An early method of measuring the speed of light makes use of arotating slotted w

Question

An early method of measuring the speed of light makes use of arotating slotted wheel. A beam of light passes through one of theslots at the outside edge of the wheel, travels to a distantmirror, and returns to the wheel just in time to pass through thenext slot in the wheel. One such slotted wheel has a radius of11.0 cm and 1000 slots at its edge. Measurements taken whenthe mirror was l = 500 m fromthe wheel indicated a speed of light of 3.0x10^5 km/s. (a) What was the (constant) angular speed ofthe wheel? 11796.407 rad/s (b) What was the linear speed of a point on the edge of thewheel? 2

Explanation / Answer

Given that The radius of the slatted wheel (r) =11.0cm                                                   = 0.11m The no of slots at the edges (x) = 1000slots Length between the wheel and mirror (L) = 500m Speed of the light(c) = 3*108m/s The angular position is                               =2/x                                 =2/1000                                 = 0.00628 rad Let the velocity time be t so                           t = 2L/c                              =2*500/3*108                              =3.34*10-6s a) The angular velocity () = /t                                      = 0.00628rad/3.34*10-6s                                       =1880.239rad/s b) The linear velocity (v) = r                                 = ( 0.11m)(1880.239rad/s)                                 = 206.82629m/s                                 ˜ 207m/s b) The linear velocity (v) = r                                 = ( 0.11m)(1880.239rad/s)                                 = 206.82629m/s                                 ˜ 207m/s

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