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Application of Newton’s Laws


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Physics    Newtonian Mechanics    Application of Newton’s Laws

The Dynamics of Uniform Circular Motion:

The uniform circular motion is the motion in which any object moves in a circular path with uniform
speed. The force that acts towards the centre of the circular path is centripetal force and the
corresponding acceleration is centripetal acceleration. The centripetal acceleration is given as:



where v is the speed of the object and r is the radius of the circular path.



Derivation is given below

Consider the figure representing the motion of an object in a circular path. The similarity results:



The acceleration of the object is given by,
Thus,
As Δt → 0, the acceleration can be further simplified to
The final acceleration (a) can be written as the vector sum of the radial component (ar) and the translation component (at): a = ar + at


Here, at is given by the expression: at = dv/dt. Since ar and at are perpendicular to each other the
magnitude of acceleration can be expressed as:





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