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Sian R
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Homework Statement
A wedge with face inclined at an angle θ to the horizontal is fixed to a rotating turntable. A block of mass m rests on the inclined plane and the coefficient of static friction between the block and the wedge is µ. The block is to remain at position R from the centre of rotation of the turntable.
Draw the forces acting on the block in a diagram and express them in curvilinear coordinates. Show that the acceleration vector of the block is given by a = Rω2nˆ, where ω is the angular velocity of the turntable.
2. Homework Equations
The Attempt at a Solution
I have resolved the forces on the block, there are 4 I think. Friction, which I have said acts in the postive r^ direction, the Normal force from the wedge which is in the ∅^ direction.
Weight I have as W=mg(-sinαr^-cosα ∅^)
centripetal force =IFI(-cosαr^+sinα ∅^)From this and the acceleration equation I have split it into r and ∅ but I am unsure how to prove
a = Rω2nˆ
When I asked my lecturer on how to switch between polar cylindrical into tangential coordinates she said "r-hat points in opposite direction to n-hat, and if the particle moves counterclockwise then t-hat equals
theta-hat"