Momentum
Vector quantity equal to mass times velocity.
Momentum, specifically linear or translational momentum, is defined in Newtonian mechanics as the product of an object's mass and its velocity. As a vector quantity, it has both magnitude and direction. Its standard unit in the International System of Units is the kilogram meter per second (kg⋅m/s), which is dimensionally equivalent to the newton-second. The relationship between momentum and force is given by Newton's second law, which states that the rate of change of a body's momentum equals the net force acting upon it. For a single particle, if a constant net force is applied over a time interval, the momentum changes by an amount equal to the impulse, measured in newton-seconds. In differential form, the instantaneous force equals the derivative of momentum with respect to time. Under constant mass, this is equivalent to mass times acceleration. For a system of multiple particles, the total momentum is the vector sum of each particle's momentum. The system's center of mass, a weighted average of particle positions, moves with a velocity such that the total momentum equals the total mass multiplied by this velocity, a principle known as Euler's first law. A crucial property is the conservation of momentum: in a closed system free from external forces, the total momentum remains constant. This follows from Newton's third law, as forces between interacting particles are equal and opposite, causing momentum exchanges that sum to zero. This conservation holds regardless of the complexity of the forces involved. Beyond classical mechanics, momentum is conserved in special relativity (with a modified formula) and, in adapted forms, in electrodynamics, quantum mechanics, quantum field theory, and general relativity. This conservation is an expression of translational symmetry, a fundamental symmetry of space and time. In advanced formulations like Lagrangian and Hamiltonian mechanics, the conserved quantity becomes generalized momentum, which may differ from kinetic momentum. This concept carries into quantum mechanics, where momentum becomes an operator on a wave function, related to the position operator by the Heisenberg uncertainty principle. In continuous systems such as fluids and electromagnetic fields, a momentum density (momentum per volume) is defined and satisfies a conservation law, leading to equations like the Navier-Stokes equations for fluids or
- definition
- Product of mass and velocity (p = mv)
- SI unit
- kilogram metre per second (kg⋅m/s)
- type
- Vector quantity
- conservation
- Conserved in closed systems in inertial frames
- related_law
- Newton's second law (F = dp/dt)
Lore & Background
In Newtonian mechanics, momentum is defined as the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction. The unit of momentum in the International System of Units (SI) is the kilogram metre per second (kg⋅m/s), which is dimensionally equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame of reference, it is a conserved quantity. This means that if a closed system is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum field theory, and general relativity. It is an expression of one of the fundamental symmetries of space and time: translational symmetry.
Reader's Guide
Momentum is a foundational concept in physics, central to understanding motion and collisions. In classical mechanics, it allows prediction of the resulting direction and speed of objects after they interact. The conservation of momentum is a powerful principle: in a closed system with no external forces, total momentum remains constant, enabling analysis of everything from particle collisions to rocket propulsion. The concept extends beyond Newtonian mechanics. In Lagrangian and Hamiltonian mechanics, the conserved quantity is generalized momentum, which differs from kinetic momentum. This generalized momentum carries over into quantum mechanics, where it becomes an operator on a wave function, related to position by the Heisenberg uncertainty principle. In continuous systems such as electromagnetic fields, fluid dynamics, and deformable bodies, a momentum density is defined as momentum per volume, satisfying a conservation law. This leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids. The relationship between force and momentum change is also expressed through impulse: the change in momentum equals the integral of force over time.
Did You Know?
- Momentum is a vector quantity, possessing both magnitude and direction.
- The SI unit of momentum is the kilogram metre per second (kg⋅m/s).
- Newton's second law states that the rate of change of a body's momentum equals the net force acting on it.
- Momentum is conserved in closed systems not affected by external forces.
Frequently Asked Questions
Who is Momentum?
Momentum is a vector quantity defined as the product of an object's mass and its velocity, often written as p = mv. It encodes both how much matter is in motion and the direction that motion takes.
What are Momentum's powers or core role?
As a true vector, Momentum carries a magnitude and a direction, fully describing a body's state of motion. Its standard SI unit is the kilogram metre per second (kg⋅m/s).
How does Momentum's story end?
In any closed system with no net external force, the total Momentum is conserved, meaning it stays constant over time when measured in an inertial frame. This conservation rule is one of the bedrock principles of classical mechanics.
Why is Momentum so important to the broader story?
Momentum sits at the heart of Newton's second law, which states that the net force on a body equals the time-rate of change of its momentum (F = dp/dt). That link makes Momentum the central quantity for describing how forces reshape motion.
What is Momentum's 'home base' or native frame?
Momentum's conservation is guaranteed specifically in inertial reference frames—those that are not accelerating. In a non-inertial frame, fictitious forces must be introduced before the conservation rule can be applied.
More in Classical Mechanics 1-21
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