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delve

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Here's a question from a book: A particle of mass m is constrained to move on the surface of a sphere of radius R by an applied force [tex]$\mathbf{F}$(\thetha, \phi)[/tex]. Write the equation of motion.

Now here is the answer, but there is something I don't understand about it:

Using spherical coordinates, we can write the force applied to the particle as [tex]$\mathbf{F}$=F_r\mbox{e_r}+F_\theta\mbox{e_\theta}+F_\phi\mbox{e_\phi}[/tex] But since the particle is constrained to move on the surface of a sphere, there must exist a reaction force that acts on the particle.

Why isn't the force just [tex]$\mathbf{F}$=F_\theta\e_\theta+F_phi\e_\phi[/tex], and therefore, no reaction force?

Now here is the answer, but there is something I don't understand about it:

Using spherical coordinates, we can write the force applied to the particle as [tex]$\mathbf{F}$=F_r\mbox{e_r}+F_\theta\mbox{e_\theta}+F_\phi\mbox{e_\phi}[/tex] But since the particle is constrained to move on the surface of a sphere, there must exist a reaction force that acts on the particle.

Why isn't the force just [tex]$\mathbf{F}$=F_\theta\e_\theta+F_phi\e_\phi[/tex], and therefore, no reaction force?

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