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, 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 cm and 500 slots at its edge. Measurements taken when the mirror was L = 500 m from the wheel indicated a speed of light of 3.0 x10^5 km/s.
What was the (constant) angular speed ofthe wheel?
(b) What was the linear speed of a point on the edge of thewheel?

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, 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 cm and 500 slots at its edge. Measurements taken when the mirror was L = 500 m from the wheel indicated a speed of light of 3.0 x10^5 km/s.
What was the (constant) angular speed ofthe wheel?
(b) What was the linear speed of a point on the edge of thewheel?

anonymous · Answer

i need help plz

anonymous · Answer

Well, the angular distance between slots would be 2*pi / 500, right?  And the time it would take to get to the mirror and back (1000 m = 1 km) would be t = 1 km / (3*10^5 km/s).  So the angular velocity must have been
$$\omega = \left(\frac{2\pi}{500}\right) \div \left(\frac{1 km}{3\cdot 10^5 km/s}\right)$$

To answer the second part of the question, for a point on the edge of the wheel,
$$v = \omega R$$
where R is the radius of the wheel.