Author: Physics Notebook
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Derive An Expression For The Moment Of Inertia Of A Rigid Body About Any Axis Through A Point, The Point Through Which Three Mutually Perpendicular Axes Pass.
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Moment of inertia about an arbitrary axis: Let us consider, three mutually perpendicular axes OX, OY and OZ meeting at the origin O. Now we want to calculate the moment of inertia of a body about any axis ON, passing through the origin O. Let us consider, be the mass of the particle of the…
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Derive An Expression For The Kinetic Energy Of Rigid Body In Terms Of Angular Velocity And Principal Moment Of Inertia.
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Let us consider three mutually perpendicular axes, OX, OY, and OZ meeting at the origin O. A body is rotating with angular velocity about the fixed point O. So we can write, , where, , and are the components of the angular velocity along the OX, OY and OZ axes respectively. Let be the position…
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Define Principal Axes Of Inertia And Principal Moment Of Inertia.
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Let us consider a frame of reference with three mutually perpendicular axes meeting at the origin O. This is fixed in a rotating body so it rotates with the body in such a way that the product of inertia about them is zero. These mutually perpendicular axes are called the principal axes of inertia of…
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Show That Homogeneity Of Time And Newton’s Second Law Of Motion Result In Law Of Conservation Of Energy.
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Time flows uniformly i.e., it is homogeneous in nature. If we perform an experiment and change the time of the experiment then the result of that experiment remains unchanged. This indicates that the result of an experiment is independent of the change in the origin of time. This phenomenon of time is known as homogeneity.…
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Gives Newton’s Classical Definition Of Time And Its Properties.
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Time: According to Sir Newton, “Absolute true and mathematical time of itself and from its own nature, flows equally without relation to anything external and is otherwise called duration.” Properties of Time: The properties of time are: One dimensional: Time flows only in one direction, i.e. time is one-dimensional. Time is independent of space and…
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Distinguish Between The Homogeneity And Isotropy Of Space.
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The homogeneity of space indicates the translational invariance of the properties of the free space. Let us consider, the frames of reference S and S’ are taken in such a way that the Y and Z axes are parallel to each other and the origins O and O’ of the frames S and S’ respectively…
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What Was Newton’s Notion Of Space? What Are The Classical Properties Of Space?
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Newton’s Notion of Space: According to sir Newton, “Absolute space in its own nature without relation to anything external remains always similar and immovable.” This indicates that space is independent of the existence of anybody, i.e. space describes something, which distinct from anybody. Properties of the space: In order to describe the motion of a…
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Derive Laws Of Conservation Of Linear Momentum From Newton’s Laws Of Motion.
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According to Newton’s 1st law of motion, everybody persists in a state of rest or of uniform motion along a straight line (i.e. with constant velocity) unless and until it is acted upon by an external force to change that state. Again according to Newton’s 2nd law of motion, the rate of change of momentum…
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State And Explain The Principle Of Conservation Of Linear Momentum.
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Linear momentum of a body is defined by the product of the mass of that body and the linear velocity of that body. If be the mass of the body and be the linear velocity of that body then the linear momentum is given by, If be the displacement vector, then Now, Where, is the…
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What Is Linear Momentum?
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Linear Momentum: Linear momentum of a body is defined by the product of the mass of that body and the linear velocity of the body. Let us consider a body of mass is moving with a linear velocity , then the linear momentum of that body is given by, Since the velocity is the…