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By B. Brown B.Sc., Ph.D., F.Inst.P (auth.)

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Tbe angular momentum of the disk is thus Iw. Assume the disk is rotating about the axis oy and let the plane of the disk, AB, precess about an axis oz perpendicular to the plane of the diagram. If the rate of precession is 1jJ, after a time dt the plane of the disk can be represented by AlB I where the angle of precession moved through is equal to IjJdt. The angular momentum, which can be represented vectorially by a line drawn normally to the plane of rotation of the disk, is represented by oe and oe for the two positions of the disk where angle COC' is equal to IjJdt.

In a second experiment a small mass m is attached to it at a distance a from the axis, and this time, after being set spinning, comes to rest in time t', during which it makes n' revolutions. Find an expression for the moment of inertia of the unloaded wheel. Tbe equation of motion of the unloaded wheel subjected to a frictional couple C is lii = -C where I is the moment of inertia of the wheel about a vertical axis through its centre. Integrating, ItJ = - CT + b where b is a constant. At time T = t, tJ = 0 b = Ct ItJ = - CT + Ct = C(t - T) The initial angular velocity ofthe wheel = Ct/I and the final angular velocity at time t is equal to zero.

9) may be written ~ Lm(xy dx yx) = L(XY - yX) .... e. the rate of change of moment of momentum of the system about any fixed origin is equal to the sum of the moments of the external forces about that origin. If the sum of the moments of the external forces about any fixed origin or axis is zero then the moment of momentum of the system about that axis is constant. 1. Perpendicular axes theorem for a laminar body Moment of momentum is also termed angular momentum and the above sentence is a statement of the principle of conservation of angular moment um.

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