Question

An eartly method of measuring the speed of light makes use of a rotating slotted wheel.

A beam of light passes through one of the slots 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 5.0 cm and 500 slots around its edge. Measurements taken when athe mirror is L = 550 m from the wheel indicate a speed of light of 3.0 x 10^8 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?

Answer 1

Step-by-step explanation:

Distance traveled by light = 2 x 550 m = 1100 m

time taken by light to travel this distance = 1100 / 3 x 10⁸

= 366.67 x 10⁻⁸ s

angle between two consecutive slots = 2π / 500 rad

= .004π

angular velocity of wheel = angle moved / time taken

= .004π / 366.67 x 10⁻⁸

= 1091π radian / s

b ) linear speed of a point on the edge of the wheel

= ω R , r is radius of wheel , ω is angular velocity.

= 1091π x 5 x 10⁻²

= 1712.8 m /s