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

Question

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 10^5 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?

1027

The book says:
(a) 3800rad/s
(b) 190m/s

Answer 1

Sparta was right, just got the math wrong.

a) Angular velocity

w=theta/T

theta = 2* Pi/500 radians.

D= 550m*2 = 1100 meters.

c=3*10^8m/sec

T = D/c = 1100 m / (3 * 10^8 m/sec)

= 3.67*10-6 sec

therefore

w=theta/T

= 2* Pi/500 radians /3.67*10-6 sec

= 3427 rads/sec


b) linear speed

v = w*r

= 3427 rads/sec * 550mm

=1884 m/sec

Snarf?

>>>>>>>Edit.

b) linear speed should be

v = w*r
= 3427 rads/sec * 5 cm {correction on radius}
= 171 m/sec

Jack -- check your book, I am off by 10% and I can't see any errors. Is L=500m? or are there 550 slots?

Answer 2

1) You want d theta/dt

in the time frame in question (dt), the wheel would have turned (2 Pi/500) radians or (Pi/250) radians.

What is the time frame? The time it takes light to travel 550*2 or 1100 meters. D= r*t, so

t = D/r = 1100 m / (3 * 10^8 m/sec)
= (1100/3)*(10^-8) seconds
= (11/3)*(10^-6) seconds, so

d theta /dt = ( (Pi/250) radians)/( (11*10^-6/3) seconds)
= (Pi/250)* (3/11)*10^(6) radians/second
= 1.32 Pi * 10^5 radians/second.

2) you want dS/dt, where S is the arc length.

S = R * theta, R is the radius, so
dS/dt = R d theta /dt or

( 5/100) m * 1.32 Pi * 10^5 radians/second
= 6.6* 10^3 meters/second

Answer 3

Eartly