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MECHANICS, The total energy of an isolated system remains constant,…

- - - - Relationship Between G and g :
        Weight(on earth) is the force on an object due to the gravitational attraction of the earth.
        g depends on how far you are from this center.
      - WHAT KEEPS A SATELLITE IN ORBIT???
        
        The satellite's speed or centripetal acceleration is caused by GRAVITATIONAL FORCE.
      - Weightlessness =condition experienced while in free-fall
      - KEPLER'S LAW
        
        FIRST LAW
        
        All planets move about the Sun in elliptical orbits, having the Sun as one of the foci.
        
        SECOND LAW
        
        A radius vector from a sun to a planet sweeps out equal areas in equal lengths of time.
        
        THIRD LAW
        
        The squares of the periods is directly proportional to the cubes of their average distances from the sun is the same for every one of the planets.
      - Gravitational Field
      - tangential speed
  - - - Dynamics of Rotational motion
        
        Moment of Inertia :
        
        parallel axis-theorem
        
        perpendicular axis-theorem
        
        Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion.
        
        Moment of inertia about any axis parallel to an axis that goes through the center of mass of an object
      - Net torque:
        
        If the net torque is zero, the vector angular momentum is conserved.
        
        Newton’s second law is valid
        even if I is not constant
        
        the total angular momentum of a rotating object remains constant if the
        net external torque acting on it is zero.
        
        if an object’s moment of inertia
        changes, its angular speed changes
    - - Law of Conservation of Momentum
        
        For translational motion, net force on system is zero, total linear momentum constant
        
        For rotational motion, if the net torque on system is zero, then the dL = constant
  - - - τ = rFsinθ
        τ = Iα
        -force need to make an object start moving
        unit : Nm
        vector quantity
        
        Rotational Kinetic Energy
        
        W= τθ
        
        Power = τω
- - - - Potential Energy and Conservation of
        Energy
        
        A conservative force is one for which work done by or against it depends only on the starting and ending points of a motion and not on the path taken
        
        A non-conservative force is one for which work depends on the path taken
        
        Potential is energy stored in an object due to its position, state or shape
        
        Gravitational Potential Energy and Escape Velocity
        
        U = mgh
        
        Escape velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero
        
        Conservation of Mechanical Energy
        
        Principle
        If only conservative forces are doing work, the total mechanical energy of a system neither increases nor decreases in any process . It stays constant and conserved
        
        Object moves in the opposite direction of a conservative net force, the potential energy will increase; and if the speed (not the velocity) of the object changes, the kinetic energy of the object also changes
        
        The Law of Conservation of Energy
        
        POWER
        
        Time rate of doing work & The rate at which energy is transferred
        
        Instantaneous Power
        P = F.v
        
        Average power is the work done divided by the time it takes to do work
        
        Potential Energy Diagrams; Stable and Unstable Equilibrium
      - Work is dot scalar product of force and displacement
        W = F.s
      - Force is being exerted at an angle θ to the displacement, the work done is W = fd cos θ
      - Kinetic energy is the energy an object has because of its motion
      - Work Energy Theorem
      - Work Done By A Variable Force
        
        Work done by a spring force
    - - Momentum
        
        From Newton's second law, the force acting on the body is the rate of change of momentum of body.
        
        Conservation of Momentum: The total momentum of a system is constant unless acted upon by an external force.
        
        Total momentum is conserved.
        
        Total kinetic energy is conserved.
        
        Total momentum is conserved.
        
        Total kinetic energy is NOT conserved.
      - Impulse=F(average)t=change in momentum
      - Center of Mass Point where any uniform force on the objects acts
      - Center of Gravity :point at which the gravitational force can be considered to act.
    - - Every body continues to be at rest or of uniform motion unless acted by an external force.
    - - Rate of change of momentum of a body is directly proportional to the resultant force on it and is in the same direction as the resultant force.
    - - Every action has a direction which is of the same magnitude but opposite in direction.
    - - Friction
        present when 2 surface slide along each other
        
        -Static friction
        -Kinetic friction
      - Banked and Unbanked ：
      - Circular Motion
        
        Motion of object in a circle at a constant speed with constant radius.
        
        Period (T) is the time taken by the object to move around a complete circle.
        
        Centripetal acceleration : Acceleration of a body in circular motion, and the direction is towards the center of the circle.
        
        Centripetal Force : Resultant force towards the center of the circle.
        
        When an object rotates with variable speed, acceleration and force have tangential components.
      - Lift
  - - - Instantaneous acceleration=dv/dt
      - Constant acceleration
      - Free falling object-Near surface of the Earth, objects experience approximately the same acceleration due to gravity(9.80 m/s^2)
  - - - Unit vectors
        -Scalar product(dot product)
        -Vector product(cross product)
        
        Kinematics vector