- #1

gnits

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- Homework Statement
- How to calculate minumum angular velocity of a mass on a spinning plate

- Relevant Equations
- f=mrw^2

**Problem Statement:**How to calculate minumum angular velocity of a mass on a spinning plate

**Relevant Equations:**f=mrw^2

Hi, here's the question:

a) A rough horizontal plate rotates with a constant angular velocity of w about a fixed vertical axis. A particle of mass m lies on the plate at a distance of 5a/4 from the axis. If the coefficient of friction between the plate and the particle is 1/3 and the particle reamins at rest relative to the plate, show that w = sqrt(4g/15a).

b) The particle is now connected to the axis by a horizontal light elastic string, of natural length a and modulus 3mg. If the particle remains at rest relative to the plate and at a distance of 5a/4 from the axis, show that the greatest possible angular velocity of the plate is sqrt(13g/15a).

c) and find the least possible angular velocity.

I have done parts a) and b). It is part c) that I don't get.

I solved part b) by equating the frictional force + the tension in the elastic string = centripetal force (mrw^2)

Solving this I get the required answer of w = sqrt(13g/15a).

I understand that if w were greater than this then the particle would start to move further away from the axis.

But I don't see how w could be less than this and still have the particle 5a/4 from the axis and of course, I therefore don't see how I would calculate this.

Thanks for any help,

Mitch.