Computing Angular Momentum of Particle on a Sphere

[portalphysics]

Homework Statement

Consider a particle confined to move inside a frictionless spherical shell on its surface and in the presence of gravity.

compute the angular momentum (in spherical co-ordinates) about the center of the spherical shell

Homework Equations

L=r x p

The Attempt at a Solution

l=m*(x,y,z) x (dx/dt,dy/dt,dz/dt) , i was going to differentiate the spherical coordinates by t and plug it in but stopped because I am pretty sure what I am doing is wrong

 

[mark726]

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Thank you for your question about computing the angular momentum of a particle confined to move inside a frictionless spherical shell on its surface and in the presence of gravity.

The correct formula for calculating angular momentum in spherical coordinates is L = r x p, where r is the position vector and p is the linear momentum vector. In this case, since the particle is confined to move on the surface of the spherical shell, we can use the radius of the shell as the position vector.

To find the linear momentum vector, we can use the equation p = m*v, where m is the mass of the particle and v is its velocity. In this case, the velocity of the particle can be found by differentiating the spherical coordinates with respect to time. However, since the particle is only moving on the surface of the shell, the velocity will only have a tangential component, which can be found using the angular velocity of the particle.

Once you have the position and linear momentum vectors, you can use the cross product to find the angular momentum vector in spherical coordinates. Remember to use the right-hand rule to determine the direction of the angular momentum vector.

I hope this helps you in your calculations. Please let me know if you have any further questions. Good luck!