### Putting Some Spin On It

University of St Andrews scientists create ‘fastest man-made spinning object’

The team then used the miniscule forces of laser light to hold the sphere with the radiation pressure of light – rather like levitating a beach ball with a jet of water.

They exploited the property of polarisation of the laser light that changed as the light passed through the levitating sphere, exerting a small twist or torque.

Light, of course, can have angular momentum, so if the ball was changing the light from linear to circular polarization (or vice versa), the angular momentum change would have to come from the ball, so it would spin.

If my calculator skills are not failing me, the ball had around 10^17 h-bar of angular momentum, which isn’t a lot for a macroscopic object. 10^17 photons is less than a tenth of a Watt-second’s worth of visible light, or 10 mW for less than 2 minutes.

Addendum:

Nick over at Fine Structure points out that the Nature Communications paper is currently free.

The technique they are using is actually using the material as a half-wave plate, which is twice as effective at imparting angular momentum to the sphere as I had described. When circularly polarized light is incident upon it it switches the direction of the polarization, imparting 2*h-bar of angular momentum.

“

The rotation rate is so fast that the angular acceleration at the sphere surface is one billion times that of gravity on the Earth surface. It’s amazing that the centrifugal forces do not cause the sphere to disintegrate.”A small body can be totaly free of flaws that nucleate tensile failure. Limiting equatorial velocity for a solid sphere then depends only on the material’s binding energy, independent of radius,

v_lim = sqrt[(2)(S)/(rho)]

where S is the yield strength and rho the density. If their rotated bodies exceeded this rule of thumb, yes, there is a surprise. Consider a strongly bound body. Diamond tensile strength does not exceed 225 GPa with density 3520 kg/m^3. Convert Pa to kg/m^2 at one gee.

v_lim (diamond) = 11,300 m/s or 7 miles/sec maximum

Spin unbinding a body arises from forces acting upon a surface element with area A of the rotating body. For an infinitesimally thin surface element, stresses are tangential as radial stresses go to zero on the surface. Said tangential stresses still yield a radial force component for a curved surface. Given a surface element with area dA and thickness dt, tangential stresses present in the surface, the normal (to the surface) force acting on this element,

dF_s = (S1/R1 S2/R2)*dAdt

where R1, R2 are the main surface radii of curvature (at the point of evaluation) and S1, S2 are stresses along the directions of the corresponding axes of curvature.

Rotation is angular velocity w. Work in the rotating reference frame. The surface element is acted upon by two forces. The elastic force simplifies to

dF_s = (S1 S2)*dAdt/R

since R1 = R2 = R, the radius of the sphere, pulling the surface element inwards towards the rotation axis. The second force is centrifugal

dF_c = R*w^2*dm

dm is mass of the surface element, given by

dm = dAdt*rho

Then,

dF_c = R*w^2*rho*dAdt

acting outward from the rotation axis. The surface element remains stationary in the rotating frame (until the sphere unbinds), the two forces dF_s and dF_c are equal.

R*w^2*rho*dAdt = (S1 S2)*dAdt/R

Cancel common factors, then

(R*w)^2 = (S1 S2)/rho

R*w is v, the velocity of the equatorial point. Neither S1 nor S2 can be larger than tensile strength S. Then,

v^2 <= 2*S/rho

with = obtaining at the limit of material unbinding. Radii cancel.

S/rho, energy/mass, is binding energy/unit mass of material. The ball remains bound if its kinetic energy/unit mass (in any locality) is less than binding energy/unit mass.