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silmaril89
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Problem 2-2 from "Classical Dynamics of Particles and Systems" By Thornton and Marion is stated as follows:
A particle of mass m is constrained to move on the surface of a sphere of radius R by an applied force [itex]\textbf{F}[/itex](θ, [itex]\phi[/itex]). Write the equation of motion.
Initially I felt that the force should only point in the [itex]\hat{r}[/itex] direction. It seems obvious to me that [itex]\textbf{F} = \frac{m v^2}{R} \hat{r}[/itex].
However, looking at the solution manual http://www.scribd.com/doc/24868308/Instructor-s-Solutions-Manual-Marion-Thornton-Classical-Dynamics-of-Particles-and-Systems-5th-Ed, they claim the solution should be of the form, [itex]\textbf{F} = F_\theta \hat{\theta} + F_\phi \hat{\phi}[/itex]. If there were a force in any direction except toward the center, then the particle would would not stay on the surface of the sphere.
Can someone explain what is going on here?
A particle of mass m is constrained to move on the surface of a sphere of radius R by an applied force [itex]\textbf{F}[/itex](θ, [itex]\phi[/itex]). Write the equation of motion.
Initially I felt that the force should only point in the [itex]\hat{r}[/itex] direction. It seems obvious to me that [itex]\textbf{F} = \frac{m v^2}{R} \hat{r}[/itex].
However, looking at the solution manual http://www.scribd.com/doc/24868308/Instructor-s-Solutions-Manual-Marion-Thornton-Classical-Dynamics-of-Particles-and-Systems-5th-Ed, they claim the solution should be of the form, [itex]\textbf{F} = F_\theta \hat{\theta} + F_\phi \hat{\phi}[/itex]. If there were a force in any direction except toward the center, then the particle would would not stay on the surface of the sphere.
Can someone explain what is going on here?