Calculate the speed with which the light spot on the clouds moves.

[bon]

Special Relativity URGENT!

Homework Statement

A laser is placed on a turntable that rotates at 1200 rev/s. The laser, whose beam makes an angle of 30 degrees with the horizontal, shines on clouds 50km away. Calculate the speed with which the light spot on the clouds moves.

Homework Equations

The Attempt at a Solution

I guessed that you have to use trig to find the radius of the circle that the laser ends up "sweeping out", then find the circumference, then find the speed..since speed = dist/time (and t = 2pi/w)..but it doesn't come to the right answer (3.3 x 10^8 m/s), so where am i going wrong?

Thanks!

 

[Doc Al]

Your method sounds good to me. Show the details of your calculation.

 

[bon]

Well, using simple trig, i get the radius of the circle to be 50000tan60 meters. therefore the total dist. traveled is 2 pi (50000tan60)..

and the time taken is 2pi/1200

but when you divide the distance by the time, it doesn't give you the right speed (which should be around 3.3 x 10^8...

any ideas?

 

[Doc Al]

Well, using simple trig, i get the radius of the circle to be 50000tan60 meters.

The distance given is the distance to the cloud. You want the horizontal component of that distance.

 

[bon]

ok so 50000sin60..it still doesn't give me the right answer..

 

[Doc Al]

ok so 50000sin60..it still doesn't give me the right answer..

It does for me. Show the steps in your calculation.

 

[bon]

dist = 50000sin60 x 2pi

time = 2pi/1200 s

dist / time =/= 3.3 x 10^8

 

[Doc Al]

dist = 50000sin60 x 2pi

Right. The distance for one revolution.

time = 2pi/1200 s

Not right. Note that the angular speed is given in rev/sec, not rad/sec.

 

[bon]

Right. The distance for one revolution.

Not right. Note that the angular speed is given in rev/sec, not rad/sec.

Ah ok great. Thanks for your help.

so angular speed is in rev/sec...what the w then in: T = 2pi/w...

please could you explain the difference..
thanks

 

[Doc Al]

Well, if the angular speed is 1200 revs/sec, then 1 rev takes 1/1200 sec.

The relationship T = 2pi/ω is only valid if ω is in rad/sec. 1200 rev/sec = 1200*2pi rad/sec.
So: T = 2pi/ω = 2pi/(1200*2pi) = 1/1200 sec.