r \frac = r\omega , where the angular rate of rotation is . (By rearrangement, .) Thus, is a constant, and the velocity vector also rotates with constant magnitude , at the same angular rate .


Relativistic circular motion

In this case the three-acceleration vector is perpendicular to the three-velocity vector, \mathbf \cdot \mathbf = 0. and the square of proper acceleration, expressed as a scalar invariant, the same in all reference frames, \alpha^2 = \gamma^4 a^2 + \gamma^6 \left(\mathbf \cdot \mathbf\right)^2, becomes the expression for circular motion, \alpha^2 = \gamma^4 a^2. or, taking the positive square root and using the three-acceleration, we arrive at the proper acceleration for circular motion: \alpha = \gamma^2 \frac.


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 the change in is a vector at right angles to and of magnitude , which in turn means that the magnitude of the acceleration is given by a_c = v \frac = v\omega = \frac


Non-uniform

In non-uniform circular motion an object is moving in a circular path with a varying
speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quant ...
. Since the speed is changing, there is
tangential acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
in addition to normal acceleration. In non-uniform circular motion the net acceleration (a) is along the direction of , which is directed inside the circle but does not pass through its center (see figure). The net acceleration may be resolved into two components: tangential acceleration and normal acceleration also known as the centripetal or radial acceleration. Unlike tangential acceleration, centripetal acceleration is present in both uniform and non-uniform circular motion. In non-uniform circular motion, normal force does not always point in the opposite direction of
weight In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar qua ...
. Here is an example with an object traveling in a straight path then loops a loop back into a straight path again. This diagram shows the normal force pointing in other directions rather than opposite to the weight force. The normal force is actually the sum of the radial and tangential forces. The component of weight force is responsible for the tangential force here (We have neglected frictional force). The radial force (centripetal force) is due to the change in direction of velocity as discussed earlier. In non-uniform circular motion, normal force and weight may point in the same direction. Both forces can point down, yet the object will remain in a circular path without falling straight down. First let's see why normal force can point down in the first place. In the first diagram, let's say the object is a person sitting inside a plane, the two forces point down only when it reaches the top of the circle. The reason for this is that the normal force is the sum of the tangential force and centripetal force. The tangential force is zero at the top (as no work is performed when the motion is perpendicular to the direction of force applied. Here weight force is perpendicular to the direction of motion of the object at the top of the circle) and centripetal force points down, thus normal force will point down as well. From a logical standpoint, a person who is travelling in the plane will be upside down at the top of the circle. At that moment, the person's seat is actually pushing down on the person, which is the normal force. The reason why the object does not fall down when subjected to only downward forces is a simple one. Think about what keeps an object up after it is thrown. Once an object is thrown into the air, there is only the downward force of earth's gravity that acts on the object. That does not mean that once an object is thrown in the air, it will fall instantly. What keeps that object up in the air is its
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
. The first of
Newton's laws of motion Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in mo ...
states that an object's inertia keeps it in motion, and since the object in the air has a velocity, it will tend to keep moving in that direction. A varying
angular speed Angular may refer to: Anatomy * Angular artery, the terminal part of the facial artery * Angular bone, a large bone in the lower jaw of amphibians and reptiles * Angular incisure, a small anatomical notch on the stomach * Angular gyrus, a region ...
for an object moving in a circular path can also be achieved if the rotating body does not have an homogeneous mass distribution. For inhomogeneous objects, it is necessary to approach the problem as in.


Applications

Solving applications dealing with non-uniform circular motion involves force analysis. With uniform circular motion, the only force acting upon an object traveling in a circle is the centripetal force. In non-uniform circular motion, there are additional forces acting on the object due to a non-zero tangential acceleration. Although there are additional forces acting upon the object, the sum of all the forces acting on the object will have to be equal to the centripetal force. \begin F_\text &= ma \\ &= ma_r \\ &= \frac \\ &= F_c \end Radial acceleration is used when calculating the total force. Tangential acceleration is not used in calculating total force because it is not responsible for keeping the object in a circular path. The only acceleration responsible for keeping an object moving in a circle is the radial acceleration. Since the sum of all forces is the centripetal force, drawing centripetal force into a free body diagram is not necessary and usually not recommended. Using F_\text = F_c, we can draw free body diagrams to list all the forces acting on an object then set it equal to F_c. Afterwards, we can solve for what ever is unknown (this can be mass, velocity, radius of curvature, coefficient of friction, normal force, etc.). For example, the visual above showing an object at the top of a semicircle would be expressed as F_c = n + mg. In uniform circular motion, total acceleration of an object in a circular path is equal to the radial acceleration. Due to the presence of tangential acceleration in non uniform circular motion, that does not hold true any more. To find the total acceleration of an object in non uniform circular, find the vector sum of the tangential acceleration and the radial acceleration. \sqrt = a Radial acceleration is still equal to \frac. Tangential acceleration is simply the derivative of the speed at any given point: a_t = \frac . This root sum of squares of separate radial and tangential accelerations is only correct for circular motion; for general motion within a plane with polar coordinates (r, \theta), the Coriolis term a_c = 2 \left(\frac\right)\left(\frac\right) should be added to a_t, whereas radial acceleration then becomes a_r = \frac + \frac.


See also

*
Angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
* Equations of motion for circular motion * *
Fictitious force A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as a linearly accelerating or rotating reference frame. It is related to Newton's second law of motion, which trea ...
*
Geostationary orbit A geostationary orbit, also referred to as a geosynchronous equatorial orbit''Geostationary orbit'' and ''Geosynchronous (equatorial) orbit'' are used somewhat interchangeably in sources. (GEO), is a circular geosynchronous orbit in altitu ...
*
Geosynchronous orbit A geosynchronous orbit (sometimes abbreviated GSO) is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours, 56 minutes, and 4 seconds (one sidereal day). The synchronization of rotation and orbita ...
*
Pendulum (mathematics) A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gr ...
*
Reactive centrifugal force In classical mechanics, a reactive centrifugal force forms part of an action–reaction pair with a centripetal force. In accordance with Newton's first law of motion, an object moves in a straight line in the absence of a net force acting on ...
* Reciprocating motion * *
Sling (weapon) A sling is a projectile weapon typically used to throw a blunt projectile such as a stone, clay, or lead " sling-bullet". It is also known as the shepherd's sling or slingshot (in British English). Someone who specializes in using slings ...


References


External links


Physclips: Mechanics with animations and video clips
from the University of New South Wales

– a chapter from an online textbook

– a video lecture on CM

– an online textbook with different analysis for circular motion {{Classical mechanics derived SI units Rotation Classical mechanics Motion (physics)