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701.


Problem 48.23 (RHK)


We may assume that a parallel of circularly polarized light whose power is 106 W is absorbed by an object. (a) We have to find the rate at which angular momentum is transferred to the object. (b) Assuming that the object is a flat disk of diameter 5.20 mm and mass 9.45 mg, we have to find the time required for the disk to attain an angular speed of (we may assume that the disk is free to rotate about its axis). Let the wavelength of the incident light be 516 nm.


Solution:           Click For PDF Version

Let be the frequency of incident light. According to light quantum hypothesis, each photon carries energy , where h is the Planck constant.

The object on which circularly polarized light is incident is a flat disk of diameter 5.20 mm. The power of the beam is 106 W. Therefore, the number of photons that are incident on the disk per second will be

.

We will assume that all incident photons are absorbed by the disk. We will use the quantum property that each photon carries angular momentum of magnitude

.

Therefore, the total amount of angular momentum transferred to the disk per second by the photons will be









Rotational inertia of a circular disk of radius R and mass M is . When the disk attains angular speed of , its angular momentum will be

Therefore, the time in which the disk will attain rotational speed of will be