The integral of power over time defines the work performed. Because this integral depends on the trajectory of the point of application of the force and torque, this calculation of work is said to be path dependent. The same amount of work is done when carrying a load up a flight of stairs whether the person carrying it walks or runs, but more power is needed for running because the work is done in a shorter amount of time. The output power of an electric motor is the product of the torque that the motor generates and the angular velocity of its output shaft. Power (physics)
In physics, a force is said to do work when it acts on a body, and there is a displacement of the point of application in the direction of the force. For example, when you lift a suitcase from the floor, the work done on the suitcase is the force it takes to lift it (its weight) times the height that it is lifted. The term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis as "weight lifted through a height", which is based on the use of early steam engines to lift buckets of water out of flooded ore mines. The SI unit of work is the newton-metre or joule (J). Work (physics)
In physics, a wave is a disturbance or oscillation that travels through space and matter, accompanied by a transfer of energy. Wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations around almost fixed locations. Waves are described by a wave equation which sets out how the disturbance proceeds over time. The mathematical form of this equation varies depending on the type of wave.
where k is a positive constant. If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude). If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Harmonic oscillator
In physics, a physical law of conservation or conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. One particularly important physical result concerning laws of conservation is Noether's theorem, which states that there is a one-to-one correspondence between laws of conservation and differentiable symmetries of physical systems. For example, the conservation of energy follows from the time-invariance of physical systems, and the fact that physical systems behave the same regardless of how they are oriented in space gives rise to the conservation of angular momentum. Conservation law
Torque Torque, moment or moment of force (see the terminology below), is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist to an object. Mathematically, torque is defined as the cross product of the lever-arm distance vector and the force vector, which tends to produce rotation. Loosely speaking, torque is a measure of the turning force on an object such as a bolt or a flywheel. For example, pushing or pulling the handle of a wrench connected to a nut or bolt produces a torque (turning force) that loosens or tightens the nut or bolt.
This gyroscope remains upright while spinning due to its angular momentum. In physics, angular momentum, moment of momentum, or rotational momentum is a measure of the amount of rotation an object has, taking into account its mass, shape and speed. It is a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a particular axis. The angular momentum of a system of particles (e.g. a rigid body) is the sum of angular momenta of the individual particles. For a rigid body rotating around an axis of symmetry (e.g. the blades of a ceiling fan), the angular momentum can be expressed as the product of the body's moment of inertia, I, (i.e., a measure of an object's resistance to changes in its rotation velocity) and its angular velocity ω: Angular momentum
There are many forms of energy, but all these types must meet certain conditions such as being convertible to other kinds of energy, obeying conservation of energy, and causing a proportional change in mass in objects that possess it. Common energy forms include the kinetic energy of a moving object, the radiant energy carried by light and other electromagnetic radiation, the potential energy stored by virtue of the position of an object in a force field such as a gravitational, electric or magnetic field, and the thermal energy comprising the microscopic kinetic and potential energies of the disordered motions of the particles making up matter. Some specific forms of potential energy include elastic energy due to the stretching or deformation of solid objects and chemical energy such as is released when a fuel burns.
Force The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object. As a formula, this is expressed as:
Like velocity, linear momentum is a vector quantity, possessing a direction as well as a magnitude by its own weight Linear momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. In classical mechanics, conservation of linear momentum is implied by Newton's laws; but it also holds in special relativity (with a modified formula) and, with appropriate definitions, a (generalized) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity. Newtonian mechanics Momentum
In physics, mass (from Greek μᾶζα "barley cake, lump [of dough]") is a property of a physical body which determines the body's resistance to being accelerated by a force and the strength of its mutual gravitational attraction with other bodies. The SI unit of mass is the kilogram (kg). As mass is difficult to measure directly, usually balances or scales are used to measure the weight of an object, and the weight is used to calculate the object's mass. For everyday objects and energies well-described by Newtonian physics, mass describes the amount of matter in an object. However, at very high speeds or for subatomic particles, special relativity shows that energy is an additional source of mass. Thus, any stationary body having mass has an equivalent amount of energy, and all forms of energy resist acceleration by a force and have gravitational attraction. Mass
Acceleration For example, an object such as a car that starts from standstill, then travels in a straight line at increasing speed, is accelerating in the direction of travel. If the car changes direction at constant speedometer reading, there is strictly speaking an acceleration although it is often not so described; passengers in the car will experience a force pushing them back into their seats in linear acceleration, and a sideways force on changing direction. If the speed of the car decreases, it is sometimes called deceleration; mathematically it is simply acceleration in the opposite direction to that of motion. Definition and properties Acceleration is the rate of change of velocity.
If there is a change in speed, direction, or both, then the object has a changing velocity and is said to be undergoing an acceleration. Constant velocity vs acceleration To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path (the object's path does not curve). Velocity
Length In geometric measurements, length is the longest dimension of an object. In the International System of Quantities, length is any quantity with dimension distance. In other contexts "length" is the measured dimension of an object. For example it is possible to cut a length of a wire which is shorter than wire thickness.
Motion (physics) If the position of a body is not changing with the time with respect to a given frame of reference the body is said to be at rest, motionless, immobile, stationary, or to have constant (time-invariant) position. An object's motion cannot change unless it is acted upon by a force, as described by Newton's first law. Momentum is a quantity which is used for measuring motion of an object. An object's momentum is directly related to the object's mass and velocity, and the total momentum of all objects in a closed system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum. The study of motion deals with (1) The study of motion of solids (mechanics). (2) study of motion of fluids (fluid mechanics) As there is no absolute frame of reference, absolute motion cannot be determined. Thus, everything in the universe can be considered to be moving.:20–21
Newton's law of universal gravitation