AccelerationIn 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 orientation of the net force acting on that object. The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes: the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force; that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass.
Equations of motionIn physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.
VelocityVelocity is the speed and the direction of motion of an object. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a physical vector quantity: both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called , being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector.
Projectile motionProjectile motion is a form of motion experienced by an object or particle (a projectile) that is projected in a gravitational field, such as from Earth's surface, and moves along a curved path under the action of gravity only. In the particular case of projectile motion on Earth, most calculations assume the effects of air resistance are passive and negligible. The curved path of objects in projectile motion was shown by Galileo to be a parabola, but may also be a straight line in the special case when it is thrown directly upward or downward.
Newton's laws of motionNewton'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 motion at a constant speed in a straight line, unless acted upon by a force. When a body is acted upon by a force, the time rate of change of its momentum equals the force. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.
MotionIn physics, motion is the phenomenon by which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of reference to an observer, measuring the change in position of the body relative to that frame with a change in time. The branch of physics describing the motion of objects without reference to their cause is called kinematics, while the branch studying forces and their effect on motion is called dynamics.
Safari (web browser)Safari is a web browser developed by Apple. It is built into Apple's operating systems, including macOS, iOS, and iPadOS, and uses Apple's open-source browser engine WebKit, which was derived from KHTML. Safari was introduced in Mac OS X Panther in January 2003. It was included with the iPhone since the latter's first generation, which came out in 2007. At that time, Safari was the fastest browser on the Mac. Between 2007 and 2012, Apple maintained a Windows version, but abandoned it due to low market share.
Angular accelerationIn physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity. Following the two types of angular velocity, spin angular velocity and orbital angular velocity, the respective types of angular acceleration are: spin angular acceleration, involving a rigid body about an axis of rotation intersecting the body's centroid; and orbital angular acceleration, involving a point particle and an external axis. Angular acceleration has physical dimensions of angle per time squared, measured in SI units of radians per second squared (rads-2).
Mac OS X TigerMac OS X Tiger (version 10.4) is the 5th major release of macOS, Apple's desktop and server operating system for Mac computers. Tiger was released to the public on April 29, 2005 for US$129.95 as the successor to Mac OS X 10.3 Panther. Included features were a fast searching system called Spotlight, a new version of the Safari web browser, Dashboard, a new 'Unified' theme, and improved support for 64-bit addressing on Power Mac G5s. Mac OS X 10.
Four-accelerationIn the theory of relativity, four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see three-acceleration in special relativity). Four-acceleration has applications in areas such as the annihilation of antiprotons, resonance of strange particles and radiation of an accelerated charge. In inertial coordinates in special relativity, four-acceleration is defined as the rate of change in four-velocity with respect to the particle's proper time along its worldline.
TrajectoryA trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously. The mass might be a projectile or a satellite. For example, it can be an orbit — the path of a planet, asteroid, or comet as it travels around a central mass. In control theory, a trajectory is a time-ordered set of states of a dynamical system (see e.
Angular velocityIn physics, angular velocity (symbol ω, sometimes Ω), also known as angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction. The magnitude of the pseudovector, , represents the angular speed (or angular frequency), the rate at which the object rotates (spins or revolves).
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Rigid bodyIn physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light.
Non-inertial reference frameA non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion are the same in all inertial frames, in non-inertial frames, they vary from frame to frame depending on the acceleration. In classical mechanics it is often possible to explain the motion of bodies in non-inertial reference frames by introducing additional fictitious forces (also called inertial forces, pseudo-forces and d'Alembert forces) to Newton's second law.
Euler's equations (rigid body dynamics)In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. Their general vector form is where M is the applied torques and I is the inertia matrix. The vector is the angular acceleration. Again, note that all quantities are defined in the rotating reference frame.
InertiaInertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law of motion. After some other definitions, Newton states in his first law of motion: LAW I. Every object perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
Euler–Lagrange equationIn the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange. Because a differentiable functional is stationary at its local extrema, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it.
SwitzerlandSwitzerland, officially the Swiss Confederation, is a landlocked country located at the confluence of Western, Central and Southern Europe. It is bordered by Italy to the south, France to the west, Germany to the north and Austria and Liechtenstein to the east. Switzerland is geographically divided among the Swiss Plateau, the Alps and the Jura; the Alps occupy the greater part of the territory, whereas most of the country's population of 8.7 million are concentrated on the plateau, which hosts the largest cities and economic centres, including Zürich, Geneva and Basel.
TimeTime is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions.
