Is the Force in r = a cos(wt) i + b sin(wt) j Conservative?

AI Thread Summary
To determine if the force associated with the particle's motion described by r = a cos(wt) i + b sin(wt) j is conservative, one must first calculate the particle's acceleration. Using Newton's second law, the force can be derived from this acceleration. Next, the work done by the force during one complete revolution should be calculated. If the work integrates to zero over this period, the force is classified as conservative. This method effectively assesses the conservativeness of the force in question.
LilithBlack
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Hello,
I have a question about conservative forces.

'A particle is moving according to r = a cos(wt) i + b sin(wt) j, where a and b are constants, w is angular velocity, r is a vector and i,j are unit vectors that point the same direction as the x and y axes, respectively. I am asked to determine if this force is conservative or not.'

Sure, the orbit of the particle is ellipse, but how can I determine if this force is conservative or not? Please, help me.
 
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First, calculate the acceleration of the particle at any point on the trajectory. Use second Newton's Law to calculate the force. Then calculate the work of the force during one revolution. If it integrates to zero, the force is conservative.
 

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