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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12

A particle is moving in a circle of radius r centred at O with constant speed v. Find the magnitude of change in velocity moving from A to B left parenthesis angle AOB space equals space 40 degree right parenthesis.


Let stack straight v subscript 1 with rightwards arrow on top space and space stack straight v subscript 2 with rightwards arrow on top be the velocities of particle at A and B.

Since the speed of the particle (straight v with rightwards harpoon with barb upwards on top) is constant.

Therefore,

          space space open vertical bar stack straight v subscript 1 with rightwards arrow on top close vertical bar space equals space open vertical bar stack straight v subscript 2 with rightwards arrow on top close vertical bar space equals space straight v

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Now,      Δv space equals space open vertical bar stack straight v subscript 2 with rightwards arrow on top minus stack straight v subscript 1 with rightwards arrow on top close vertical bar

                  equals square root of straight v subscript 2 superscript 2 plus straight v subscript 1 superscript 2 minus 2 straight v subscript 2 straight v subscript 1 cos 40 to the power of degree end root 

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                    equals square root of 4 straight v squared sin squared 20 degree end root

equals space 2 vsin 20 degree

This is the required change in magnitude of the velocity on moving from A to B. 
                    
                       

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