56 items with this tag.
C4-5 KeyConcept Claim Stated formally, If rigid body [$A$ → When we read this, it is telling us that $A = text{coupling strength to } hat{G}text{, not accumulated virtue} in a more natural way.] acts on [$B$ → When we read this, it is telling us that kappa sim ell_P^2/k_B approx 10^{-69} in a more n...
C4-3 KeyConcept Claim Stated formally, When a superposition of forces is applied to a body it’s velocity varies with constant acceleration, in the direction of the force applied.
C4-1 KeyConcept Stated in Principia Mathematica The Laws Newton’s first law of motion (glass ketchup bottles) When the net force on a body is zero, then its motion does not change.
C4-2 KeyConcept Claim Stated formally, When observed from an intertial frame, a body acted on by no net force exhibits: with constant (possibly zero) velocity, and zero acceleration.
C7-1 KeyConcept WaitWhat does this encode causality? Definition The total amount of energy stays the same.
C14-4 A KeyConcept similar to conservation where models establish a test volume or area, and consider physical quantities through.
C5-1 C11-1 KeyConcept Discussion This is so important it keeps buildings from toppling.
C7-1 KeyConcept The general concept that certain physical quantities are constant. a quantity that always has the same value is called conserved.
C3-5 KeyConcept Description The velocity as measured by an observer, a physical quantities.
C2-1 KeyConcept Definition Describes motion.
C8-5 KeyConcept Taken in terms of center of mass, rigid body motion is quite similar to motion in space Consider that for each particle composing the mechanical system we may take something like the relative velocity to the velocity of the center of mass.
C3-3 KeyConcept When we discount air resistance and consider only surface gravity, discounting gravity, like the tidal force we can construct the motion of a projectile with a simple parabola.
C3-4 KeyConcept The direction component of velocity changes.
C3-1 C3-2 KeyConcept We extend the notion of position, velocity to incorporate all components.
C2-1 KeyConcept Choose a coordinate system for a particle [$B$ → When we read this, it is telling us that kappa sim ell_P^2/k_B approx 10^{-69} in a more natural way.] and it’s position, [$x_i$ → When we read this, it is telling us that Phi = max_i(phi_i) in a more natural way.] to travel along a st...
C9-1 KeyConcept Definition A type of velocity in kinematics of rotational motion of rigid bodies Formulas We also define angular velocity $$\omega_z = \lim_{\Delta t \rightarrow 0}{\Delta \theta \over \Delta t} = {d\theta \over dt}$$ at any instant, every part of a rotating rigid body has the same a...
C4-2 KeyConcept velocity / speed are zero, relative to a specific reference frame. relative Canonical Hub: CANONICAL_INDEX.
C8-1 KeyConcept Definition Momentum is a vector quantity that can be used alongside impulse in order to describe interactions between bodies.
C8-1 KeyConcept Definition Impulse is a vector quantity relating a particle acted on by a force over a duration.
C8-1 KeyConcept Definition The change in momentum of a particle during a time interval equals the impulse of the net force that acts on the particle during that interval.
C10-5 KeyConcept Definition Analogous to momentum, the rate of change of angular momentum of a particle equals the torque of the net force acting on it.
C10-1 KeyConcept Definition The twisting or turning motion related to the force that caused them, as measured relative to a specific position.
C4-1 KeyConcept Superposition forces on a body have the same effect equal to their sum So a resultant force has the formula $$\vec{R} = \sum_{i=1}^n {F_i}$$ Note that this implies that forces can be written as the superposition of their component values.
C4-6 KeyConcept As a model this break down the kinds of behavior into a well-characterized component.
C1-7 C4-1 KeyConcept Definition An interaction between two bodies, or a body and its environment.
KeyConcept External Introduced in C4-3, a force is external to a body via a completely intuitive definition.
C4-5 KeyConcept In the context of Newton’s third law of motion when two bodies interact, this forms — and the force is equal-and-opposite.
C6-2 KeyConcept We also have the following: the work done by the net force on a particle equals the change in the particle’s kinetic energy which gives the formula $$W_{\text{tot}}=K_f-K_0=\Delta K$$ Caution Notice too that with$$F = ma = \frac{1}{2}{{mv_f^2-mv_0^2} \over s}$$In computing a force re...
C6-1 KeyConcept Definition In the context of law of conservation of energy the amount of energy stored in a system.
C9-4 KeyConcept Definition A rigid body can be thought of as being composed of moving, massive elements, and its kinetic energy based on the law of conservation of energy corresponds to the sum of the energy of its components.
C6-2 KeyConcept Definition A particle with mass and velocity can be said to have an intrinsic amount of energy, as a scalar quantity.
C8-1 KeyConcept Definition It is a type of motion where bodies interact for a short time.
C4-2 KeyConcept A reference frame moving with constant relative velocity, and therefore subject to Newton’s laws of motion.
C4-2 KeyConcept The tendency for motion to remain constant, or to resist change.
C7-3 KeyConcept Definition A conservative force acts such that its total work has: The force can be represented as a difference between the intitial values of a potential-energy function WaitWhat what in nature violates this? It is reversible It is independent of the path of the body and depends onl...
C3-5 KeyConcept Simply, an observer.
C1-1 KeyConcept How physical systems behave. Specific Examples motion Canonical Hub: CANONICAL_INDEX.
C7-1 KeyConcept As opposed to physical systems this is a modelling abstraction for describing collections of objects in a vacuum.
C8-2 KeyConcept A collection of particles with no external forces acting. Implies that the center of mass is in equilibrium.
C1-1 KeyConcept Definition A nascent explanation or models of a pattern relating phenomena of nature.
C1-1 KeyConcept Definition A statement regarding a phenomena of nature which: has a range of validity follows from describing outcomes and development of physical theories.
C2-1 KeyConcept Definition The property of having displacement that can be experimentally measured after passage of some time.
C2-1 KeyConcept Definition The study of the relationships among force, material, and motion.
C2-1 KeyConcept Definition Relates motion to what causes motion, or causality, namely force, and can be extended to describe the motion in more detail of rigid bodies and many other abstractions Types Classical Mechanics Elucidated in Principia Mathematica, dynamics are described by Newtonian mechan...
C1-4 KeyConcept Definition The fact that, given formulas when filled in with appropriate physical quantities the standard systems of units are correct.
KeyConcept Definition A rigid body has a definite size and a definite shape.
C1-1 KeyConcept Definition Literally anything which can be subjected to experiment or measurement. Canonical Hub: CANONICAL_INDEX.
C1-1 KeyConcept Definition A process, the results of which used to test and refine hypotheses models.
C4-6 WaitWhat Caution KeyConcept The process by which physical laws and principles are assumed and interrogated logically — resulting in hypotheses for experimentation.
C2-1 KeyConcept Description A vector quantity describing motion.
C2-1 KeyConcept Description Relative to a selected coordinate system a particle’s position is a vector quantity. Closely related to displacement.
C1-7 KeyConcept Definition A measure of the length in space between an initial point and a final point. Canonical Hub: CANONICAL_INDEX.
C1-7 KeyConcept Description A vector quantity that describes the change in velocity over time.
C6-4 KeyConcept Definition Power is a physical quantities relates work done over time.
C6-1 KeyConcept Definition A physical quantities for how to quantify how bodies within a mechanical system contain and exchange force.
C1-3 KeyConcept Definition Any number used to describe a phenomena of nature quantitatively.