Anonymous

A massless spring of spring constant k is mounted on a turntable of rotation inertia I.the turntable is on a frictionless vertical acle,though initially it is not rotating.the spring is compressed a distance dx from its equilibrium,with a mass m placed against it.when the spring si released,the mass leaves the spring moving at right angles to a line through the center of the turntable,at a distance b from the denter,and slides without friction across the table and off find expression for a)the linear speed of the mass and b) the rotational speed of turntable?

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• Anonymous

Yes, seems hard. I assume that the spring is attached to the turntable. In this case, it is a matter of conservation of angular momentum and energy.

Initial angular momentum is 0 (nothing moving)

Final angular momentum is Iw for the turntable and mvb for the mass m. Note that one of these is negative (why?)

Note that we assume the spring is massless!

Now apply energy conservation.

Initial energy is the PE of the spring 1/2k(dx)^2

Final energy is KE of mass = 1/2 mv^2 and KE of the turntable 1/2Iw^2.

You have two equations for the two unknowns (v and w)

create the expressions in terms of I, m, dx, k and b.