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A smooth sphere of radius R is moving in a straight line with an acceleration a=g. A particle kept on the top of the sphere is released from there at 0 velocity WRT the sphere. What is the speed of the particle WRT the sphere as a function of the angle theta as it slides down?
in the reference frame of the sphere, there are two forces: g(downward gravity) and horizontal inertial force a,let the particle slide an angle theta, Work done by the two forces=mRasinθ +mRg(1-cosθ)=mv2/2,v2=2R(asin(theta)+g(1-cos(theta)), v=√(2R(asinθ+g(1-cosθ)))
in the reference frame of the sphere, there are two forces: g(downward gravity) and horizontal inertial force a,
let the particle slide an angle theta, Work done by the two forces=mRasinθ +mRg(1-cosθ)=mv2/2,
v2=2R(asin(theta)+g(1-cos(theta)), v=√(2R(asinθ+g(1-cosθ)))
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