One of the earliest methods of measuring the speed of light c makes use of a rot

Question

One of the earliest methods of measuring the speed of light c makes use of a rotating slotted wheel. A beam of light passes through a slot at the outside edge of the wheel of radius R as shown in the Figure below. It travels to a distant mirror and returns to the wheel just in time to pass through the next slot in the wheel. Consider the situation of one such slotted wheel that has N slots, each one formed by a protrusion and a hole.

Evaluate ? and v for N = 500 slots, L = 500 m, R = 5 cm, and c = 3.0 x 105 km / s.

Here is what I did. Is this correct?

Solving for omega delta theta = 2 pi /N delta theta = omega delta t delta t = 2L/c Therefore delta theta = omega 2L/c set the two equations equal to each other 2 pi /N = omega 2L/c Isolate for omega omega = pi c/NL Sub in N = 500 slots L = 500 m, R = 5 cm, and c = 3.0 x 105 km/s omega = pi (3.0 x 108)/(500)(500) s-1 omega = 3769.9 s-1 solving for v v = omega R omega = 2 pi c/NL Sub in omega v = Rpic/NL Sub in N = 500 slots, L = 500 m, R = 5 cm, and c = 3.0 x 105 km/s v = (0.05)pi(3.0 x 108)/(500)(500) m/s v = 188.5 m/s

Explanation / Answer

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.