Question

The figure shows a method once used for measuring the speed of light. The method uses a spinning wheel with small slots around its rim. A beam of light passes through a slot at the edge of the wheel, travels to a distant mirror, and is reflected back to the wheel. If the wheel is turning at the correct angular speed, the returned light ray will arrive just in time to pass through the slot adjacent to the one it originally passed through.

In this example, the wheel has a radius of 7 cm and 620 slots around its edge. The mirror is L = 579 meters from the wheel and the speed of light is 3.0 x 108 m/s. What is the angular speed of the wheel? You can assume the speed is constant.

Question 1 2 pts The figure shows a method once used for measuring the speed of light. The method uses a spinning wheel with small slots around its rim. A beam of light passes through a slot at the edge of the wheel, travels to a distant mirror, and is reflected back to the wheel. If the wheel is turning at the correct angular speed, the returned light ray will arrive just in time to pass through the slot adjacent to the one it originally passed through In this example, the wheel has a radius of 7 cm and 620 slots around its edge. The mirror is L= 579 meters from the wheel and the speed of light is 3.0 x 108 m/s. What is the angular speed of the wheel? You can assume the speed is constant. Remember that the distance traveled by the light ray to the mirror and back is 2L Your answer should be in rad/s, but enter only the numerical part in the box. Light Ray Light Source Mirror perpendicular to light ray Rotating Slotted Wheel

Answer 1

angular separation between two adjacent slots,

theta = 2*pi/620

= 0.01013417 rad

time taken for the light to move to the mirror and come back to the spinning wheel,

delta_t = 2*L/c

= 2*579/(3*10^8)

= 3.86*10^-6

angular speed of the wheeel, w = theta/delta_t

= 0.01013417/(3.86*10^-6)

= 2625 rad/s