A child's toy consists of a small wedge that has an acute angle θ. The sloping side of the wedge is frictionless, and an object of mass m on it remains at constant height if the wedge is spun at a certain constant speed. The wedge is spun by rotating, as an axis, a vertical rod that is firmly attached to the wedge at the bottom end. Show that, when the object sits at rest at a point at distance L up along the wedge, the speed of the object must be v = (gL sin(θ))1/2.

see explanation

Explanation:

Net force along x axis is

Net force along y axis is

The object can along accelerate down the stamp.

Thus F(net) is at the angle down the stamp

where r = L in the direction of acceleration

where are the vectors ?

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