Particle constrained to move on a sphere

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SUMMARY

The discussion centers on deriving the equation of motion for a particle of mass m constrained to move on a sphere of radius R under an applied force F(theta, phi). The correct expressions for the coordinates are x = R sinθ cosφ, y = R sinθ sinφ, and z = R cosθ. Participants emphasized that the force must be expressed as a vector, considering both radial and angular components, and clarified that the "del" operator is not applicable in the context of Newton's Second Law, which requires a second time derivative.

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Homework Statement


A particle of mass m is constrained to move on a sphere of radius R by an applied force F(theta,phi). Write the equation of motion.


Homework Equations


x=vtRcos(phi)sin(theta)
y=vtsin(phi)sin(theta)


The Attempt at a Solution


F=m(del)2(x+y)
 
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Hi dray. Welcome to PF.

Forces are vectors. How would you write the given force as a vector? What does the problem say? Is this a force in the radial direction only or does it have angular components?

What does your attempt at a solution represent? It cannot be an expression of Newton's Second law because the "del" operator has to do with spatial derivatives and the Second Law involves a second time derivative.

Your relevant equations should be

x = R sinθ cosφ
y = R sinθ sinφ
z = R cosθ

There is no explicit time dependence in these expressions, but theta and phi themselves are functions of time.
 

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