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dyn

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- Homework Statement
- A particle of mass m moves in a circular path of radius R in the plane z=0 described by position vector r( t ) = ( Rcos(wt) , Rsin(wt) , 0 ). The particle's motion results from a force ; prove this force is conservative

- Relevant Equations
- Newton's 2nd law and for a conservative force , curl F = 0

I have done this question and also seen the model answer but i just want to check my method is ok. I differentiated the position vector twice and multiplied by m to get the force

Is my method ok ? Is it ok to write the components as functions of time even though the differential operators in curl are derivatives of x , y and z ?

Thanks

**F.**I then used the determinant method to find the curl of**F**which i found to be zero thus proving the force is conservative. What i want to check is this ; i wrote the components of**F**as functions of time such as F_{x}= -mRω^{2}cos(ωt) and this method worked . The model solution writes the components of**F**such as F_{x}= -mω^{2}x.Is my method ok ? Is it ok to write the components as functions of time even though the differential operators in curl are derivatives of x , y and z ?

Thanks