Question

A particle is moving along a circular path with a constant speed of 10m/s what is the magnitude of the change is velocity of the particle, when it moves through an angle of 60° particle, when it moves through an angle of 60°around the center of circle

Answer 1

Answer:

Given:

An object is going Uniform Circular Motion at a speed of 10 m/s

To find :

Change in velocity when the object has moved by an angle of 60° with respect to the centre.

Trick:

This formula can be applied only for MCQs. Please don't use this in School exams.

Let change in velocity be denoted as ∆v

So,

∆v = 2v × sin(θ/2)

where θ is the angle made at the centre (in this case θ is 60°)

Full Calculation:

First please refer to the attached photo to understand the diagram.

∆v = √{ v² + v² + 2v²cos(120°)}

=> ∆v = √{ 2v²( 1 + cos120°)}

=> ∆v = √{ 2v² ( 1 - ½)}

=> ∆v = √ { 2v² × ½}

=> ∆v = √ {v²}

=> ∆ v = v = 10 m/s.

If you have any confusion regarding the calculations, please let me know.

Answer 2

answer;

∆v = √{ v² + v² + 2v²cos(120°)}

=> ∆v = √{ 2v²( 1 + cos120°)}

=> ∆v = √{ 2v² ( 1 - ½)}

=> ∆v = √ { 2v² × ½}

=> ∆v = √ {v²}

=> ∆ v = v = 10 m/s

Explanation:

thanks