Kinetic energy of an object sliding down a sphere

bob1256
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A particle of mass m slides down a fixed, frictionless sphere of radius R. starting from rest at the top. Theta is the amount of degrees down the side of the sphere that the particle has slid...

a. In terms of m, g, R. and theta, determine each of the following for the particle while it is sliding on the
sphere.
i. The kinetic energy of the particle
ii. The centripetal acceleration of the mass

iii. The tangential acceleration of the mass

b. Determine the value of theta at which the particle leaves the sphere.Any help would be extremely helpful...
 
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Welcome to PF, bob. Before we can help, you should show your attempts at solving it.
 
Start by looking at the kinetic energy, and write that in terms of the potential energy. careful...you don't know the height explicitly.
 
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The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
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