# Homework Help: Particle sliding down a frictionless sphere

1. Nov 5, 2008

### attilathedud

1. The problem statement, all variables and given/known data
A particle of mass m slides down a fixed frictionless sphere of radius R starting from rest at the top.
a. In terms of m, g, R, and Θ, 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 Θ at which the particle leaves the sphere.

2. Relevant equations
None given.

3. The attempt at a solution
a.
i.
Ki + Vi = Kf + Vf
0 + mgy = 1/2mv^2 + 0
gy = 1/2v^2
g(R/2) = v^2/2
v = sqrt(gR)

ii.
ar = v^2 / R
ar = gR/R
ar = g

iii.
v = r(dΘ / dt)
sqrt(gR) = R(Θ/t)
gR = (R(Θ / t)) ^ 2
t = d/v
gR = (R(Θ / d / sqrt(gR))^2
gR = R(Θsqrt(gR)/d)^2

b. Pretty sure the fact I massively screwed up part iii is making this section impossible. And having the centripetal acceleration equal gravity seems incorrect as well.

Edit: Seems like I wasn't the first one to post this. My apologies.

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