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    Advanced Mechanism Design (Ue19Me544) : Potential Energy Kinetic Energy Conservation of Energy

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    Syed Hafeez Peeran Quadri
    The document discusses different types of energy and momentum in mechanical systems. It defines potential energy as stored energy due to an object's position, and kinetic energy as energy due to an object's motion. The law of conservation of energy states that the total energy in an isolated system remains constant. Momentum is defined as mass in motion, and depends on both an object's mass and velocity. Angular momentum is the momentum of a rotating body, calculated by multiplying linear momentum by the distance from the center of rotation. Generalized momentum in analytical mechanics is defined as the partial derivative of the Lagrangian with respect to the generalized coordinate velocities.

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    Advanced Mechanism Design (Ue19Me544) : Potential Energy Kinetic Energy Conservation of Energy

    Uploaded by

    Syed Hafeez Peeran Quadri
    34 views1 page
    The document discusses different types of energy and momentum in mechanical systems. It defines potential energy as stored energy due to an object's position, and kinetic energy as energy due to an object's motion. The law of conservation of energy states that the total energy in an isolated system remains constant. Momentum is defined as mass in motion, and depends on both an object's mass and velocity. Angular momentum is the momentum of a rotating body, calculated by multiplying linear momentum by the distance from the center of rotation. Generalized momentum in analytical mechanics is defined as the partial derivative of the Lagrangian with respect to the generalized coordinate velocities.

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    Energy and Momentum

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    The document discusses different types of energy and momentum in mechanical systems. It defines potential energy as stored energy due to an object's position, and kinetic energy as energy due to an object's motion. The law of conservation of energy states that the total energy in an isolated system remains constant. Momentum is defined as mass in motion, and depends on both an object's mass and velocity. Angular momentum is the momentum of a rotating body, calculated by multiplying linear momentum by the distance from the center of rotation. Generalized momentum in analytical mechanics is defined as the partial derivative of the Lagrangian with respect to the generalized coordinate velocities.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    34 views1 page

    Advanced Mechanism Design (Ue19Me544) : Potential Energy Kinetic Energy Conservation of Energy

    Uploaded by

    Syed Hafeez Peeran Quadri
    The document discusses different types of energy and momentum in mechanical systems. It defines potential energy as stored energy due to an object's position, and kinetic energy as energy due to an object's motion. The law of conservation of energy states that the total energy in an isolated system remains constant. Momentum is defined as mass in motion, and depends on both an object's mass and velocity. Angular momentum is the momentum of a rotating body, calculated by multiplying linear momentum by the distance from the center of rotation. Generalized momentum in analytical mechanics is defined as the partial derivative of the Lagrangian with respect to the generalized coordinate velocities.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
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    of 1

    ENERGY AND MOMENTUM

    ADVANCED MECHANISM DESIGN (UE19ME544)

    ENERGY POTENTIAL ENERGY KINETIC ENERGY CONSERVATION OF


    All object possess
    ENERGY
    energy. This can Potential energy is defined Kinetic energy is the energy The law of conservation of
    come from having as mechanical energy, stored that an object has because of energy states that the total
    work done on it at energy, or energy caused by its motion. This energy can energy of an isolated system
    some point in time. its position. The energy that be converted into other remains constant. it is said to
    Generally, there are a ball has when perched at a kinds, such as gravitational be conserved over time. This
    two kinds of energy top of a steep hill while it is or electric potential energy. law, first proposed and tested
    in mechanical about to roll down is an by Emilie du Chatelet,
    systems, potential an example of potential energy means that energy can
    d kinetic. Potential neither be created nor
    energy is due to the destroyed, rather, it can only
    position of the be transformed or
    object and kinetic transferred from one form
    energy is due to its to another.
    movement.
    EQUIBRIUM AND KINETIC ENERGY OF
    STABILITY A SYSTEM
    Equilibrium is the condition of a Consider a system of N particles, and
    system when neither its state of motion let 𝑟𝑖 be the position vector of the 𝑖𝑡ℎ
    MOMENTUM nor its internal energy state tends to particle relative to the point O fixed
    Momentum can be change with time. For a single particle, in the initial frame as shown in figure
    defined as "mass in equilibrium arises if the vector sum of below.
    motion." All objects all forces acting upon the particle is
    have mass; so if an zero.
    object is moving, Stability refers to the ability of a body
    then it has to restore to its original static
    momentum - it has equilibrium, after it has been slightly
    its mass in motion. displaced.
    The amount of
    momentum that an
    object has is
    dependent upon two
    variables: how much
    stuff is moving and
    how fast the stuff is
    moving. ANGULAR MOMENTUM GENERALIZED MOMENTUM
    Angular momentum is about the The generalized momentum of
    momentum of a rotating body. For analytical (Lagrangian, Hamiltonian)
    example, if a body rotates at r distance formulations of classical mechanics is
    SUBMITTTED BY from centre of rotation we calculate defined as the partial derivative of the
    angular momentum by multiplying the Lagrangian with regards to the time
    Syed Hafeez Peeran
    linear momentum p=mv by a fixed derivative of generalized coordinates:
    Quadri
    radial distance r. Hence, angular pi=∂L∂˙qi. where: pi is the 𝑖𝑡ℎ
    PES1PG19ME011
    momentum L= r x mv. Angular coordinate of the generalized
    momentum is a vector quantity. momenta.

    REFERANCE – Greenwood D T, 1977, “Classical Dynamics”, Dover Publications, New York.

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