Circular Motion

Question 1

If a particle is moving in a cone/ paraboloid/ hemisphere in an equilibrium position so speed at which it has to move and the radius about which it will be revolving?

Answer 1

R = H tan θ
Vp = √ [( R g cot θ)]

Where tan θ = rg / Vp^2

R = point where it is rotating

Question 2

V max & ω max for banking of road without slipping ?

Answer 2

V max = √ [ Rg ( tanθ + μs / 1 - μs Tanθ )]

ω max = √ [ g/ R ( tanθ + μs / 1 - μs Tanθ )]

Question 3

V min & ω min for banking of road without slipping?

Answer 3

V min = √ [ Rg ( tanθ - μs / 1 + μs Tanθ )]

ω min = √ [ g/ R ( tanθ - μs / 1 + μs Tanθ )]