mean motion

Examples of mean motion in the following topics:

• Defining Kinematics

  • Kinematics is the study of the motion of points, objects, and groups of objects without considering the causes of its motion.
  • Kinematics is the branch of classical mechanics that describes the motion of points, objects and systems of groups of objects, without reference to the causes of motion (i.e., forces).
  • The study of kinematics is often referred to as the "geometry of motion."
  • Objects are in motion all around us.
  • The word "kinematics" comes from a Greek word "kinesis" meaning motion, and is related to other English words such as "cinema" (movies) and "kinesiology" (the study of human motion).

• Overview of Non-Uniform Circular Motion

  • What do we mean by non-uniform circular motion?
  • The answer lies in the definition of uniform circular motion, which is a circular motion with constant speed.
  • This means that the centripetal acceleration is not constant, as is the case with uniform circular motion.
  • The circular motion adjusts its radius in response to changes in speed.
  • This means that the radius of the circular path is variable, unlike the case of uniform circular motion.

• Key Points: Range, Symmetry, Maximum Height

  • Projectile motion is a form of motion where an object moves in parabolic path.
  • Projectile motion is a form of motion where an object moves in a bilaterally symmetrical, parabolic path.
  • The time of flight of a projectile motion is exactly what it sounds like.
  • Bilateral symmetry means that the motion is symmetrical in the vertical plane.
  • Construct a model of projectile motion by including time of flight, maximum height, and range

• Simple Harmonic Motion

  • Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement.
  • Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement (i.e., it follows Hooke's Law) .
  • In addition, other phenomena can be approximated by simple harmonic motion, such as the motion of a simple pendulum, or molecular vibration.
  • For one-dimensional simple harmonic motion, the equation of motion (which is a second-order linear ordinary differential equation with constant coefficients) can be obtained by means of Newton's second law and Hooke's law.
  • Each of these constants carries a physical meaning of the motion: A is the amplitude (maximum displacement from the equilibrium position), ω = 2πf is the angular frequency, and φ is the phase.

• Free-Falling Objects

  • The motion of falling objects is the simplest and most common example of motion with changing velocity.
  • Air resistance opposes the motion of an object through the air, while friction opposes motion between objects and the medium through which they are traveling.
  • The best way to see the basic features of motion involving gravity is to start by considering straight up and down motion with no air resistance or friction.
  • This means that if the object is dropped, we know the initial velocity is zero.
  • Once the object is in motion, the object is in free-fall.

• Center of Mass and Translational Motion

  • Our study of motion has been limited up to this point.
  • Different parts of a body have different motions.
  • This means that such bodies may not behave like a point particle, as earlier suggested.
  • Describing motions of parts or particles that have different motions would be quite complicated to do in an integrated manner.
  • Support the presence of COM in three dimensional bodies in motion

• The First Law: Inertia

  • Newton’s first law of motion describes inertia.
  • When a first object exerts a force on a second object, the second object simultaneously exerts a force on the first object, meaning that the force of the first object and the force of the second object are equal in magnitude and opposite in direction.
  • This means that an object that is in motion will not change its velocity unless an unbalanced force acts upon it.
  • This is called uniform motion.
  • Newton says that a body in motion will stay in motion until an outside force acts upon it.

• Motional EMF

  • Motion in a magnetic field that is stationary relative to the Earth induces motional EMF (electromotive force).
  • Motion is one of the major causes of induction.
  • In this Atom, we concentrate on motion in a magnetic field that is stationary relative to the Earth, producing what is loosely called motional EMF.
  • (The right hand rule requires that I be counterclockwise, which in turn means the top of the rod is positive, as shown. )
  • (a) A motional emf=Bℓv is induced between the rails when this rod moves to the right in the uniform magnetic field.

• The Third Law: Symmetry in Forces

  • The third law of motion states that for every action, there is an equal and opposite reaction.
  • Newton used these laws to explain and explore the motion of physical objects and systems.
  • When a first object exerts a force on a second object, the second object simultaneously exerts a force on the first object, meaning that the force of the first object and the force of the second object are equal in magnitude and opposite in direction.
  • You have undoubtedly witnessed this law of motion.
  • When a swimmer pushes off the wall, the swimmer is using the third law of motion.

• Harmonic Wave Functions

  • In such condition, if we oscillate the free end in harmonic manner, then the vibrations in the string are simple harmonic motion (SHM), perpendicular to the direction of wave motion.
  • We know that a traveling wave function representing motion in x-direction has the form:
  • The particle attains the greatest speed at the mean position and reduces to zero at extreme positions.
  • On the other hand, acceleration of the particle is greatest at extreme positions and zero at the mean position.
  • It means that displacement of the particle from the mean position at a given position such as x=0 has same value after time period "T" for: