An early method of measuring the speed of light makes use of a rotating slotted

Question

An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through a slot at the outside edge of the wheel, as in the figure, travels to a distant mirror, and returns to the wheel just in time to pass through the next slot in the wheel. One such slotted wheel has a radius of 5.2 cm and 170 slots at its edge. Measurements taken when the mirror is L = 720 m from the wheel indicate a speed of light of 3.0 x 105 km/s. (a) What is the (constant) angular speed of the wheel? (b) What is the linear speed of a point on the edge of the wheel?

An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through a slot at the outside edge of the wheel, as in the figure, travels to a distant mirror, and returns to the wheel just in time to pass through the next slot in the wheel. One such slotted wheel has a radius of 5.2 cm and 170 slots at its edge. Measurements taken when the mirror is L = 720 m from the wheel indicate a speed of light of 3.0 x 105 km/s. (a) What is the (constant) angular speed of the wheel? (b) What is the linear speed of a point on the edge of the wheel?

Explanation / Answer

time taken for light beam to travel past the wheel and come back to the wheel

=total distance travelled/speed of light measured

=2*L/(3*10^8 m/s)

=2*920/(3*10^8)=6.133*10^(-6) seconds

between that time, the wheel should rotate the angle equivalent to

angular distance between two slots.

now, it is given that the wheel has 170 slots.

as total angle of a wheel is 360 degrees,

angular distance between two slots=360/170 degrees=2.1176 degrees=0.03696 radians

then angular speed=angular displacement/time taken=0.03696/(6.133*10^(-6))=6026.41 rad/sec

part b:

linear speed=angular speed*radius

=6026.41 *7.9*0.01=476.086 m/s

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