P.S. if i want to find the the velocity of the particle from the frame of earth then? and can you tell me what is your last diagram for? it looks like a parabolic motion of some body i don't understand it because the particle is supposed to move "on" the surface of sphere
]]>Let the sphere move towards left with an acceleration ‘a’ and let us examine the particle’s motion from the sphere, i.e. assuming the sphere at rest.
Let m = mass of the particle
Now, the particle is moving in a circle on the surface of the sphere.
The free body diagram of the particle is
When the particle has slid through an angle θ, let its velocity be ‘v’.
Tangential acceleration = mdv/dt = macosθ + mgsinθ
We know that v = Rdθ/dt
Therefore, mvdv/dt = macosθ(Rdθ/dt) + mgsinθ(Rdθ/dt)
or mvdv = maRcosθdθ + mgRsinθdθ
Integrating both sides;
v^2 /2 = aRsinθ – gRcosθ+ c
Given that the particle starts from rest, i.e. v = 0 at θ = 0
Therefore, c = +gR
Hence, v^2 = 2aRsinθ – 2gRcosθ+ 2gR
or v = [2R(asinθ – gcosθ +g)]^½
]]>i hope i will get a quick reply i am breaking my head over this problem....
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