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TERMS:Conservative force - Any force which conserves mechanical energy, as opposed to a nonconservative force. See statement of conservation of mechanical energy. Conservative System - A system in which energy is conserved. Energy - The ability to do work. Kinetic Energy - The energy of motion. Nonconservative Force - Any force which does not conserve mechanical energy, as opposed to a conservative force. Path independence - Property of conservative forces which states that the work done on any path between two given points is the same. Potential energy - The energy of configuration of a conservative system. For formulae, see Definition of potential energy, gravitational potential energy, and Definition of potential energy given a position-dependent force. Total mechanical energy - The sum of the kinetic and potential energy of a conservative system. See definition of total mechanical energy. Work - A force applied over a distance. For formulas, see work done by a constant force parallel to displacement and work done by any constant force, and work done by a position-dependent force. Joule - The units of work, equivalent to a Newton-meter. Also units of energy. Power - Work done per unit time. For formulas, see Formula for average power, Definition of instantaneous power, and formula for instantaneous power. Watt - Unit of power; equal to joule/second.
WORK, ENERGY & POWER
FORMULAS:Work done by a constant force parallel to displacementW = Fx Work done by any constant forceW = Fx cosθ Work-Energy TheoremW = ΔK Formula for average power= Definition of instantaneous powerP = Formula for instantaneous powerP = Fv cosθ Work done by a position-dependent forceW =F(x)dx force. Definition of potential energy.ΔU = - W Gravitational potential energy.U G = mgh Statement of conservation of mechanical energy.Δ(U+K) = 0 Definition of total mechanical energy.U + K = E Definition of potential energy given a position-dependent force.ΔU = -F(x)dx
DYNAMICS
TERMS:Force - A force is defined as a push or a pull. Inertia - The tendency of an object to remain at constant velocity. Inertial reference frame - Any frame in which Newton's Laws are valid. Mass - The amount of matter in a given body. Newton - The name given to a unit of force. One Newton is enough force to cause a 1 KG body to accelerate at a rate of one meter per second per second. Newton's Three Laws - First Law: IfF = 0 then a = 0 and v = constantSecond Law:F = ma Third Law: F AB = - F BA Weight - The gravitational force exerted on a given mass. Free Body Diagram - A diagram of all forces acting upon a given object. Normal Force - The force caused by two bodies in direct contact that is perpendicular to the plane of contact. Frictional Force - The force caused by the electrical interaction between two bodies in direct contact that is parallel to the plane of contact and in the opposite direction of the motion of one object relative to the other. Tension Force - The force felt by a rope or cable that transmits another force. Static Frictional Force - The frictional force on two bodies at rest. Coefficient of Static Friction - Defines the proportionality between F N and F sfor two given materials. Kinetic Frictional Force - The frictional force on two bodies in motion relative to one another. Coefficient of Kinetic Friction - Defines the proportionality between F N and F kfor two given materials. Centripetal Acceleration - The acceleration, directed toward the center of a circle, which causes uniform circular motion. Centripetal Force - The force, directed toward the center of a circle, which causes uniform circular motion.
KINEMATICS
TERMS:Kinematics - Kinematics is concerned with describing the way in which objects move. Displacement - An objects total change in position. If a man runs around an oval 400 meter track, stopping at the precise location he began, though he ran a distance of 400 meters, his total displacement was 0. Dynamics - Dynamics focuses on understanding why objects move the way they do. Reference frame - The coordinate system with respect to which motion is being described. Speed - A measure of how fast an object is moving. Average velocity - The time-average of the velocity function over a specified time-interval. (See formula below.) Instantaneous velocity - The value of the velocity function at a particular instant in time. (See formula below.) Gravitational acceleration - The gravitational acceleration of objects near the earth's surface is the same for all objects regardless of mass and is given by the number g = 9.8m/s2 . Scalar-valued function - A function that outputs scalars (regular numbers). Most common functions that you are probably familiar with are scalar-valued functions. Vector-valued function - A function that outputs vectors. This means that while the domain of the function may consist of scalars, the values in the range are all vectors. Position function - A position function can be either scalar-valued (for motion in one dimension) or vector-valued (for motion in two or three dimensions). At each point in time its value represents the position of an object at that time. Velocity function - This function is the time-derivative of the position function, and gives the velocity of an object at each point in time. Acceleration function - This function is the time-derivative of the velocity function, and the second time-derivative of the position function. It gives the value of the acceleration of an object at each point in time. Time-derivative - The time-derivative of a function is a new function whose value at each point represents the rate of change of the original function with respect to time. Simple harmonic motion - Periodic motion that can be described by special types of position functions. Examples of simple harmonic motion include an object moving in a circle and a ball bouncing up and down on a spring.
The average velocity for an object with position function x(t) over the time interval (t 0, t 1) .v avg = The instantaneous velocity at time t for an object with position function x(t) .v(t) =
Work, energy, power
dynamics
kinematics
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